Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design Ioannis Chatzikonstantinou Thesis Supervisors: Dr. Ir. Michael Bittermann Prof. Dr. Ing. Patrick Teuffel
Ioannis Chatzikonstantinou
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Graduation Thesis for the MSc Building Technology at TU Delft. June 2011 Thesis Supervisors: Dr. Ir. Michael Bittermann Prof. Dr. Ing. Patrick Teuffel
To my sister, Anastasia
Ioannis Chatzikonstantinou
/ Contents 8
Introduction 1. Research Methodology 1.1. Passenger Terminal Typology 1.2. Parametric Model 1.3. Delveopment of the Evolutionart Algorithm Component 1.4 Testing and Case Studies
10 10 10 11 11
2. The Design of the Passenger Terminal 2.1. Passenger Terminal Positioning 2.2. Functional Organization 2.3. Operational Efficiency and Movement 2.4. Retailing and Commercial Activity 2.5. The Level Of Service (LOS) Standards 2.6. Energy Performance
12 12 14 15 16 17 17
3. Defining a Design Model 3.1. The Airport Terminal Model 3.1.1. Generative Principles 3.1.2. Design Parameters 3.2. Performance Criteria 3.2.1. Cost 3.2.2. Accessibility 3.2.3. Energy Performance 3.2.4. Retail Suitability 3.3. Constraints 3.3.1. Self Intersenction 3.3.2. Aircraft Circulation 3.3.3. Capacity 3.3.4. Fuzzifying Goals 3.3.5. Combining Hard and Soft Constraints
19 19 19 21 21 22 24 26 28 29 29 30 30 31 32
4. Optimizing Solutions 4.1. Evolutionary Computation 4.1.1. Structure and Function of EAs 4.1.2. Single and Multi-Objective EAs 4.1.3. Objective Functions and Constraints 4.2. The NSGA-II 4.2.1. Process 4.2.2. Elitism 4.3. The Implemented Algorithm
38 38 38 39 40 40 40 42 43
5. Testing and Case Study 5.1. The ZDT-1 Test 5.2. Model Testing 5.2.1. Preparation 5.2.2. Testing 5.2.3. Discussion
44 44 44 44 46 46
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
5.3. Case Study 5.3.1. Site Conditions 5.3.2. Adapting the Parametric Model 5.4. Moving on to Detail 5.4.1. The Parametric Definition of the Envelope 5.4.2. Optimizing Solutions
47 47 48 51 51 53
6. Conclusions
62
7. References
63
Appendix A1
66
Appendix A2
70
Appendix A3
76
Appendix A4
84
Appendix A5
90
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Ioannis Chatzikonstantinou
Fig. 1 Overview of the final case study that has been designed using the proposed computational optimization method, both regarding the layout as well as the facade development.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
/ Introduction It is without doubt that airport terminals are some of the most complex building types in existence. Their scale, the nature of their functions, the strict security measures as well as the function-specific components and building equipment that is present in such buildings are all factors that increase their level of complexity as a building type. In a real design situation, dealing with the variety of design parameters that the design of an airport terminal incorporates can be a difficult task to manage and may sometimes become an impediment to the design process. Furthermore, solely because of the enormous amount of possible design solutions that exists even for a relatively small set of design parameters1, the discovery of optimal or near optimal solutions through a traditional design approach is not guaranteed to happen. Standardization is the traditional remedy to this kind of complexityinduced problems and it’s results are clearly evident in buildings such as airport terminals. However, the existence of a wide range of different design contexts, goals and requirements, as well as arbitrarily defined case-specific issues, gives birth to a “design space” that is wide enough to be worthwhile of exploration. Given these assumptions, it is proposed within the context of this thesis that the design of layouts for airport terminals be addressed by the use of computation-based design methods. Specifically, the method outlined in this report is centered around the design of a Parametric Model that represents a spectrum of airport terminal designs and an Evolutionary Algorithm to search for solutions within this spectrum that are optimal according to predefined efficiency and sustainability related criteria. The method will be evaluated by applying it to a case study, which will be the investigation of an alternate proposal for the New Doha International Airport in Qatar.
1 This situation is commonly referred to in literature as “Combinatorial Explosion”. It occurs when a huge number of possible combinations are created by increasing the number of entities which can be combined--forcing us to consider a constrained set of possibilities when we consider related problems. It outlines vividly the enormous design domains that are encountered even in relatively simple problems, let alone in complex design fields such as architecture.
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Ioannis Chatzikonstantinou
1 / Research Methodology The methodology that the thesis is based on can be broadly divided into four different parts: 1.
Research on the Passenger Terminal Typology
2. Design of a Parametric Model that is able to generate a range of Airline Passenger Terminal layouts 3. Implementation and development of an Evolutionary Algorithm (NSGA-II) into a component for the Grasshopper Parametric Design Environment 4. Testing of the coupled Parametric Model with the EA; investigation of a case study using the proposed design method. Advancement of one picked solution to a greater level of detail.
1.1. Passenger Terminal Typology This stage includes all literature study that has been done to identify the particular characteristics and priorities that take part in the design of airport terminals. Topics that will be covered range from the study of movement within terminals to the climate design and suitability for retail use. A detailed overview of this stage and the findings regarding the design of airport passenger terminals are discussed in the 2rd section of this report.
1.2. Parametric Model This stage includes the work done on the generation of the parametric model of the airport terminal, the implementation of the design objectives into parametric functions related to the input parameters of the model and finally the development of the EA itself into a component for the Grasshopper Parametric Modelling Environment. The development of the parametric model of the airport terminal is discussed in section 3 of the report.
Fig. 2 Computer rendering of a generated solution.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
1.3. Development of the Evolutionary Algorithm Component Two stages comprise this part of the study. The first is the literature review and research on Evolutionary Algorithms (EAs), and especially the study of the NSGA II algorithm, which is a widely referred to, fast and robust Genetic Algorithm, developed by Deb et al. (2002). The second part is the implementation of the NSGA-II algorithm into a Grasshopper component. This includes all the necessary programming to transfer the logic of the algorithm, it’s advancement by incorporating state of the art features, as well as the design of the connection between the algorithm and Grasshopper. I should mention at this point that, during this stage, the expertise and willingness of my main mentor, Dr. Michael Bittermann was indispensable and crucial to my understanding of the concepts behind and the inner workings of the aforementioned algorithm. This topic is covered extensively in part 4 of the report.
1.4. Testing and Case Studies The implemented EA is then evaluated against a series of known test problems, as well as in combination with the parametric model in order to determine how it performs. As a final stage of the thesis project, the results of the design stage (the parametric model together with the EA) are applied to an actual design scenario of an airport terminal. The site that will be studied is the new International Airport in Doha, Qatar. Initially, the parametric model will be adjusted to the specifics of the site and building program. As a next step, the EA will be applied in order to perform a search for optimal configurations. Finally, one of these configurations will be manually chosen and developed in detail, focusing on the detailing of the shell structure. This stage will be discussed extensively in section 5 of the report. Lastly, the report will be summed up by presenting a discussion and conlusions on the project.
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Ioannis Chatzikonstantinou
2 / The Design of the Passenger Terminal The design of airline terminals is an enormously complex design task. There are two main factors that contribute to this. The first one is the large amount of often contradicting performance factors that are being pursued and come into play during the design of airline terminals. One can think of the various different goals that a terminal needs to achieve: Efficiency, aesthetics, safety and security and so on. Adding to this is the enormous amount of possible solutions that exist to the problem of arranging an airline terminal, stemming from the large scale, the complexity of operation and the relatively free form of this type of building. These factors eventually make up an extremely complex design task. In figures 3-6 four different representations of contemporary airline terminals are depicted, which demonstrate clearly the variety of design approaches. The rest of chapter 2 of this report attempts to elaborate on the general design factors that take part during the design of an airport terminal, from a perspective that seeks to present an all-round framework for assessing the performance of an airline terminal design at the layout level.
2.1. Design Requirements & Principles The brief for the 2007 Dallas / Fort Worth “New Visions of Security: Re-Life of a DFW Airport Terminal” competition mentions six design factors that should become the focus of any passenger terminal design proposal, which are summarized below: 1.
Accommodating current and emerging security requirements
2. Incorporating sustainable design 3. Optimizing operational efficiencies 4. Incorporating space for retail and concessions 5. Converting its 1970’s architecture into a 21st century statement 6. Incorporating the airport’s new train system, SkyLink Apart from points 5 and 6 which are specific to the particular design case, the rest could be recognized as key design factors in any modern airport terminal design case. According to Edwards (2005), five distinct terminal and pier concepts exist, each with its own advantages, and each appropriate for different situations: •
Central terminal with pier/finger (centralized terminal)
•
Open apron or linear (semi-centralized or decentralized terminal)
•
Remote apron or transporter (centralized terminal)
•
Central terminal with remote satellites (centralized terminal)
•
Unit terminal (semi-centralized or decentralized terminal).
Some arrangements that are directly repreentative of the above typologies are visible in figure 7. Between these well defined typologies, though, there is certainly space for innovation at the layout level. It is, after all, evident if we take a look at just a few of all the different terminal configurations that exist (figure 8). Innovative designs may be reached by generating “hybrids” that combine individual properties of each terminal type. A suitable manner of generating a model that can incorporate all above typologies, as well as in-between arrangements, is a parametric definition.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 3 Doha Intl. Airport Architect: HOK Architects
Fig. 4 Shenzen Airport Architect: Massimilliano Fuksas
Fig. 5 Shanghai Pudong Intl. Airport Architect: Rogers Stirk Harbour
Fig. 6 Bangkok Intl. Airport Architect: Murphy Jahn
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Ioannis Chatzikonstantinou
Fig. 7 Standard Terminal Types. (Ashford, 1992)
2.2. Passenger Terminal Positioning Because the terminal building is part of a larger system of airport elements (including roads, apron areas and aircraft taxiways), its position is determined precisely by the masterplan. This will prescribe a specific location, the means by which connections are made to other facilities, and the extent of the footprint and height of the passenger terminal building. The geometry of the terminal building reflects in a direct fashion the wider geometry of the airport: a point that designers need to bear in mind if passengers are not to become disorientated. The distance that the aircraft needs to taxi between the terminal building and the runway has a large bearing upon airline costs. Long taxi length means longer flight times, increased fuel costs, and the potential for ground traffic delay. The relationship between the location of the terminal and that of the runways (and taxiways) is crucial. Different configurations of termi-
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 8 Examples of various terminal layouts of airports in the United States.
ANC – Ted Stevens Anchor age Intern ational Airpor t
BHM – Birmingham Airpor t
BNA – Nashville Intern ational Airpor t
DAL – Dallas Love Field
ABQ – Albuquerque Intern ational Airpor t
BOS – BostonLoganIntern ational Airpor t
BDL – Bradley Intern ational Airpor t
BWI – BaltimoreW ashington Intern ational Airpot
CHS – Charleston Intern ational Airpor t
CVG – GreaterCincinn atiIntern ational Airpor t
CLE– Cleveland HopkinsIntern ational Airpor t
nal buildings, taxiways and runways affect design to a significant degree (Edwards, 2005).
2.3. Functional Organization Most terminal buildings consist of six distinct territories on departure (Edwards, 2005): •
Entrance concourse
•
Flight check-in and information
•
Shops, bars, restaurants, cinemas etc.
•
Passport control
•
Departure lounge and duty-free shops
•
Pier and gate to plane
and four territories on arrival: •
Arrivals lounge
•
Baggage reclaim
•
Customs and immigration control
•
Exit hall
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Ioannis Chatzikonstantinou
According to a scheme presented by Manataki and Zografos (2009), the passenger terminal can be also divided into Functional Areas. According to this scheme, the different parts which constitute the airport terminal in its entirety are: 1.
Unrestricted Airport Functional Area, including all facilities in the airport terminal area before the Boarding Pass or Pass- port Control facility for departing passengers, and after the Arrival Hall for arriving passengers; it is accessible by all airport users. Particularly, the facilities that may exist in the Unrestricted Functional Area include: Ticketing, Checkin, Boarding Pass/Ticket Control, Passport Control, Waiting Lounges, Arrival Halls, and Ancillary Service facilities (i.e., Retail and Food & Beverage facilities).
2. Controlled Airport Functional Area, including all facilities in the area defined after the Boarding Pass or Passport Control facility and before gates area; it refers only to departing passengers. It may include the following facilities: Security Screening, Waiting Lounges, and Ancillary Service facilities. 3. Gates Airport Functional Area, including all facilities that may exist around gates; it refers only to departing passengers who have passed through Security Screening. This functional area may include Gate Lounges, Passport Control and Ancillary Service facilities. 4. Arrivals’ Controlled Airport Functional Area, including all facilities arriving passengers may pass through after entering the terminal (from the airside) and before proceeding to the arrivals hall. This functional area is denoted only to arriving passengers and includes the following facilities: Passport Control, Baggage Claim, Customs, and Ancillary Service facilities. The classification of terminal areas according to their function is of particular importance for the development of a generative model for the passenger terminal, since it introduces a structured approach regarding it’s layout, which in turn is highly compatible with parametric generation methods. Following such a distinction a parametric model could reflect a layout and at the same time a functional organization, an implied sequencing of it’s functions.
2.4. Operational Efficiency and Movement In their essence, airport passenger terminals are movement systems. Therefore, the operational efficiency of a terminal is mainly translated into the efficiency of movement and distribution of it’s users. Passenger terminals are called in general to facilitate at least two different passenger flows, the ones departing and the ones arriving, as well as two baggage flows, again of those arriving and those to be loaded on planes (Edwards, 2005). It is important therefore that the imperative of movement is recognized in the allocation of space, the ordering system of structure, and the handling of light. Six basic criteria should be observed in the design of passenger movement in the terminal building: •
Easy orientation for the travelling public
•
Shortest possible walking distances
•
Minimum level changes
•
Avoidance of passenger cross-flows
•
Built-in flexibility
•
Separation of arriving and departing passengers.
Two groups of opposing design “imperatives” begin to appear already regarding passenger movement within the terminal: The first, passenger-oriented, drives terminal design towards minimal configurations, clean movement paths and orientation; the other, aiming to satisfy
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
capacity, often has to impose complicated arrangements (level changes, direction changes etc.) in order to reach economical spatial layout solutions.
2.5. Retailing and Commercial Activity The revenue that is generated through non aviation-related activities within a passenger terminal is of continuously increasing importance. The lack of interest of many governments to fund airport development, combined with the rapidly increasing cost of expansion has demanded that serious consideration be given to the revenue-generating potential of any airport from the initial concept stage. The volume of passengers within an airport terminal is large in comparison with airport and airline staff and, as the prime reason for having the facility the passenger is seen as a major source of airport income during the time that he or she spends in the terminal. However, the disadvantages that uncontrolled placing and expansion of commercial facilities brings to the achievement of the terminal’s primary function, which is to facilitate movement between land and airside, are more profound than the benefits in terms of increased terminal income from the retail facilities (Freathy and O’Connell 1998). Therefore, decisions regarding placement of retail facilities are of primary importance in terminal design. Doganis (1992), cited in Freathy and O’Connell (1998) maintains that retail facilities should be located in the direct line of the passenger flow and as close to the departure gates as possible. Because many travellers experience a degree of anxiety when travelling by air, few will deviate from the main passenger routes in order to purchase retail products. Bingman (1996), cited in Freathy and O’Connell (1998) sees the configuration of the retail offer as a dilemma for the airport operator: If concentrated in one specific part of the departure area, it creates the visual appeal of a shopping centre, which in turn creates synergy between outlets and increases the propensity of customers to spend. Alternatively, if the retail offer is spread out accross the whole of the departures area, it provides the passenger with a greater number of opportunities to purchase. Finally, it is important for the passengers to have the retail outlets in their line of vision before actually encountering them. This will help stimulate purchasing behaviour and possibly trigger impulse sales.
2.6. The Level Of Service (LOS) Standards The Level Of Service (LOS) is a standardization proposed by the IATA to provide a common reference for evaluating the level of service provided by passenger terminals for a given situation. Here the term is related to the spatial comfort that one experiences within a terminal. The LOS standards therefore classify conditions in terminals according to the space available to each terminal occupant. LOS Level A equals to excellent conditions, level D equals to desirably the lowest level achieved in peak operation and level F is the point of system breakdown or congestion (Ashford, 1992). Usually, Level of Service C is a good design tradeoff for most airport terminals, Level of Service B is an excellent design practice if the budget allows it and Level of Service A is usually too prohibitive to implement (Trani, 2002). The concept of Level of Service, apart from specifying spatial requirements for standing conditions, has been expanded to address flows of pedestrians (Fruin, 1993). In Table 1 the standards for pedestrian flows are presented and in figure 9 a graphic representation of passenger flow for various conditions is available.
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Ioannis Chatzikonstantinou
Value
Pedestrian Average Area (m²/p) Flow (p/ m-min)
Remarks
A
<23
>3.3
Excellent service; free flow conditions; excellent level of comfort
B
23-33
2.3-3.3
High level of service; condition of stable flow; very few delays
C
33-49
2.4-2.3
Good level of service; stable flow; few delays
D
49-66
0.9-1.4
Adequate level of service; condition of unstable flow; acceptable delays
E
66-82
0.5-0.9
Inadequate level of service; condition of unstable flow; unacceptable delays
F
Variable Flow
<0.5
Unacceptable level of service; condition of cross flows; system breakdown
Table 1 Level Of Service standards for pedestrian movement (Trani, 2002)
Fig. 9 Pedestrian flow for various conditions. (Trani, 2002)
2.7. Energy Performance Energy performance is becoming an increasingly important design factor for new buildings. Airline passenger terminals are no exception, on the other hand, the need for improvement on the energy efficiency of this type of buildings is of particular significance given the large amounts of energy required to maintain them, which is mainly due to their scale and continuous operation. This need is further amplified by the fact that contemporary airport operators face increasing costs due to the rising fuel prices, as well as the enforcement of strict regulations regarding the environment. The approach to energy efficient and sustainable design of airline passenger terminals is no different from other public buildings. After all, setting aside the specialized functions of the terminal, in their essence they are typical large scale public buildings that mostly consist of large connected spaces. That being said, the design of airline passenger terminals that are energy efficient depends on many factors, among which are layout, type of construction, site specific climate etc. Furthermore, principles of energy-efficient design such as natural ventilation, energy recovery, adequate use of daylight etc. are of great importance when aiming for a “Green” passenger terminal.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
3 / Defining a design model Following the identification of the essential concepts behind the design and evaluation of the passenger terminal and how these can be applied to the early conceptual design stage, the next step is to establish a parametric model that accurately expresses a design domain that contains as much as possible meaningful solutions corresponding to airport passenger terminal designs, as well as to introduce to that model a series of evaluation functions that can judge the efficienvy of each generated solution. Parametric design is a relatively recent advancement in the design industry that introduces a new paradigm of defining geometrical objects and relations between them. In it’s simplest form, a geometrical object is defined by a generator function that accepts a number of input variables or parameters. In the case of a circle, for example, the input parameters would be, just like in a regular CAD program, the coordinates of it’s center and it’s radius. The generator function would include the suitable algorithm to draw the actual circle in the correct position. What is revolutionary about this approach to design is that parameters may be linked between them, resulting into quite complex geometrical definitions. By linking different parameters more complex design tasks can be achieved in an elegant way.
3.1 The Airport Terminal Model In order to achieve the aforementioned goal of reaching a meaningful design domain that represents the range of possible configurations for passenger teminal layouts, careful consideration should be given to the generative principles that determine the solutions produced. In particular, it should be taken care that the range of solutions produced is complex enough for innovative ones to come up, but still as simple as possible, ruling out unnecessary complexity.
3.1.1. Generative Principles A decision was made to base the model on radial branching patterns, whose parametrization regarding the type, frequency and direction of branching would produce the required design space. The resulting parametric model is based on a main linear element that defines the principal arrangement of the terminal, whether it follows a straight or radial arrangement, and what it’s overall layout shape is. Two levels of branching elements that form the terminal’s piers, where boarding gates are placed at regular intervals, conclude the model. Some solutions that depict all of the Parametric Model’s features are available in figure 10. In detail, the parametric model consists of the following segments: •
A linear concourse of variable length, width and curvature (ranging from straight to 270 degree curved).
•
A variable amount of piers that extend from the concourse towards the paron side at regular intervals, with variable lengths, widths and angles.
•
A second series of branching piers that extend from the edge of each pier of the first series, with variable lengths, widths and extension angles.
This scheme allows a wide variety of solutions to be generated, from highly branched designs to linear ones as well as various mixed types in between. Some extreme cases of layout arrangements include the main concourse having a length of zero, in which case a radial arrangement is generated, and the piers having a length of zero, in which case a completely linear arrangement is generated. A representative generated solution that demonstrates the
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Ioannis Chatzikonstantinou
Fig. 10 A selection of generated configurations.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
aforementioned features can be seen in Figure 13.
3.1.2. Design Parameters The parameters based on which each individual solution is generated are divided into 3 categories: Design constants, design variables and design requirements. Design constants represent values that are well established in general such as dimensions of aircrafts, safety dimensions and climate calculation constants. These values are the base for many of the model’s calculations. The design constants included in the model are: •
Capacity-related values, such as average capacity of aircrafts, number of aircrafts per gate per hour etc.
•
Cost related values, such as costs for various operations or materials and assemblies.
•
Thermal and weather related values, such as climate data, temperature ranges, thermal properties of materials etc.
Design variables are parameters that directly affect aspects of the design. The precise topological and gemoetrical features that a particular solution will include, based on the generative principles, is governed by this set of parameters. The design variables included in the model are the following: •
Lengths of main concourse, first and second level branches
•
Curvature of main concourse
•
Angle between concourse and first-level piers
•
Angle between branching piers
•
Main concourse section width
•
Piers section width
•
Entrance location
•
Option to mirror layout (boolean)
Design constraints are variables which express desired traits of the design. While they do not directly affect the design itself, they are used to indicate, in combination with performance criteria such as those discussed in 3.2, whather the design is close to the desired parameters. The model’s design constraints consist of the following parameters: •
Target capacity of the design
•
Percentage of reatil area
•
Percentage of circulation area
•
Percentage of glazed envelope
•
Shading factor
A comprehensive list of all the parameters of the model, along with their units of measure and ranges is available in Table 2.
3.2. Performance Criteria The evaluation of the performance of a single resulting design is centered around four different aspects: •
The cost of the solution.
•
It’s accessibility.
•
It’s energy performance
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Ioannis Chatzikonstantinou
No. Gates x Cost/Gate
Cost
Total Floor Area x Cost/m2
Total Shell Area x Cost/m2
Avg. Walking Distance
Accessibility
Level Of Service (LOS)
Objectives Heating / Cooling Load
Energy Performance
Suitable for Natural Ventilation?
Retail Area
Retail Suitability
Suitability of Area
Capacity (Gates)
Constraints
Max. Retail Area %
Max. Movement Area %
•
It’s retail suitability
These high level design aspects are abstract in nature and are for each solution generated determined by combining one or more specific evaluation functions. Figure 11 demonstrates the high-level design criteria and the essential evaluation functions that they are made up of. Following is an explanation and discussion on each of these design aspects, the evaluation functions that they are based on, as well as the methods for combining them.
3.2.1. Cost Calculating even an approximate cost figure for such a complex project as the design of an airline terminal is surely impossible given the relatively low level of complexity of the parametric model in use. Still, relative figures that can be used as indices to compare different solution are feasible. The cost estimation that is proposed takes into account three different factors: •
The number of gates the terminal.
•
The terminal’s total floor area.
•
The terminal’s shell structure surface.
These three factors are a reflection of three different aspects of architectural/construction projects that contribute to their cost: Structure, skin and, specific for the airline terminal, equipment. Each of the three factors receives a user-determined weight. This way, their contribution to the cost can be adjusted. The formula by which the cost is estimated is the fol-
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Fig. 11 Objective functions, constraints and their components
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Name
Unit
Min
Max
Design Variables Arm Length Inner Radius
m m
100 400
400 1800
No. Sides Angle
deg
2 0
5 270
Relative Rotation Mirrored
deg -
0
75
Main Width Section Width
m m
40 0.6
180 0.9
Sec. Arm Length Sec. Angle
m deg
90 0
300 60
Branch Count Sec. Section Width
m
1 0.5
3 0.9
1000 500
5000 1500
100000
500000
FALSE
TRUE
Design Constants
Table 2 List of parameters taking part in the generation and evaluation of the parametric model
Cost/Floor Surface Cost/Envelope
€/m2 €/m2
Cost/Gate
€
Pedestrian Speed
m/sec
0.2
2
Aircraft/Day-Gate Avg. Aircraft Capacity Avg. Wingspan Safety Distance
persons m m
5 80 30 5
20 500 85 20
Avg. Dwell Time in Retail Peaking Factor TPV
min -
3 1
20 1.5
ZTA Qsun Heat Per Person Lighting Heat Equipment Heat Air Change Rate Heat Recovery Infiltration Rate Tin Tout Design Constraints
W W W W ℃ ℃
0.5 300 60 20 50000 0 0.3 0 16 -5
0.9 1000 200 200 800000 1 0.7 0.3 27 35
Target Capacity
p/h
1000
8000
Max. Circulation Area Max. Retail Area
% %
10 5
50 30
Glass Ratio Shading Factor
% %
40 0
80 80
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Ioannis Chatzikonstantinou
lowing:
Where ngates
the number of gates
fgates
approximate cost per gate
Afloor
total floor area (m2)
ffloor
cost per m2 of floor area
Asheel
total shell area (m2)
fshell
cost per m2 of shell area
3.2.2. Accessibility The level of accessibility offered by a specific solution depends on two factors: The average Walking distance within the terminal and a measure of the degree of crowdedness for pedestrian movement in the terminal movement areas, as defined in the Level of Service (LOS) Standards applied to pedestrian flows. 3.2.2.1. Walking Distances An aircraft passenger is the main user of the terminal building. Passengers arriving at the terminal will go through a series of stages which end in them boarding an aircraft. Arriving passengers will again follow a path that will lead them to some other means of transportation at one of the airport’s access points. The overall layout of the various terminal functions that a passenger must visit is therefore of primary importance. A probabilistic approach for calculating the average travelling distance from a single starting point to multiple endpoints has been implemented. This approach may be used to calculate the average distance between a single entry point of the airport terminal and the boarding gates. Multiple entry points may then be evaluated by applying the formula multiple times, each time for the right percentage of the population. An evenly distributed number of gates along the terminal’s piers and main concourse is supposed for the calculation of the average distance. For each segment of the layout, it’s walking distance from the entrance of the terminal to it’s midpoint is calculated and multiplied with the segment’s length. These distances are summed up and divided by the total length of the layout. Since the gates are uniformly distributed, the length of a segment can be used to determine the number of gates that it can contain, and therefore the percentage of the population that heads towards that segment. The calculation formula for finding the average walking distance for each pier is as follows:
Where: l
the average walking distance
a, b
the lengths of the first-level and second level pier segments respectively
nb
the number of branches of the second level pier segments
Having calculated the average walking distance for each pier (with all piers being identical),
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
the total average walking distance from a single entrance in the middle of the main concourse can be calculated as follows:
Where: n
the number of piers in the design
lt
the total average walking distance
di
the distance of the ith pier from an entrance
l’i
the average walking distance for a single pier
pi/p0
the fraction of the population that has the ith pier as a destination
The above formulas can function for any case of branching-like structure with at most two branching levels, although they can be easily extended for more complex branching structures. The walking paths taken into account in this probabilistic scheme can be visualized in figure 12. 3.2.2.2. Pedestrian Flow and Crowdedness (LOS) Given the linear nature of the spaces within the layouts and the significan flow of people, the unobstructed movement should be assured, taking care to avoid crowding. Therefore, a measure that is of significance is the available section width of the generated layout for people to walk. Whether a given section offers adequate space for people to move is in turn linked to the rate of flow of the people and therefore to the topological and geometric characteristics of the layout (length of segments, amount and branching of piers etc.). To determine the degree of comfort while moving through the terminal, the concept of Level Of Service for pedestrian flows is used, as described in 2.5. Trani (2002) mentions that the pedestrian flow can be calculated using a hydrodynamic analogy. The formula then is:
Where: f
Pedestrian volume measured in pedestrians per meter width of traffic way per min-
ute (pr/m-min) s
Average pedestrian speed
a
Average area per person
The average area per person can be calculated using the user-defined Passengers Per Hour figure that determines the capacity of the terminal, the average pedestrian speed and the average distance, whose calculation has been demostrated in 3.2.1.1. The formula is the following:
Where: A
total area assigned to movement
s
average pedestrian speed
Fh
capacity (passengers/hour)
d
average walking distance within the terminal
Using these formulas together with the values established from Table 1, a value that estimates the Level of Service of a specific solution (using average values) can be extracted and used
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Fig. 12 The various different walking paths taking part in the calculation of the average walking distance.
for evaluation.
3.2.3. Energy Performance In order to measure energy performance, the required amount of power for heating or cooling the terminal building is used. This figure normally relies on many different climate aspects, however here, for reasons of reduced computational complexity, a basic steady state model for the calculation of energy gain/loss is used. There are three basic factors affecting the need for heating or cooling of a building: 1.
Heat gain through solar radiation
2. Heat loss through transmission 3. Heat gain through internal heat production
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
5
4
1 2
Fig. 13 Individual parts of the Parametric Definition: 1. Main Concourse 2. First-Level Piers 3. Second-Level (branching) Piers 4. Alternative entrance positions
3
4. Heat gain/loss through ventilation In order to calculate the required heating/cooling amount, the worst combination of these factor is calculated. Since some contribute to heating and some to cooling, a different combination should be used depending on the conditions. Heat gain through solar radiation is calculated by nultiplying the glazed area of the envelope with the ZTA value of the glass and the intensity of the radiation: Qsun = Aglass * ZTA * Qspm Where: Aglass
the glazed area that receives solar radiation
ZTA
the ZTA value of the glass
Qspm
the solar radiation heat per square meter
Heat loss through transmission is calculated by multiplying the transparent and solid parts of the building envelope with their respective U-values and multiplying their sum with the temperature difference between inside and outside: Tloss = (Aclosed * Uclosed + Awindow * Uwindow) * (Tinside - Toutside) Internal heat production is calculated by multiplying the population within the building with the heat produced per person and adding it to heat generated by lighting, equipment etc: Qint = nP * Qpp + Qlight + Qeq Finally, heat gain/loss through ventilation is a component of two different sub-factors: The normal ventilation flow and the unintentional or accidental air exchange that takes place, also known as infiltration. The way these factors determine the heat loss/gain is expressed by the following formula: Qvent = (Qforced * (1-hrp) + Qinf) * ρ * c * (Tinside - Toutside)
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Where: Qforced
the heat los through forced/mechanical ventilation
hrp
the percentage of heat that is recovered
Qinf
the heat loss because of infiltration
ρ
the volumic mass of the air
c
the specific heat capacity of the air
The Qforced and Qinf values are in turn calculated using the following formulas: Qforced = V * nh Where: V
the volume of the building
nh
the air change rate per hour
Qinf = V * ninf Where: V
the volume of the building
nh
the infiltration rate
The total heating/cooling demand is determined by summing up the factors relevant to the specific condition we are investigating, out of the ones mentioned. For cooling, ti would be a combination of internal and external heat gain and ventilation cold loss. For heating it would be a combination of heat loss through transmission and heat loss through ventilation. The parameters that take place in the calculation of the steady state model are available as design constants within the parametric model.
3.2.4. Retail Suitability Evaluating the suitability of a specific terminal design for retail activities is certainly a complex and controversial design aspect. From an architectural point of view, the spatial organization of the retail area of a passenger terminal is certainly a factor that largely determines it’s degree of efficiency, and therefore the non-aviation revenue that the terminal generates. Apart from the specific placement and arrangement of the retail units, the overal organization of the retail area plays a significant role to it’s success. Factors such as the line of sight of the passenger, the concentration of retail units, the overall form of the retail area, are of primary importance in assessing it’s performance. The methods that is implemented utilized as a measure of retail effectiveness the “visual conectedness” of the retail space, favoring arrangements that allow the user either a complete or a progressive visual overview. The first step to the method is to measure the available retail area of the terminal. This is performed as proposed in Freathy and O’Connell (1998). The formula for the calculation is:
Where: T
average dwell time in shops (minutes, e.g. 14)
F
peaking factor (suggested value 1.2)
TPV
target penetration for visits (suggested value 0.65)
DFR
design flow rate (passengers/hour)
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
In the next step, two factors are used to determine the suitability of the retail area. The first expresses the concentration of retail units and the second is a measure of the “visual connectedness” within the area. The concentration of retail units is expressed as the distance of the endpoints of the main concourse. The visual connectedness measure takes into account the curvature of the concourse, it’s width and it’s length. The corresponding formula is:
Where: A
the angle of the main concourse
L
the length of the main concourse
W
the width of the main concourse
The result of the above formula is essentially a measure of the “compactness” of the retail area. It evaluates based on the visual connectivity (how much curved is the area?) and the proportions of the area (is it a rectangular area or is it linear?). The formula is used in conjunction with the total retail floor area of the terminal, in order to give a figure that reflects the retail suitability of a generated solution:
Where: A
either the calculated retail area or the maximum retail area provided by the user,
whichever is found to be smaller. SR
the suitability factor calculated earlier.
It should be noted that the method described here takes into account the presence of a main retail area situated in the main terminal concourse. Individual, secondary retail areas close to the gates are not taken into account, since their performance relies more on smaller-scale features and is therefore not measurable at this level of abstraction. Some arrangements and their respective evaluation regarding retail performance are presented in figure 14.
3.3. Constraints The parametric model that has so far been described corresponds to a cetrain range of possible outcomes, or solutions, which are limited by it’s compositional principles, as well as by the range of values that it’s defining parameters are allowed to take. Within this solution space, it is unavoidable that some solutions will be either unrealistic or irrelevant to the requirements expressed by the user. In order to allow these solutions to be automatically identified, constraints are implemented, in addition to performance criteria. The role of the constraints is primarily to ensure two design qualities: It’s feasibility and it’s adherence to user-defined requirements. The first kind of constraints refer to whether the design is valid (e.g. if a part of the layout is intersecting with another one the design is clearly infeasible, no matter how well it did in the evaluation). Through these constraints, the parametric model gains a sort of “self-awareness”, being able to judge it’s feasibility automatically. The second class is represented by a sole constraint, that of the design capacity in terms of aircraft docking positions. This type of constraint is meaningful in limiting solutions to a spectrum of values equal or bigger than the desired capacity.
3.3.1. Self-intersection
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The first check that is performed on a solution in order to determine it’s feasibility is self collision. Self collision happend when, some part of the procedurally generated solution overlapss with another part. This is quite common in procedurally generated layouts and is due to potential incompatibilities of parameters in certain ranges (e.g. small spaces between subsequent piers with wide branching). In order to exclude the solutions that exhibit overlapping between members, a collision detection is performed on every generated solution. If it is true and therefore collision is present within the solution, it receives the maximum penalty. In order to reduce the computational complexity of the collision calculation, only the parts of a layout that are mostly possible to collide between them are checked. These are the first nd last segments of the subsequent 2nd level branches as well as first level piers. The former are evaluated for collision between them and with the latter. The collision scheme is presented in Figure 15.
3.3.2. Aircraft Circulation In order to ensure that aircrafts may circulate and reach the docking positions, measurements of the distances between edges of the branching segments of the layout are performed. Two kinds of measurements are performed, which are visible in Figure 16: 1. Measurements between the closest poinst of subsequent branching piers and 2. Measurements between closest points of branching piers and the main concourse. These two groups of measurements ensure adequate space for aircraft access to all calculated docking positions. The minimum for each dimension is determined by adding a safety factor to the maximum specified aircraft dimension. If a dimension is found to be less than the minimum, the particular solution’s feasibility measure (expressed through the constraint parameter) is penalized accordingly. In contrast to the penalty value for self-intersection, which gives out a binary value denoting either violation or it’s absence, this value is linearly related to the amount of violation below the allowed minimum that the smallest of the measured distances demonstrates.
3.3.3. Capacity An essential characteristic of an airport terminal is it’s capacity in terms of aircraft docking positions. It is what actually determines the scale of the building, as well as it’s layout. Within the parametric model the user is able to define a desired capacity, against which the capacity of the generated layout is compared. The aircraft capacity of a particular design is measured based on the actual geometry of the design. As a first step, docking positions are laid out along the perimeter of each segment of the layout. This leads to a uniform distribution of aircraft positions, however due to the branching topology there’s a high probability that some of the positions will overlap. Addressing this issue leads to the second step of the calculation, which involves the resolution of collisions between docking positions. Finally, the number of available positions is compared with the number of required ones. The layout gets a good score if it satisfies the required capacity. Layouts that fall short are accordingly penalized. Layouts that supersede the required capacity do not receive a higher score but are not penalized either. The scoring formula is based on a Gaussian cumulative distribution function (CDF), which takes the form:
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 14 Formations of the main concourse and their value as retail areas
Fig. 15 Checks performed to avoid self-intersection of the model
Where: r
the resulting score
a
the desired capacity
b
a measure of the “strictness” of the evaluation
erf
the error function
The graph of this function for values of a = 150 and b = 12 can be seen in Figure 20.
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Fig. 16 Measurements performed to determine viability of circulation. Distance between subsequent 2nd level branching piers. Distance between 2nd level piers and main concourse.
Fig. 17 A series of solutions that are considered invalid because of self-intersection, or violation of minimum distances between piers.
3.3.4. Fuzzifying goal components Each of the various components that make up the evaluation scheme is expressed in it’s own units and range of values. If we were to directly compare them, it would be necessary to somehowindicate the significance of each, which is not a trivial process. If we were, for example, to combine the average distance with the Level of Service to get an idea of how efficient a design is in terms of transportation, there wouldn’t be any robust way to do it directly. It is for this reason that, before using the objective function to drive the evolutionary search, a fuzzification of their values is performed. The first step to this process, is to establish the extreme well and badly performing values for each objective function. Then, these values are laid out on a graph and a curve-fitting process is performed, which maps the original values to a sigmoid function. The sigmoid has the benefit of varying between zero and one and therefore it is easy to derive the “goodness” of each solution regarding the particular design aspect, instead of an arbitrarily ranging value. Furthermore, since all the objective values range between zero and one, comparing them is straightforward. The sigmoids resulting from the curve-fitting for three different objective functions are visible 32
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
in figure 19.
3.3.5. Combining hard and soft constraints Of the constraints that have been described, some are of a continuous and some of a binary nature. The constraint that regards self-intersection, for example, can only have two values: Either a design intersects itself at one or more points, or it does not. On the contrary, the constraint that measures how close to the required number of gates a design is, outputs an integer that corresponds to the difference between the actual and the required. Because we want any design to absolutely satisfy all constraints, we could ideally perform an evaluation for every one of them and, if they are all satisfied, only then the design could be considered valid. However, having information about how much the constraints are violated is beneficial to a computational optimization process such as an Evolutionary Algorithm, as we will se in Part 4 of this report. The Evolutionary Algorithm can “guide” the search away from solutions that violate constraints and this requires the degree of violation to be determined. The most suitable way of dealing with partial requirement satisfaction is using fuzzy logic. The constraints described are already expressed as a fuzzy set, with values ranging between -1 (worst constraint violation) to 0 (no constraint violation). It is therefore possible to form a fuzzy rule out of the combination of the constraint violation values. Since we are looking for the satisfaction of all constraints in the system, the individual constraint satisfaction values must be combined using AND operations. In fuzzy logic such a rule can be expressed in a generalized form as the Zadeh-Mamdani fuzzy rule: if X1 is 0 AND X2 is 0 AND ... AND Xk is 0 THEN V is 0 With X1-k being each individual constraint violation check and V being the total constraint violation. One way of calculating the outcome of such an expression, according to Mamdani, cited by Bittermann (2009), is by taking the minimal membership function value, so that:
This way, all individual constraint violation values can be combined into a single variable that corresponds to the total constraint violation that a solution exhibits. The total constraint violation obtained through this fuzzy rule for various values of the individual constraints is presented in Figure 21.
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Fig. 18: Overview of the parametric model
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
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Ioannis Chatzikonstantinou
Fig. 19 Plots of the Sigmoid function used to fuzzify the absolute objective values. Each graph shows the points used to derive the function parameters. I. Cost II. Level of Service III. Retail Suitability
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 20 Plot of the Gaussian CDF for a=150 and b=12
I
II
Fig. 21 Two different functions that could be outputs of constraints (I, II) and their combined minimum (III)
III
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Ioannis Chatzikonstantinou
4 / Optimizing Solutions The parametric model of the airport terminal that has been described in chapter 3 contains both generative logic, as well as functions for evaluating each resulting design’s performance according to a set of performance criteria. Because of this functionality, whether a solution is performing well or not in a particular aspect need not be identified through manual evaluation, but can be performed automatically and in real-time, as the model’s parameters change. This feature is of particular significance in order to identify and generate optimal designs. It enables the possibility of combining the model with an iterative optimization strategy, such as an Evolutionary Algorithm, through which optimal solutions can be reached.
4.1. Evolutionary Computation There is a variety of different strategies for optimization. One of the most prominent category is Evolutionary Algorithms (EAs). An EA uses some mechanisms inspired by biological evolution, in order to search for optimal solutions: reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the environment within which the solutions “live” (see also cost function). Evolution of the population then takes place after the repeated application of the above operators. This heuristic is routinely used to generate useful solutions to optimization and search problems.
4.1.1. Structure and Function of EAs In most cases, an evolutionary algorithm consists of two main components: •
A selection operation that usually selects individuals with some sort of bias towards the good solutions.
•
A combination operation that combines the chromosomes of selected members using crossover and mutation functions.
In order to effectively function, an Evolutionary Algorithm requires two more elements, although these are usually external to the algorithm itself and depend on the model to be optimized. These are: •
A generative function, which constructs each solution from the specification encoded in each member’s chromosome.
•
One or more objective functions that evaluate the manifested solutions as to how close to the desired goals they are and produce a fitness value.
A typical Evolutionary Algorithm begins with a population of random solutions and iterates over the following steps: •
Each individual’s chromosome is translated by the generative function into a phenotypic representation.
•
Each individual’s “fitness” is evaluated through the application of the objective function(s) to each individual design.
•
Good individuals are selected by the EA and combined to form a new population.
This process is then repeated iteratively until and end condition is reached, which could be any predefined limit set, such as a maximum number of generations, a target fitness value and so on.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
4.1.2. Single- and Multi-Objective EAs In traditional EAs, each individual of the population has a single fitness value, which may come as a result of a single evaluation parameter or the artificial combination of many different ones. This type of EA is known as “Single-Objective”. In order to tackle multi-objective problems using a single objective EA, each of the individual objective functions that make up the evaluation scheme is assigned a weight depending on it’s importance and afterwards is combined with the rest of the functions to form a single objective function which then can be used by the EA. This kind of “artificial” combination of objective functions has become the weakest point of Single Objective EAs, since it implies that an assumption about the relative significance of each performance factor has to be made a priori by the user of the algorithm. Since it is not always possible to formulate such an assumption about the relationship between goals, it is possible to arrive to an unrealistic evaluation scheme and subsequently to results which are not optimal. A Multi-Objective Evolutionary Algorithm (MOEA) adopts a different approach than that of a single objective algorithm: It evolves a population based on multiple fitness values until it reaches a set of solutions, each of which are good at some particular aspect, expressed by an objective function. These solutions are non-dominated solutions. A solution is non-dominated if there exists no other solution that performs better in every respect (Bittermann, 2009). These solutions are also termed Pareto optimal solutions. A set of Pareto optimal solutions forms a Pareto surface, or Pareto front within the dsign space. The function of a MOEA then can be described as identifying the Pareto front of a given problem. In the case of this project, deriving the best alternatives, or Pareto Optimal solutions from the evolutionary process is of primary importance, since it is mostly expected that for such a complex design task as the design of an airport terminal, alternatives with strong and weak points are more likely to occur rather than “all-round” performers. Furthermore, the relative importance between design criteria need only be expressed when the designer desires, allowing a commitment to be made with great awareness (Bittermann, 2009).
Fig. 22 The user interface of the EA component
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Ioannis Chatzikonstantinou
4.1.3. Objective Functions and Constraints It is often the case of problems whose solutions should be in one or more ways restricted within a specific parameter domain. Such restrictions could for example represent the maximum plot that a building is allowed to occupy. Solutions that violate these restrictions are mostly meaningless in the context of the particular problem. Such restrictions are termed constraints and are treated separately from objective functions in a MOEA. The reason is that solutions which lie outside the solution space defined by the set of constraints in use should not be represented as part of the Pareto front, since they are not valid. Therefore, a MOEA gives precedence to the constraint violation check over the objective functions, in order to make sure that the population stays roughly within the valid solution space. In most MOEAs there is a single constraint input, in contrast to the multiple objective functions inputs. This suggests that if there are more than one constraints, they should be merged in some way into one before being input to the EA.
4.2. The Non-dominated Sorting Genetic Algorithm II The NSGA II (Non-Dominated Sorting Genetic Algorithm - II) is a Multi-Objective Evolutionary Algorithm(MOEA) developed by Deb et al, (2002), which is widely referred to and known for its speed and robustness. Being a multi-objective EA, NSGA II operates on one or more design parameters as well as one or more objective functions. Furthermore, constraint satisfaction is also addressed, with constraints being treated separately from objective functions. The algorithm is based on the following components: •
A ranking component, which ranks each member of the chromosome population according to it’s Pareto Optimality.
•
A component that scores each chromosome according to it’s “uniqueness” within the solution performance space.
•
A tournament selection module, through which the selection of the “parents” of the next population is performed.
•
A simulated binary crossover (SBX) module, which allows for crossing over of chromosomes consisting of decimal values.
•
A mutation module, which allows for mutation of decimal values within a chromosome.
4.2.1. Process Initially, a random population is generated. In each iteration the algorithm generates a new population of solutions. The process through which this happens is outlined below: 1.
The current population is sorted according to its non-domination. Each solution (population member) is assigned a value equal to it’s nondomination level, with 1 being the best, 2 the next best and so on. A completely non-dominated individual is one where an improvement in one objective (fitness) results in a deterioration of at least one other objective, when compared to other individuals of the population.
2. Each population member is then assigned a “Crowding Distance” value, a measure of how unique this particular solution stands within the solution space. 3. Individuals that will form the new population are at this point selected and put into a so called “mating pool”. The selection follows a Tournament Selection strategy, with individuals going through a pair-wise, 3-step comparison process: After two random individuals are picked from the population, they are first compared regarding their violation of a constraint, if one is set. If both violate the constraint, the one with the less violation
40
Fig. 23 Schematic diagram of the loop that is being performed during the evolutionary search.
41
Crossover (SBX) Mutation
< Old Population
START
Function Evaluation
Pareto Ranking
Crowding Distance
Population Reduction
Tournament Selection
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Ioannis Chatzikonstantinou
is picked. If just one violates, the other one is picked. If none do, the next step is carried out which compares the ranking value of each of them. The one with the best ranking is picked. If the ranking of both individuals is the same, the final comparison step is performed, which compares their crowding distance values. The one with the largest value (whos neighbors are essentially further away in the solution space) is picked. 4. The selected individuals from the mating pool are then crossed over and mutated (according to a predefined probability) until a new population of the same size as the old is formed.
4.2.2. Elitism The convergence rate of the algorithm can be improved through applying the principle of elitism. Elitism is the process of selecting the better individuals, or in other words, selecting individual with a bias towards the better ones. It is based on the principle that, if only the best parents are kept, and replace always the worst, the population will converge quicker towards better solutions. In this case, elitism is applied as follows: 1.
Just before the first step, the previous population is copied to the current one. Step 1 and 2 take place in the combined population (of double the normal population size).
2. Just before step 3 the population is reduced to the normal size in a two step process: The individuals are first inserted starting with the best-ranked ones until the rank that will not fit to the original population size. This particular rank is then sorted accodring to the crowding distance of every individual, with the ones with the largest crowding distance
Fig. 24 Distribution of individuals in the solution space after 14 generations for the ZDT-1 problem.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
going in first, until there are no more free spots. A graphic representation of the function of the algorithm and the efect of the implementation of elitism in the process is available in figure 23.
4.3. The implemented algorithm The implemented EA includes all the features of the NSGA II and is suitable for use in the Grasshopper Parametric Design environment. Althought the EA was primarily developed to be used as part of this specific project, it was a design decision to make it an independent component, so that it can be of general use within Grasshopper. The user interface can be seen in figure 22. In this specific implementation of the NSGA II a new concept have been introduced, which is the implementation of the so called “Relaxed Angle” Pareto ranking. this concept has an effect during the non-dominant sorting of the population (Stage 1 of the above process): It basically allows each solution to determine itself how “strictly” it should be ranked, rewarding afterwards the solutions according to how strict each of them was found to be. The observed effect of this approach during an optimization using a test problem (ZDT1, explained in 5.1.) is that solutions tend to converge faster to the Pareto Front. The user interface of the implemented algorithm has been design to be minimalistic and intuitive, fitting well with the design workflow of the Grasshopper environment. Basic usage requires no parameters to be specified at all by the user, so that even inexperienced designers can easily make use of the EA. For the more advanced users, there is a range of parameters that can be set with respect to the Optimization Process. Resulting designs are displayed in a 2-D graph, with the user having a choice of which objective values to display, as well as being able to select a specific individual of the population to display the design right away in Grasshopper.
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Ioannis Chatzikonstantinou
5 / Testing and Case Studies 5.1. Initial EA testing - ZDT-1 For the purpose of testing the behavior of the implemented algorithm, the ZDT-1 problem has been implemented using Grasshopper tools and connected to the EA. The ZDT-1 is a test problem developed by Zitzler et al. (2000) which has become a part of a series of standardtests, carried out when evaluating the performance of a multi-objective EA. The resulting population distribution in the solution space shows that implemented EA performs as expected when applied to this test problem. The resulting distribution of individuals after 14 generations can be seen in figure 24. The progress of the ZDT-1 test for two different EA configurations (onw with adaptive Relaxation angle disabled and one enabled), as well as the results table, is available at appendix A1.
5.2. Terminal Model testing combined with the implemented EA The implemented EA has been initially tested with the Parametric Terminal model. The purpose of these tests was to determine the outcome of the EA, in order to evaluate whether the objective functions have the expected output, as well as to investigate the progression of the solutions population during the course of the optimization process.
5.2.1. Preparation The first step in preparing for the test run was to assign the design variables of the parametric model that can be manipulated by the EA, the objective functions that form the evaluation scheme and the total constraint violation output. The implemented EA aims at minimization of the objectives it is related with. Within the parametric model, some objective functions are maximizing and some minimizing. Therefore, the maximizing functions have to be converted. This is done through the application of a simple inversion function: R’ = 1/R This function has been applied at the output of the Retail Suitability and Accessibility objectives.
5.2.2. Testing The purpose of these series of tests was to investigate both the performance of the EA using different parameters (population size/relaxation angle/adaptive angle), as well as to evaluate the solutions themselves and investigate any correlations between objective functions. For each of the evaluation run, a set of realistic constants and average design constraints was specified. The algorithm was let ro run for increments of four generations, each time capturing the graphic representation of the population state. The process ended after 35 generations. Following the completion of the process, data such as graphs of all objective functions and a table representing the internal state of each Chromosome, were recorded. In total there were five tests performed, each focusing on a specific parameter of the EA. The first test’s parameter set consisted of standard values: A population of 100 members and no relaxed or adaptive angle Pareto ranking. An equally standard progression of individuals
44
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 25 Diagram demonstrating the effect of Relaxed Angle Pareto Ranking on two different individuals. This figure helps outline the pressure that peripheral solutions receive from the Relaxed Pareto Ranking. Individual I. on the left is a second-rank solution. Individual II. on the right is a 4th-rank solution. However, if the ranking was performed without Relaxation, the individual II. would be 1st rank, while individual I. would remain in rank 2.
I.
II.
towards better solutions can be observed in this test. After 10 generations the Pareto front is still not well shaped, while even during the final step of the process (generation 34 to 35), individuals that spreaded along the Pareto front could still be observed. The final result was a relatively well shaped Pareto front for most pairs of values. A graphical representation of the progress, as well as results are available in appendix A2. For the second test, the population was raised from 100 to 150. This parameter change had a profound effect in the shaping of the Pareto front, and a benefit to the number of generations to reach a well-shaped Pareto front, which now happens already from the 13th generation. In terms of computational time, a linear change was observed. While being in contrast with the computational complexity of the NSGA-II algorithm which is O(MN2) (Deb et al, 2002), it is justified by the fact that the processor time to compute the solution is much more than the time the EA takes to advance one generation. Therefore, the additional time comes almost exclusively from the solution of the additional 50 solutions in Grasshopper. The progress and results of this test are available in appendix A3. The third test drops down the population back to 100, but this time a relaxed Pareto ranking is used, with a relaxation angle value of 8 degrees. All other parameters remain the same as with the previous, as well as the first test. As a first observation, an increased convergence speed should be mentioned, even bigger than that of the increased population. The algorithm converged to a subset of the Pareto front in less than 5 generations. However, after thet
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Ioannis Chatzikonstantinou
convergence, almost no expansion on the Pareto front was observed. Indeed, the solutions remained within an area away from the edges of the Pareto surface. That behavior could be attributed to the relaxed angle Pareto ranking, which even for small Relaxation angle values would penalize solutions towards the edges. Such a condition is illustrated in figure 25. The progress and results of this test are available in appendix A4. The fourth and final test is based on the same EA parameters, only now an Adaptive Relaxation angle strategy is enabled. The results are mixed. While the speed of convergence seems to be at least as fast as the fixed-Relaxed angle pareto ranking, the formation of the Pareto front itself doesn’t seem so obvious. The result is a population that is rather spread out and inconsistent, and even seems to drift away from the front sometimes during the course of the evolutionary process, but this could also be a result of the limited perception that the visualization graph offers (solutions could be arranged on a multidimensional surface that is not visible in a 2-d graph). The progress and results of this test are available in appendix A5.
5.2.3. Discussion In general, it can be concluded that the resulting solutions of the algorithm do indeed demonstrate a variety and, as per Pareto definition, are performing well on different design aspects. As far as the translation of each individual into design features is concerned, some of them are pretty much expected (such as the minimization of section width in the least costly solutions), while others are quite surprising (such as the emergence of solutions with wide and straight concourses and almost no branching, which perform particularly well in retail evaluation, while maintaining accessibility and capacity). The beneficial effect of population increase to the formation of the Pareto front and the speed of convergence is verified. On the other hand, the application of the Relaxed Pareto ranking in this particular problem had mixed results, essentially trading off speed of convergence for variety between individual solutions and even spread along the Pareto front. Still, further investigation and testing should be performed before safe conclusions are reached. An approach to analyzing and interpreting the outcome of a MOEA is to identify visually any correlations that may exist between the various objective functions. In our case, some such observations can be made. As it can be derived from looking at figure 26, the most obvious correlation can be made between the Cost and the Heating/Cooling load function, a linear correlation with some individuals deviating especially in middle ranks. This is quite predictable, since both objective functions rely on the building envelope surface as an input measurement. A clear inverse correlation can be observed in the graphs of Cost and Retail Suitability and consequently in the Cooling Load-Retail Suitability graphs (since Cost and Cooling load are strongly correlated in a linear fashion). Finally, a concentration of individuals in the Retail Suitability-Accessibility graph can be observed. Regarding the quality of the generated solutions, it has been observed to be quite high. As already mentioned previously, all-round performers do not tend to appear, but that is more or less expected in a multi-faceted problem such as the one in question. As far as apron arrangements are concerned, the algorithm succeeds in exploring the boundaries set by the distance constraints between the piers, frequently resulting into solutions that are quite effective in their use of space.
5.3. Case Study Following the tests mentioned previously, a case study regarding the design of an airport terminal will be carried out. It has been decided that this case study will be on the site of the New International Airport in Doha, Qatar. The current airport witnessed a high growth in passenger and cargo levels in recent years, and its terminal suffers from under-capacity. This
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 26 Correlations between objective functions 1. Cost - Cooling Load (Linear Correlation) 2. Retail Suitability - Accessibility (Concentration) 3. Cost - Retail Suitability (Inverse Correlation) 4. Retail Suitability Cooling Load (Inverse Correlation)
rapid growth was mainly brought by the fast expansion of Qatar’s state airline Qatar Airways. Other growth came from the booming economy of Qatar. Planning took place in 2003 and construction began in 2004 and the first two phases are scheduled to open in January, 2012 while the third and final phase is scheduled for 2015. The airport will be built over 22 square kilometers, half of which is on reclaimed land. A map of the area can be sen in figure 28. The terminal building that will be constructed is shown in figure 29. To the first end, the airport will be able to handle 24 million annual passengers at its opening, three times as many as the current airport capacity. Upon completion, it will be able to handle 50 million passengers. However, the menareport.com financial news website mentions that the expected capacity would be up to 93 million passengers, making it the second largest capacity holder in the region after Dubai. A passenger terminal for such a large capacity airport is an ideal design scenario for the design method that is proposed, since the sheer amount of different solutions that can be investigated will provide a fertile ground for an Evolutionary Search.
5.3.1. Site Conditions The new airport is being constructed on a rectangular plot along the two long sides of which are the runways. The terminal building occupies a central position, with both of it’s sides being available for aircraft docking. The proposed design for the terminal follows a branching layout, with a central pier branching into two more, as well as two piers that extend from the main building sideways.
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The fact that the local landscape is completely flat, combined with the proximity of the airport to the sea offers a good opportunity of taking advantage of the naturally occuring local drafts for natural ventilation. Consequently, the shape of the building envelope must be suitable for natural ventilation, allowing the air to flow unimpeded as much as possible, and ensuring that all parts of the aterminal receive the same amount of fresh air.
5.3.2. Adapting the Parametric Model Before performing the evolutionary process, a series of adjustments need to be made in order to ensure that all case-specific criteria are taken into account. The first point of focus is the climate management, and specifically the optimization of the design for taking advantage of natural ventilation. In order to insert a natural ventilationrelated evaluation to the process, the cooling load objective will be complemented or completely replaced by a simple, orientation-based evaluation of the natural ventilation suitability of the terminal. The second focus point is the relationship of the terminal building with the runways. Since the existing runway layout will be preserved for the purpose of this study, an evaluation of aircraft taxi traffic shoul dbe performed. The layout of the terminal should not be one that will obstruct traffic or lead to an inefficient taxying pattern.
Fig. 27 Graph demonstrating the morphology of the generated solutions related to their performance. X Axis: Cost. Y Axis: Retail Suitability
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 28 Map of the area around the new International Airport in Doha, Qatar.
Fig. 29 The proposed design for the Doha International Airport Terminal, HOK architects
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Fig. 30 Plan of the selected solution, superimposed over the environment.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 31 Aerial photography of the site of the New Doha International Airport, along with the allowed area for the development of the terminal.
5.4. Moving into Detail The final step for this thesis project entails the advancement of one solution from the abstract layout stage to a greater level of detail. The solution to work on has been picked manually from a Pareto surface that was generated as a result of performing the first optimization, taking into account the site-specific parameters. The aim of the building envelope design was for the envelop to emerge out of a performanceconsidering process, just as in the case of the terminal layout design. Therefore, the building envelope has been generated as a parametric definition, the same way the original layout generation was defined. The envelope definition has been formulated on the basis of the local climate and consists of a series of shading elements of variable geometry. The elements can vary in width, angle and density, accordingly altering their capacity to provide shadow, their ability to allow view to the outside and so on. An axonometric that depicts the layered envelope structure is available in figures 32 and 33. A photorealistic impression of the envelope is available in figure 34.
5.4.1 Parametric Definition The building envelope design becomes a problem of optimizing the aforementioned characteristics of each of the shading elements to introduce the desired function, which in most cases would be efficient shading while still allowing visual contact with the outside, especially the airside area of the airport. However, controlling each of the element parameters individually
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1
3 2
Fig. 32 Axnonometric of the proposed facade system. 1. Shading system 2. Glass Layer 3. Structure
Fig. 33 Axnonometric of the Shading system and the various interconnections between it’s instances.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 34 Photorealistic representation of the shading elements and the gradient effect generated by their varying angles.
would be prohibitive in practice, because of the large number of elements that ranges in the thousands to tens of thousands for a reasonably sized facade. In order to come around this limitation, the definition of the elements’ geometry, orientation and position was abstracted to a number of “control points”, which are points on the surface of the envelope where the desired characteristics of the shading elements are explicitly stated. The shading elements acquire characteristics according to how close they are to each control point. A 2-dimensional “influence field” is thus created on the envelope surface, with control points being the modifiers and the shading elements being the receptors. The parametric definition, as expressed in Grasshopper, is visible in figure 35 and the distribution of the control points on the envelope is visible in figure 36.
5.4.2. Optimal Configurations Using this strategy, the number of parameters required for the definition of a single facade or building envelope come to the range of 10-50, depending on the density of the control points, which is user configurable. The dramatic decrease in control parameters enables the parametric definition to be combined with the Evolutionary Solver in order to search for optimal configurations of the facade. In order for that to happen of course, evaluation criteria expressed through objective functions need to be added to the parametric definition. The objective functions in these case are related to three design goals: 1.
Minimization of material.
2. Optimum shading. 3. View outside at eye level, towards the airside. The minimization of material is simply expressed as the total area of all the shading elements added together. Support structures are considered to be directly related to the area of the elements and are therefore not taken into account separately. For the calculation of the
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Fig. 35 Axnonometric of the Shading system and the various interconnections between it’s instances.
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
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1
1
2
2
3
3
A
B
optimum shading, the linear projection of all the elements is calculated and then compared to the interior area. Optimum shading is achieved when the shading area covers the entire interior. However, larger shading areas have no effect. Finally, the outside view at eye level is obtained for each individual element by comparing the normal of the element’s surface to the view vector; if they are perpendicular (dot product = 0) the view is optimal, since the surface is parallel to the view vector. While for this study the two different scales of the building, layout and envelope, have been treated as discrete optimization scenarios mainly in order to limit the computational complexity of the model, in an ideal case they would both be included in the same iteration, i.e. both layout and building envelope would participate at the same time in a single optimization run, with performance being measured by the characteristics of both. Due to time issues, the coupling with the evolutionary algorithm has not been performed for the envelope design. Still, the representations shown in figures 36-40 depict a design iteration which performs quite well regarding all aspects of the aforementioned evaluation scheme.
56
Fig. 36 Control Point system on the facade to parametrically adjust the inclination and distribution of the shading elements in the parametric model.
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
Fig. 37 - 41 Photorealistic renderings of the selected solution.
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6 / Conclusions An investigation regarding the design of airport terminals using an approach which blends parametric design with evolutionary computation to achieve optimal solutions has been presented in this report. A parametric model that generates layouts for airline passenger terminals is developed based on assenger terminal design theory and observations on existing designs. Through the use of the proposed parametric model, a wide range of terminal designs is obtainable. As part of the parametric model, evaluation functions which test the suitability of the design with regard to heterogenous design aspects are also implemented. These characteristics of the parametric model are mostly suitable for being combined with an evolutionary algorithm (EA), so that a search for optimal solutions within the design domain offered by the parametric model can be carried out through the use of computation. The EA that has been implemented for this project is based on the NSGA-II algorithm by Deb et al, (2002), introducing also some new concepts, such as the Adaptive Relaxation Angle. The implementation of the algorithm is generic and may be used apart from the specific design problem. Initial testing of the algorithm using standard testing and evaluation functions (such as the ZDT-1) show promising results. The application of the algorithm to the airport terminal design problem also demonstrates a wide variety of interesting solutions. A case study regarding the design of a terminal building using the proposed approach has been carried out. The site is that of the new Doha International Airport in Qatar. The focus of the case study has been the adaptation of the parametric model to local conditions, as well as the further development of a building envelope for the selected design iteration. The designs that were generated by the Evolutionary Algorithm show a good adaptation to the site specific constraints and parameters, and good variation, within the limits that are imposed by the capacity and the plot geometry. It is the intention of the author to further develop the implementation of the Evolutionary Algorithm that has been discussed, with the goal of ultimately producing a software that is beneficial both as a design and a research tool.
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7 / References Ashford, N., 1992, Airport Engineering, Wiley-Interscience Bittermann, M., 2009, Intelligent Design Objects (IDO), PhD Thesis, Delft: Delft University of Technology Deb, K., Pratap, A., Agarwal, S., Meyarivan, T, 2002, A Fast and Elitist Multiobjective Genetic Algorithm: Nsga-Ii, IEEE Transactions On Evolutionary Computation, Vol. 6, No. 2, April 2002, P. 182-197 Edwards, B., 2005, The Modern Airport Terminal, Spon Freathy, P. and O’Connel, F., 1998, European Airport Retailing, London: MacMillan, p. 59-68 Fruin, J.J. , 1993, Designing for Pedestrians. in Public Transportation Systems. Hoel and Gray: Editors. New York : John Wiley and Sons. Goldberg, D., 1989, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Gulfnews.com, 2008, Qatar targets 24m annual passengers in new airport, http://gulfnews.com/business/aviation/qatar-targets-24m-annual-passengers-in-new-airport-1.84325 [accessed 06/05/2011] Luke, S., 2010, Essentials of Metaheuristics, http://cs.gmu.edu/∼sean/book/metaheuristics/ [accessed 12/2/2011] Manataki, I., Zografos, K., 2009, A generic system dynamics based tool for airport terminal performance analysis, Transportation Research Part C 17, 428-443 New Visions Of Security: Re-Life Of A Dfw Airport Terminal, 2007 Park, HJ, 2008, Parametric Variations of Palladio’s Villa Rotonda, International Journal of Architectural Computing, issue 02, volume 06, p. 146-169 Trani, A., 2002, Airport Landside Analysis and Modelling [shown at Advanced Airport and Airspace Capacity Seminar, Virginia Tech] [viewed on 05/04/2011] Zitzler, E., Deb, K., Thiele, L., 2000, Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation, 8(2):173-195, 2000
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A1 / Appendix: ZDT-1 Test Results Population 100
Rel. Angle
Adaptive? 0 No
S
Crossover P. 0.90
-
Progress Graphs (generation indexing is zero-based)
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nc 10
Mutation P. 0.05
nm 30
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
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Population 100
Rel. Angle
Adaptive? 15 Yes
S 5
Crossover P. 0.90
Progress Graphs, Adaptive Angle (generation indexing is zero-based)
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nc 10
Mutation P. 0.05
nm 30
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
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A2 / Appendix: 1st Model Test Results Population 100
Rel. Angle
Adaptive? 0 No
S
Crossover P. 0.90
-
nc
Progress Graphs. X: Cost, Y: Retail Suitability (generation indexing is zero-based)
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Mutation P. 0.05
nm 30
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Result Graphs after 34 generations X: Cost, Y: Retail Suitability
X: Cost, Y: Accessibility
X: Cost, Y: Cooling Load
X: Retail Suitability, Y: Accessibility
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Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
X: Retail Suitability, Y: Cooling Load
X: Accessibility, Y: Cooling Load
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Ioannis Chatzikonstantinou 6408721 4817331 8411258 4962733 8338165 8341115 6372092 9183128 5631365 4369605 6014099 6021419 3472055 3662096 3281145 3363237 1731729 2492993 3137060 5399652 4344243 4811018 7934745 7765881 7047150 5061385 4160184 9126223 7973159 6073162 8778713 6940108 4248705 8213327 8445314 4223362 9624631 8280737 6321252 7504914 3376448 6361067 6271001 2982989 1966871 8023468 5225441 9725861 4200296 4644003 7719586 8000916 6666562 2236089 3798676 8423864 6862019 2023436 6216260 6819734 4057826 2443292 4808393 2501944 8739063 8262664 7171310 5109080 6613432 6488288 4822540 1590525 1656136 2210147 6100402 5796558 8853616 6160009 5443652 6170571 1839853 1778953 9073450 5897755 7195949 5136171 4062884 4520138 6488048 5287885 9973402 6114206 4074592 1129822 2406417 9137730 6655977 8228080 3108428 6990761
A-Pier Length 382.118 249.994 389.306 380.725 300.970 388.137 278.775 387.246 383.003 269.585 379.835 300.970 389.221 379.835 387.950 389.221 395.528 387.414 395.392 389.167 387.414 384.826 268.998 397.999 275.432 375.886 280.834 395.528 389.167 395.542 279.443 387.733 383.003 283.087 376.096 295.902 281.514 277.134 389.306 378.683 387.733 285.024 399.777 389.167 395.508 314.709 300.970 279.715 382.118 389.167 286.240 286.471 389.239 389.221 371.826 376.266 387.143 387.542 301.952 387.414 388.907 388.081 270.371 397.226 389.167 382.118 251.696 278.775 387.950 386.520 398.233 286.240 316.841 276.454 271.253 271.253 291.636 395.528 386.520 378.655 303.745 285.024 314.709 395.307 395.528 399.763 387.638 379.835 381.635 386.639 386.944 387.246 380.461 380.504 387.950 381.635 382.118 303.745 380.585 286.240
Radius 1,997.812 2,000.000 1,995.780 1,978.586 1,989.176 2,000.000 1,572.091 636.232 1,971.976 1,754.790 659.042 1,758.685 1,997.597 592.895 1,998.165 1,254.527 1,745.984 2,000.000 1,985.318 1,942.356 2,000.000 2,000.000 1,984.761 887.638 2,000.000 1,167.930 1,962.554 1,745.984 1,942.356 2,000.000 605.593 2,000.000 1,952.189 1,268.159 1,936.794 1,268.159 1,959.678 1,997.096 1,566.945 1,252.828 2,000.000 1,268.159 1,356.731 1,254.909 800.434 1,729.979 1,989.176 2,000.000 1,997.812 1,942.356 1,956.423 605.593 1,999.867 1,254.527 1,940.276 1,568.960 1,748.232 1,585.643 1,757.776 2,000.000 2,000.000 2,000.000 1,959.357 1,590.617 800.434 1,997.812 1,996.816 1,999.885 1,998.148 2,000.000 1,235.946 615.798 1,870.950 1,999.894 1,745.984 1,745.984 1,284.830 621.068 2,000.000 1,310.620 2,000.000 2,000.000 1,729.979 2,000.000 1,747.069 1,757.966 1,998.148 1,978.678 1,995.508 1,996.891 1,997.812 1,998.136 2,000.000 1,993.680 1,998.148 1,997.812 1,997.795 2,000.000 1,999.921 523.153
No. Sides
Angle 2 2 3 1 1 1 2 1 2 3 2 3 2 2 3 1 1 2 3 3 1 2 1 2 2 1 2 1 3 3 1 3 3 1 1 1 1 2 3 3 3 1 2 3 3 2 3 3 1 3 1 1 3 3 1 2 3 2 3 2 3 1 1 2 3 3 2 2 3 2 3 1 3 2 1 2 2 1 2 3 1 3 1 3 1 2 3 2 3 3 3 1 1 3 3 3 3 1 1 1
3.306 3.247 3.480 3.271 3.429 3.163 3.472 3.105 3.495 3.212 3.167 3.434 3.163 3.167 3.458 3.163 3.459 3.192 3.284 3.480 3.455 3.487 3.435 3.293 0.440 3.474 3.454 3.459 3.197 3.481 3.463 3.500 3.496 3.476 3.497 3.476 0.626 0.654 3.480 3.140 3.500 3.476 3.302 3.480 3.471 3.468 3.429 3.476 3.421 3.482 3.422 3.463 3.116 3.201 3.494 3.473 3.219 3.473 3.441 3.455 3.475 3.163 3.500 3.167 3.480 3.459 3.433 3.454 3.484 3.112 3.284 0.339 3.184 3.454 3.441 3.163 3.302 3.459 3.112 3.302 3.271 3.476 3.302 3.279 3.459 3.302 3.484 3.171 3.457 3.480 3.458 3.105 3.133 3.461 3.484 3.458 3.485 0.005 0.266 3.422
Rel. Pier Rotate -0.547 -0.630 -0.669 -0.052 -0.017 -0.096 -0.687 -0.580 -0.608 0.240 0.551 -0.020 -0.411 -0.593 -0.614 -0.627 -0.364 -0.611 -0.640 -0.661 -0.611 -0.649 -0.667 -0.669 -0.040 0.087 0.596 -0.364 -0.661 -0.621 -0.681 -0.643 -0.610 0.087 -0.609 0.087 0.643 -0.006 -0.678 -0.688 -0.643 -0.711 -0.568 -0.664 -0.678 -0.591 -0.019 -0.697 -0.810 -0.661 -0.611 -0.681 -0.669 -0.627 -0.685 -0.678 0.227 -0.678 -0.006 -0.611 -0.806 -0.699 -0.364 0.551 -0.669 -0.810 -0.596 -0.069 -0.586 -0.611 -0.661 -0.610 -0.595 -0.053 -0.362 -0.372 -0.568 -0.592 -0.583 -0.699 -0.052 -0.697 -0.522 -0.640 -0.364 -0.568 -0.660 -0.593 -0.810 -0.661 -0.810 -0.576 -0.630 -0.660 -0.614 -0.810 -0.810 -0.052 -0.108 -0.610
74
Main Width 138.167 61.828 138.137 33.052 92.078 96.547 126.863 31.097 96.949 57.979 137.598 131.230 136.523 140.000 138.311 136.523 129.358 96.387 130.664 138.234 96.387 131.110 131.047 129.078 62.892 30.467 135.647 129.358 138.234 130.708 61.055 131.829 97.851 30.472 138.286 30.472 138.896 35.066 138.088 61.124 139.739 30.472 128.079 61.445 130.708 137.414 93.367 35.999 138.167 137.145 68.678 61.055 138.137 136.523 138.509 130.702 137.566 130.702 131.230 96.387 35.999 35.300 129.490 130.956 138.137 138.167 34.002 126.863 138.310 128.190 61.054 31.654 30.000 31.817 129.399 132.605 32.358 129.358 140.000 129.536 32.634 35.999 137.414 130.713 129.358 130.851 138.310 134.749 138.167 138.219 138.167 69.876 62.715 138.167 138.310 138.167 138.167 58.462 99.966 30.130
Section Frac. 0.651 0.627 0.608 0.653 0.652 0.629 0.601 0.660 0.640 0.609 0.603 0.652 0.614 0.603 0.792 0.614 0.608 0.602 0.622 0.602 0.603 0.619 0.608 0.640 0.626 0.603 0.659 0.608 0.614 0.641 0.635 0.643 0.640 0.603 0.609 0.624 0.600 0.600 0.608 0.688 0.643 0.603 0.604 0.603 0.641 0.622 0.650 0.602 0.651 0.604 0.662 0.635 0.608 0.614 0.677 0.609 0.609 0.609 0.623 0.603 0.608 0.603 0.608 0.630 0.608 0.651 0.601 0.655 0.800 0.602 0.640 0.693 0.600 0.659 0.608 0.608 0.602 0.608 0.602 0.622 0.653 0.603 0.622 0.622 0.608 0.607 0.800 0.603 0.609 0.624 0.641 0.660 0.632 0.633 0.800 0.640 0.659 0.600 0.695 0.602
B-Pier Length 262.408 235.256 290.452 110.473 260.956 262.130 251.667 94.213 286.971 291.675 247.973 290.584 287.629 247.973 289.815 280.683 248.169 257.979 260.656 263.848 250.113 267.056 275.971 275.978 229.541 227.309 257.335 248.169 263.848 275.978 262.741 267.056 287.409 262.129 263.116 262.218 106.882 108.803 258.366 258.735 270.072 217.739 260.683 263.848 275.978 269.821 260.956 218.783 289.855 260.680 97.624 262.741 290.452 280.683 252.031 258.560 290.568 258.560 260.956 257.979 221.242 261.952 249.029 247.973 289.317 289.855 114.518 271.547 289.317 269.451 262.473 97.624 248.244 251.390 287.975 287.975 260.728 247.953 270.137 260.683 98.980 221.242 269.821 271.101 248.169 268.918 289.317 235.631 294.375 264.509 296.835 259.341 259.539 289.855 289.317 294.375 289.357 90.000 98.551 97.624
Angle 4.545 2.012 4.448 4.509 4.421 5.474 2.993 3.610 4.463 3.543 6.219 4.541 3.350 6.219 4.122 3.350 4.605 6.173 4.539 4.451 4.464 4.318 5.474 4.448 2.012 6.280 4.317 4.605 4.473 4.451 4.012 4.332 4.463 4.308 3.633 4.312 3.608 3.604 4.448 4.194 2.990 4.312 2.911 4.451 4.498 4.394 4.421 4.433 3.356 4.451 3.621 4.012 3.017 4.540 3.613 2.997 3.656 2.997 4.513 4.464 4.433 5.673 3.619 4.492 4.448 4.545 3.604 4.518 4.122 3.013 4.195 3.620 2.137 4.312 3.313 3.313 3.017 4.773 3.006 2.911 4.509 4.433 3.678 4.675 4.684 2.935 4.122 6.219 4.550 4.451 4.545 3.610 3.591 4.555 4.122 4.545 4.545 4.813 3.598 3.621
No. Branches 2.910 1.627 1.723 1.576 1.716 1.804 2.339 1.717 1.724 2.134 2.336 1.597 2.345 2.336 1.761 2.345 2.105 1.723 1.742 1.727 1.730 2.872 1.782 1.665 1.627 1.742 2.335 2.105 2.313 1.724 1.720 2.877 1.724 2.859 1.769 2.795 2.319 1.740 1.723 1.684 1.697 1.742 1.686 1.728 1.699 2.320 2.346 2.823 2.294 1.727 1.814 1.727 1.723 2.889 1.683 1.768 2.177 1.732 2.314 1.726 1.715 1.633 2.319 2.336 1.726 2.838 2.319 2.327 1.763 1.592 1.643 1.727 2.401 2.339 2.331 2.331 1.686 2.105 1.594 1.686 1.576 1.715 2.386 2.139 1.751 1.686 1.758 2.336 2.838 1.727 1.730 1.814 2.039 2.840 1.761 2.838 2.838 1.000 2.374 1.727
Section Frac. 0.505 0.657 0.653 0.524 0.524 0.654 0.518 0.501 0.543 0.500 0.523 0.549 0.521 0.541 0.560 0.502 0.504 0.806 0.519 0.525 0.806 0.548 0.655 0.553 0.517 0.566 0.517 0.504 0.525 0.553 0.663 0.517 0.543 0.566 0.506 0.573 0.519 0.545 0.649 0.654 0.517 0.515 0.506 0.526 0.553 0.551 0.524 0.567 0.557 0.500 0.502 0.664 0.658 0.502 0.653 0.507 0.506 0.507 0.518 0.806 0.567 0.656 0.507 0.519 0.653 0.557 0.659 0.656 0.666 0.835 0.655 0.501 0.587 0.517 0.507 0.511 0.506 0.504 0.666 0.506 0.518 0.567 0.551 0.656 0.837 0.506 0.843 0.541 0.653 0.571 0.653 0.551 0.657 0.557 0.837 0.653 0.833 0.664 0.520 0.501
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design Cost 1,618,092,023.079 685,504,867.129 1,789,523,986.387 257,922,985.479 657,899,044.698 776,696,766.114 1,099,793,547.132 118,986,103.070 1,085,585,724.652 665,707,433.248 731,941,306.025 1,495,175,006.341 1,534,343,131.815 709,688,202.639 1,903,005,171.001 756,746,458.760 831,169,660.757 1,130,515,447.473 1,636,896,212.302 1,679,964,896.946 726,994,006.199 1,527,019,088.337 926,505,645.667 862,606,733.784 747,921,527.968 171,035,782.314 1,424,717,067.344 831,169,660.757 1,699,541,610.464 1,677,145,489.578 217,848,682.721 1,771,152,531.059 1,245,857,064.305 192,493,579.023 947,014,601.276 195,944,014.096 1,401,802,348.003 414,847,483.605 1,492,588,607.109 634,493,761.457 1,764,644,194.559 167,528,730.053 1,068,242,905.679 590,666,950.405 979,529,201.982 1,328,181,479.316 1,149,311,281.899 498,215,919.002 1,029,008,926.467 1,657,144,687.277 452,091,044.682 219,316,669.832 1,808,011,054.536 1,369,681,796.985 997,732,148.939 1,184,492,371.515 1,579,931,787.270 1,199,209,396.638 1,440,542,850.804 1,115,832,744.150 492,059,794.418 307,685,530.940 854,534,846.363 1,236,790,792.850 1,053,956,241.207 1,911,678,018.874 366,272,186.516 1,398,964,290.141 1,964,586,732.812 1,512,020,835.452 619,991,551.751 143,409,944.269 401,458,300.464 379,209,886.960 808,673,437.700 1,283,237,951.636 283,115,350.616 439,654,961.758 1,599,884,509.697 1,214,864,877.255 246,772,689.502 467,801,871.492 905,094,811.136 1,704,268,561.223 885,584,786.649 1,316,874,152.250 2,059,394,783.297 1,466,710,209.698 1,933,604,081.826 1,745,834,080.402 1,825,307,271.501 574,492,186.381 519,505,977.476 1,890,237,301.194 2,056,502,845.860 1,968,562,750.708 2,100,166,001.814 600,287,478.371 1,089,018,207.655 87,047,234.803
Retail 0.0005330 0.0016660 0.0004462 0.0050017 0.0013535 0.0013241 0.0007848 0.0079090 0.0007883 0.0013012 0.0008467 0.0004960 0.0006075 0.0008381 0.0004453 0.0010055 0.0009261 0.0009606 0.0005254 0.0004725 0.0012142 0.0005416 0.0010078 0.0007560 0.0107426 0.0046019 0.0006645 0.0009261 0.0005215 0.0004998 0.0025713 0.0004400 0.0006264 0.0044647 0.0008476 0.0043938 0.0056729 0.0184210 0.0004975 0.0013056 0.0004650 0.0052228 0.0007376 0.0011463 0.0005769 0.0006324 0.0007371 0.0020366 0.0007920 0.0004760 0.0028887 0.0024311 0.0004975 0.0004722 0.0008470 0.0006902 0.0004861 0.0006903 0.0005389 0.0008392 0.0021086 0.0036510 0.0010159 0.0007100 0.0005086 0.0003882 0.0036734 0.0007180 0.0004420 0.0006935 0.0012303 0.0568999 0.0027728 0.0028439 0.0009855 0.0007321 0.0031237 0.0010754 0.0006352 0.0006312 0.0059288 0.0022671 0.0009671 0.0005261 0.0009526 0.0006638 0.0004452 0.0007131 0.0004085 0.0004728 0.0004554 0.0018123 0.0020003 0.0003904 0.0004420 0.0004084 0.0003854 0.1291314 0.0152195 0.0089923
Accessibility 0.813 0.856 0.819 1.188 1.062 0.951 1.023 2.413 0.828 1.110 1.435 0.940 0.784 1.462 0.818 1.268 1.134 0.793 0.819 0.839 1.033 0.821 1.074 1.273 0.759 1.985 0.833 1.134 0.833 0.817 2.118 0.842 0.870 1.924 1.069 1.916 0.615 0.803 0.988 1.352 0.819 1.897 1.058 1.364 1.321 0.928 0.865 1.192 1.011 0.840 1.080 2.150 0.810 1.093 1.073 0.980 0.903 0.967 0.942 0.811 1.125 1.224 1.113 0.948 1.315 0.843 0.952 0.819 0.819 0.782 1.363 1.914 1.272 1.135 1.187 0.915 1.610 1.591 0.782 1.106 1.116 1.112 1.134 0.813 1.133 0.879 0.819 0.793 0.840 0.820 0.817 0.969 1.002 0.845 0.819 0.840 0.843 0.613 0.600 2.912
Cooling Load 41,080,239.557 16,257,867.688 47,428,599.146 6,630,280.900 15,809,356.065 19,106,371.627 26,491,714.750 4,279,371.908 27,037,577.037 17,547,909.996 24,255,548.885 39,506,130.862 36,753,344.340 24,348,392.492 53,415,224.461 20,663,837.335 20,808,941.718 28,451,270.785 41,893,365.139 42,896,383.159 18,627,361.565 39,034,245.459 22,013,379.200 27,376,984.405 16,859,414.542 5,563,686.888 32,933,427.246 20,808,941.718 43,527,803.795 43,966,483.179 7,951,541.152 48,524,488.306 33,151,569.693 6,320,466.682 22,960,997.062 6,498,450.672 25,690,398.905 9,457,391.439 41,978,448.580 20,253,689.242 45,546,304.661 5,099,775.481 28,620,797.317 17,991,141.472 34,137,263.850 32,438,305.507 28,888,138.923 13,838,860.081 25,648,059.744 42,056,846.968 10,082,565.962 8,022,787.315 47,765,881.852 42,930,338.179 25,538,270.735 30,104,653.627 42,072,729.663 30,537,726.466 36,657,754.645 28,263,066.265 13,589,630.278 8,294,829.388 19,522,282.233 31,611,999.377 37,035,131.121 53,762,288.227 8,661,188.053 33,549,817.054 56,723,105.979 38,067,761.749 19,723,182.813 4,379,536.005 11,405,028.590 9,923,029.166 19,425,071.596 30,192,278.378 8,300,833.856 15,306,226.998 38,872,198.722 35,162,622.180 6,084,702.837 12,345,094.377 22,057,264.181 45,087,298.280 23,662,645.462 32,623,661.885 61,743,948.859 34,218,121.818 54,936,742.500 45,097,031.867 49,253,545.300 14,237,731.492 13,096,795.656 52,714,512.374 61,589,623.998 56,762,223.443 63,760,783.049 11,583,908.648 21,638,191.500 3,282,460.157
Rank 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Cr. Distance 5,014,123.686 5,099,745.186 5,105,412.568 5,135,225.553 5,135,379.038 5,167,927.862 5,225,260.473 5,270,772.888 5,278,832.997 5,326,788.762 5,333,491.142 5,368,983.446 5,545,410.007 5,579,342.365 5,622,123.383 5,630,328.790 5,660,331.860 5,663,766.550 5,678,052.360 5,720,517.613 5,736,872.203 5,739,057.126 5,821,893.191 5,829,365.069 5,854,136.802 5,945,474.880 6,017,178.378 6,048,608.847 6,093,164.222 6,094,926.039 6,124,925.801 6,169,252.755 6,233,290.551 6,330,494.911 6,381,739.249 6,416,229.482 6,464,890.469 6,468,971.330 6,489,198.951 6,493,753.459 6,515,799.993 6,588,523.610 6,590,472.653 6,718,685.892 6,836,250.724 6,863,302.609 6,944,289.321 6,959,974.024 7,057,868.022 7,059,993.040 7,123,530.689 7,316,823.788 7,459,943.073 7,489,643.279 7,615,073.746 7,632,085.008 7,638,213.278 7,690,048.830 7,726,831.759 7,750,992.982 7,789,027.984 7,903,871.649 7,933,796.062 7,973,498.216 7,991,548.295 8,030,107.217 8,085,939.929 8,180,527.827 8,192,253.616 8,420,287.400 8,610,680.890 8,872,029.768 8,884,394.997 8,952,822.121 9,218,108.560 9,235,838.819 9,380,406.091 9,439,146.889 9,590,684.724 9,669,644.842 9,840,773.863 10,298,385.082 10,441,036.779 10,671,583.570 10,861,124.601 11,336,997.486 11,458,578.751 13,054,923.568 13,967,382.923 15,208,659.930 16,492,344.515 18,118,489.825 19,380,200.823 20,261,644.801 23,953,439.501 24,195,657.767 -
75
Ioannis Chatzikonstantinou
A3 / Appendix: 2nd Model Test Results Population 150
Rel. Angle
Adaptive? 0 No
S
Crossover P. 0.90
-
Progress Graphs. X: Cost, Y: Retail Suitability (generation indexing is zero-based)
76
nc 10
Mutation P. 0.05
nm 30
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
77
Ioannis Chatzikonstantinou
X: Cost, Y: Retail Suitability
X: Cost, Y: Accessibility
X: Cost, Y: Cooling Load
X: Retail Suitability, Y: Accessibility
78
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
X: Retail Suitability, Y: Cooling Load
X: Accessibility, Y: Cooling Load
79
Ioannis Chatzikonstantinou 4130483 9182117 7775897 7770179 8713140 9794316 4833747 6963096 5071544 9026497 1601046 5579917 4668826 8376277 4726073 8318444 6398064 8875748 9482343 3636695 4398599 5417990 5300149 2559651 7243080 1801841 8365995 7070004 3410371 9480789 7039366 3779542 9652436 5932982 9491538 5036019 5316659 5851310 2747814 8584740 4660591 1644517 9895753 5930612 2399963 6382486 8143165 6203161 2243353 6959715 6015403 8783359 6865781 8744314 1274622 5041034 3920935 4522594 1623428 8203896 3916184 5113276 9315169 7031754 7929094 4431933 1096285 4157144 3212732 8942500 3051358 1127996 8444573 5358611 9879934 4045693 9883548 7629584 9352746 5280593 3410527 2436813 8667224 2511837 3249070 1536605 2375093 3271147 4840176
A-Pier Length 286.730 374.194 380.455 369.198 376.634 371.912 377.705 373.591 377.527 376.247 365.220 376.810 376.887 376.990 286.730 389.463 376.633 366.856 381.292 260.889 386.867 376.992 342.465 377.575 377.111 369.121 325.276 377.028 371.694 284.984 370.986 370.202 374.740 381.384 375.780 378.608 391.993 260.889 370.495 360.337 371.925 303.826 394.546 380.235 303.674 307.607 381.597 300.399 376.990 382.239 338.651 371.212 380.552 376.633 380.945 370.334 379.944 376.948 280.608 384.030 376.892 381.270 380.647 400.000 382.778 382.601 366.136 368.596 371.694 369.469 380.681 366.599 338.060 374.219 366.558 298.221 306.618 381.550 378.608 373.591 343.003 370.334 400.000 262.924 337.108 370.986 371.617 380.259 376.978
Radius 1,964.868 2,000.000 1,942.899 1,985.089 1,994.999 1,999.840 1,999.537 506.411 2,000.000 2,000.000 1,977.131 502.677 1,964.718 1,997.746 1,964.065 1,999.992 1,999.337 1,994.930 1,997.815 1,724.483 1,724.483 2,000.000 1,026.724 617.747 1,998.818 1,998.093 2,000.000 2,000.000 1,984.793 1,941.735 1,996.273 1,964.842 634.837 1,995.104 1,997.065 1,996.906 1,998.601 1,724.483 1,945.048 1,724.483 1,984.793 1,041.675 1,947.221 1,991.037 502.677 638.518 500.286 1,882.859 1,987.997 1,996.313 1,992.106 510.261 1,995.163 1,997.694 1,997.851 799.654 1,991.037 1,802.722 1,962.358 1,998.866 624.415 1,980.622 1,994.568 588.970 1,979.779 1,996.411 548.878 1,954.979 1,984.793 1,996.387 646.243 1,994.634 2,000.000 829.757 1,957.040 2,000.000 2,000.000 2,000.000 1,996.453 575.778 1,026.724 802.561 561.068 1,732.365 1,980.463 1,996.434 1,997.797 1,949.897 2,000.000
No. Sides
Angle 1 3 4 1 2 1 4 1 2 1 3 1 4 3 1 1 1 4 1 1 1 3 1 2 3 1 1 2 3 1 1 2 2 4 3 4 3 1 1 1 3 1 3 4 1 1 1 1 2 3 3 1 2 1 4 3 4 4 2 1 2 4 4 1 4 4 2 1 1 1 4 3 3 4 4 1 1 2 4 1 1 1 1 1 4 1 1 2 3
1.428 3.448 3.338 3.309 3.334 3.030 3.443 3.434 3.443 3.443 3.340 3.333 3.334 3.500 1.418 1.429 3.346 3.477 1.182 3.310 3.161 3.342 3.453 3.436 2.939 0.087 3.070 3.488 3.435 1.417 1.145 3.457 3.110 3.373 3.319 3.434 3.306 3.161 1.457 3.500 3.435 3.432 3.306 3.290 3.333 3.082 3.081 3.333 3.341 3.345 3.339 3.339 3.345 3.346 3.338 3.345 3.290 3.373 3.338 3.482 3.435 3.345 3.338 3.330 3.446 3.345 3.497 2.971 3.309 0.087 3.079 3.342 3.341 3.429 3.447 1.379 3.305 3.069 3.429 1.567 3.453 3.458 3.500 1.526 3.342 1.145 0.087 3.338 3.339
Rel. Pier Rotate -0.212 -0.188 -0.192 -0.134 0.784 -0.182 -0.189 -0.210 -0.198 -0.189 -0.447 0.347 -0.188 0.648 -0.212 -0.156 -0.432 -0.846 0.655 -0.447 -0.428 -0.194 -0.259 -0.907 -0.227 -0.275 -0.543 -0.191 -0.269 0.712 -0.217 -0.225 -0.187 -0.161 -0.256 -0.191 -0.186 -0.447 -0.217 -0.456 -0.269 -0.151 -0.196 -0.062 0.002 0.347 -0.022 0.373 0.595 -0.513 -0.447 0.347 -0.513 -0.414 -0.192 -0.527 -0.062 -0.188 -0.212 -0.447 -0.907 -0.167 -0.162 -0.851 -0.139 -0.189 -0.195 -0.207 -0.134 -0.521 -0.201 -0.177 -0.447 -0.290 -0.107 -0.529 -0.180 0.655 -0.217 -0.223 -0.259 -0.292 -1.000 -0.447 -0.189 -0.217 -0.186 -0.186 -0.190
80
Main Width 83.118 149.987 150.000 57.829 55.755 55.841 150.000 57.026 149.987 149.987 71.897 51.880 149.988 149.975 136.542 130.298 105.607 56.537 132.566 134.191 134.527 149.974 148.445 150.000 149.987 105.787 57.611 149.916 78.076 50.033 50.302 148.734 55.606 57.445 130.938 150.000 133.138 134.527 150.000 53.469 77.114 51.119 150.000 78.062 50.751 50.579 76.952 50.751 149.787 132.268 150.000 130.029 132.268 109.128 150.000 103.534 78.838 149.999 150.000 106.911 150.000 149.757 149.787 106.106 129.579 132.268 50.000 105.607 57.829 132.714 138.821 110.946 150.000 150.000 150.000 64.209 50.048 55.606 150.000 56.660 135.889 102.700 105.715 133.246 149.738 53.897 128.883 147.574 86.569
Section Frac. 0.701 0.751 0.707 0.703 0.604 0.696 0.706 0.637 0.751 0.751 0.606 0.720 0.615 0.765 0.705 0.758 0.630 0.655 0.615 0.635 0.633 0.765 0.814 0.607 0.763 0.702 0.697 0.743 0.703 0.721 0.606 0.611 0.605 0.656 0.604 0.626 0.710 0.633 0.611 0.635 0.702 0.609 0.773 0.609 0.720 0.722 0.720 0.720 0.765 0.609 0.606 0.732 0.714 0.630 0.708 0.611 0.710 0.764 0.680 0.633 0.761 0.762 0.765 0.720 0.720 0.609 0.600 0.630 0.703 0.609 0.627 0.712 0.606 0.759 0.720 0.753 0.710 0.615 0.608 0.635 0.700 0.611 0.600 0.605 0.606 0.606 0.709 0.618 0.704
B-Pier Length 137.546 299.145 284.563 109.907 105.217 285.457 285.610 102.209 284.564 284.564 291.321 283.332 284.576 291.402 147.390 299.830 300.000 284.696 263.988 281.898 281.898 291.397 282.177 293.001 286.283 101.306 290.937 283.950 291.842 119.440 297.570 288.543 244.704 299.811 281.466 282.877 286.430 281.898 298.635 282.193 286.116 293.001 299.017 286.315 300.000 270.261 300.000 287.512 291.469 298.540 291.321 299.070 298.540 300.000 284.739 297.593 286.554 285.288 286.243 283.397 293.001 299.581 291.450 149.002 284.560 286.353 91.470 282.483 300.000 91.688 282.877 283.174 300.000 282.160 284.563 292.255 239.931 267.193 285.463 119.495 282.177 299.970 90.000 281.898 299.661 285.417 300.000 285.957 285.806
Angle 2.426 4.521 4.416 4.517 3.362 4.263 4.416 3.732 4.517 4.337 2.472 5.075 3.537 5.052 2.323 2.999 4.448 4.677 3.430 3.293 3.293 4.991 5.067 3.713 5.033 2.958 5.078 5.070 3.632 2.950 2.283 2.966 3.458 4.820 2.400 5.669 4.570 3.293 2.283 3.293 3.628 3.713 4.570 4.630 4.533 4.612 2.122 4.514 3.446 2.737 4.358 4.514 4.303 4.448 4.416 2.966 4.630 4.521 5.005 3.201 3.713 4.695 3.685 4.522 4.397 4.592 4.447 4.448 4.517 2.958 5.322 4.982 4.439 3.201 4.416 4.935 3.337 3.459 5.304 3.732 2.488 2.959 4.520 4.279 4.680 2.283 3.037 5.060 5.100
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design No. Branches 2 2 3 2 2 2 3 3 3 2 3 2 2 3 2 3 2 2 2 2 2 3 3 3 2 2 3 2 2 3 2 2 2 3 2 3 3 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 3 2 2 3 2 2 2 3 2 2 2 2 3 2 3 2 3 3 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 3 2
Section Frac. 0.677 0.663 0.666 0.675 0.660 0.636 0.736 0.727 0.676 0.676 0.641 0.633 0.618 0.872 0.677 0.623 0.635 0.621 0.854 0.645 0.632 0.861 0.755 0.857 0.679 0.659 0.636 0.632 0.610 0.654 0.621 0.667 0.618 0.760 0.678 0.747 0.643 0.632 0.621 0.738 0.610 0.857 0.649 0.678 0.606 0.605 0.634 0.605 0.745 0.626 0.606 0.636 0.623 0.681 0.638 0.667 0.678 0.677 0.672 0.635 0.857 0.617 0.604 0.631 0.679 0.623 0.737 0.636 0.610 0.675 0.745 0.735 0.632 0.737 0.735 0.622 0.652 0.886 0.628 0.629 0.759 0.667 0.629 0.645 0.600 0.621 0.610 0.635 0.639
Cost 834,172,612.387 2,080,860,855.848 2,419,230,998.055 430,426,200.501 600,673,272.281 491,388,266.572 2,519,361,011.790 183,020,633.268 1,938,402,731.395 1,178,488,027.229 1,023,277,236.684 208,346,734.906 2,075,986,693.098 2,451,869,064.160 1,360,579,770.618 1,533,240,369.936 817,970,867.143 848,718,803.569 1,470,439,485.695 889,378,241.889 967,380,794.147 2,451,026,902.599 919,537,058.226 1,053,496,111.700 2,106,747,002.023 1,158,186,262.678 530,604,824.534 1,767,100,216.987 1,061,934,439.982 521,567,464.656 573,593,940.455 1,656,865,604.441 321,642,151.173 1,013,415,132.548 1,694,588,956.510 2,397,217,690.758 1,968,199,715.186 921,673,696.342 1,549,227,943.351 378,506,773.657 1,045,593,381.501 271,493,057.994 2,280,054,573.929 1,140,136,878.190 193,497,859.771 214,731,413.723 311,026,345.469 392,202,509.081 1,841,213,499.889 1,713,817,035.341 2,023,870,390.612 497,005,467.458 1,565,709,167.325 851,570,408.664 2,432,730,080.756 804,672,725.741 1,212,244,054.212 2,414,817,390.120 1,669,957,087.743 795,386,453.459 1,033,175,434.723 2,506,281,449.442 2,267,234,294.537 372,603,905.171 1,949,143,114.385 1,860,170,784.058 241,971,214.729 870,119,085.460 512,185,228.107 1,416,391,021.044 1,370,800,813.796 1,679,200,491.463 1,906,802,038.103 1,531,945,258.216 2,496,231,251.801 715,953,253.579 399,516,234.523 693,738,808.667 2,096,022,043.243 231,326,114.017 782,577,139.918 438,900,236.416 300,809,944.704 1,206,642,562.394 2,043,489,153.169 608,656,616.693 1,503,110,777.979 1,754,066,340.718 1,186,147,833.558
Retail 0.0034741 0.0003183 0.0002300 0.0022696 0.0016822 0.0017422 0.0002343 0.0027087 0.0003367 0.0005949 0.0007027 0.0019807 0.0002862 0.0002882 0.0021359 0.0012927 0.0008471 0.0007532 0.0018223 0.0007902 0.0007289 0.0002960 0.0005933 0.0004190 0.0003699 0.0268964 0.0015702 0.0003918 0.0006210 0.0061021 0.0047836 0.0004087 0.0015769 0.0006417 0.0003890 0.0002349 0.0003121 0.0008134 0.0012702 0.0016948 0.0006466 0.0019289 0.0003085 0.0005530 0.0021225 0.0025538 0.0014691 0.0019305 0.0004126 0.0003932 0.0003307 0.0007804 0.0004747 0.0008198 0.0002290 0.0006199 0.0005475 0.0002296 0.0004425 0.0008246 0.0004575 0.0002464 0.0002673 0.0013919 0.0003206 0.0003235 0.0026435 0.0009532 0.0014348 0.0213551 0.0003848 0.0003903 0.0003472 0.0003094 0.0002239 0.0031501 0.0020916 0.0013044 0.0002752 0.0058194 0.0006835 0.0010160 0.0016014 0.0015421 0.0002912 0.0042663 0.0151457 0.0003686 0.0005926
Accessibility 0.671 0.819 0.904 1.032 0.826 1.029 0.883 2.257 0.820 1.021 0.963 2.254 0.869 0.841 0.672 0.697 0.992 1.112 0.660 1.165 1.055 0.838 1.389 1.346 0.810 0.600 1.069 0.802 0.925 0.712 0.773 0.814 1.905 1.177 0.822 0.884 0.847 1.119 0.701 1.315 0.920 1.829 0.843 0.992 2.383 2.103 1.884 1.199 0.798 0.818 0.857 1.625 0.795 0.992 0.887 1.390 0.988 0.952 0.828 1.030 1.402 0.881 0.860 1.857 0.872 0.863 2.006 0.925 1.128 0.598 1.410 0.880 0.827 1.347 0.908 0.730 1.115 0.921 0.859 1.858 1.389 1.525 2.134 0.802 0.876 0.766 0.626 0.829 0.877
Cooling Load 17,135,140.585 58,745,308.946 76,671,978.393 10,462,035.672 13,983,521.694 12,766,313.124 80,575,412.649 6,966,547.723 54,709,925.099 31,343,738.204 29,424,594.902 8,409,248.913 57,922,311.031 78,523,757.085 27,439,454.524 37,857,059.335 20,657,786.655 24,826,408.530 32,566,260.393 21,970,496.110 24,757,987.208 78,151,335.619 33,202,800.029 41,174,740.214 59,357,655.994 23,180,424.326 14,523,011.988 45,866,308.304 29,497,801.370 11,591,066.216 13,194,647.625 41,056,557.819 11,343,851.835 32,911,685.202 44,580,146.586 74,066,534.776 58,251,447.786 22,317,934.501 33,666,203.361 10,748,136.722 28,967,224.357 8,930,092.510 70,430,480.303 32,694,010.283 7,688,446.811 7,785,562.476 12,190,885.636 10,540,259.355 49,606,292.658 45,208,739.600 55,570,557.036 19,508,439.646 40,444,142.921 21,694,673.436 75,925,713.897 28,432,298.660 36,280,642.348 80,266,932.511 40,994,970.207 20,309,703.886 40,088,175.002 80,454,182.623 67,454,291.198 13,324,819.323 58,052,094.537 51,853,357.989 8,648,967.552 21,059,546.997 14,620,949.516 27,101,862.912 56,849,719.001 50,637,413.266 49,221,996.939 59,545,376.006 80,476,118.027 16,490,033.144 10,343,645.409 18,386,671.795 58,215,002.984 7,208,212.211 27,215,834.521 14,953,723.701 10,267,239.937 26,002,861.035 55,838,143.723 13,816,915.975 33,009,564.447 46,460,667.474 32,884,751.405
81
Rank 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Cr. Distance 3,964,217.027 3,967,562.771 4,026,256.493 4,064,476.666 4,117,813.649 4,120,932.622 4,192,612.146 4,230,612.363 4,238,392.523 4,277,338.298 4,335,818.299 4,358,642.232 4,363,376.493 4,370,424.455 4,372,863.940 4,388,699.527 4,401,402.663 4,423,201.902 4,512,422.251 4,513,468.415 4,553,974.920 4,586,618.464 4,604,727.512 4,620,652.983 4,641,654.676 4,650,000.099 4,656,773.817 4,679,198.415 4,692,929.178 4,698,067.552 4,707,738.367 4,728,408.576 4,738,391.500 4,749,094.669 4,752,675.499 4,782,232.432 4,978,499.137 5,051,615.919 5,070,113.950 5,100,549.106 5,149,611.292 5,228,004.661 5,255,246.842 5,278,456.123 5,283,465.082 5,285,398.045 5,317,687.980 5,323,890.495 5,325,761.041 5,332,929.009 5,381,890.855 5,407,022.337 5,436,009.443 5,505,388.362 5,645,789.578 5,681,148.539 5,683,940.945 5,689,817.598 5,736,825.480 5,748,840.389 5,768,045.324 5,834,736.377 5,871,163.025 5,916,422.379 6,023,255.441 6,069,536.814 6,069,682.807 6,150,150.251 6,170,526.426 6,175,121.981 6,203,392.710 6,263,313.745 6,303,638.402 6,324,715.155 6,337,689.677 6,365,757.602 6,422,956.404 6,497,470.762 6,521,374.856 6,611,781.192 6,661,919.205 6,739,264.223 6,794,873.647 6,814,992.701 6,818,569.714 6,877,601.022 6,937,398.021 6,988,300.131 7,049,818.212
Ioannis Chatzikonstantinou 5145966 1285197 6968164 4960521 9003165 6795910 4544413 9249514 2068675 2766988 3669755 9096314 3383446 8306662 2777831 4118391 6022800 7660072 9092265 2114038 3714117 6812772 3978219 3453571 6204163 3916084 7027858 9169047 3758267 3793057 8207439 1158788 4767476 4423258 5736297 5298794 5065269 3390188 6295682 8635666 1403652 7747376 7587958 6659651 3718106 2717354 8302666 8527291 9416544 7568627 3290820 8317317 3808667 8251805 2456446 4017094 2800660 3790417 6576981 1686835 9061041
260.889 286.192 370.910 373.232 367.863 303.842 303.762 303.751 372.507 377.622 376.892 373.814 274.770 373.591 377.011 381.301 361.644 374.567 366.514 303.322 361.876 381.074 380.455 310.852 381.015 326.614 304.617 367.707 260.889 380.983 370.986 361.250 371.694 376.983 376.978 388.807 377.109 376.990 365.174 380.183 260.889 367.839 359.282 371.001 337.108 371.104 281.573 380.842 370.986 100.000 376.947 391.993 382.028 374.118 381.507 374.366 377.527 369.578 303.322 366.136 369.121
1,724.483 1,964.868 2,000.000 1,724.483 1,984.674 502.980 1,928.585 1,028.323 1,834.978 1,998.604 617.747 713.226 829.757 506.411 1,962.358 1,933.440 1,911.321 1,996.892 1,957.164 502.677 1,979.779 1,997.814 1,942.899 1,986.551 634.837 1,796.704 1,827.394 1,979.110 1,724.483 1,980.190 2,000.000 1,963.171 1,983.149 1,997.030 1,999.803 1,999.528 1,998.818 1,721.535 1,976.656 1,990.942 1,724.483 813.921 1,990.942 1,983.923 2,000.000 2,000.000 1,942.899 1,996.892 2,000.000 2,000.000 1,987.617 1,998.601 1,998.815 2,000.000 1,995.231 2,000.000 2,000.000 1,998.031 502.677 561.068 1,998.093
4 1 1 1 4 1 1 1 2 4 2 1 4 1 3 1 1 4 4 1 4 1 4 1 2 1 2 4 1 3 1 2 3 2 3 1 4 4 4 3 1 4 3 3 3 1 4 4 1 4 3 4 3 1 4 4 4 1 1 1 1
3.288 1.418 1.428 3.307 3.435 3.320 1.350 3.172 3.340 3.443 3.436 3.453 3.429 3.434 3.336 1.458 3.500 3.291 3.443 3.333 3.446 1.182 3.338 3.500 3.089 3.366 3.334 3.430 1.458 3.428 3.327 3.483 3.233 3.341 3.339 1.429 3.321 3.341 3.483 3.456 3.500 3.427 3.456 3.434 3.415 3.479 3.338 3.270 1.457 3.448 3.342 3.306 3.319 3.454 3.373 3.448 3.443 0.062 3.333 3.500 0.087
-0.447 -0.212 -0.054 -0.447 -0.211 -0.113 -0.186 -0.183 -0.181 -0.186 -0.907 -0.295 -0.290 -0.223 -0.069 -0.447 0.331 -0.185 -0.188 0.337 -0.107 0.655 -0.192 -0.301 -0.141 -0.190 -0.181 -0.225 -0.447 -0.197 -0.266 0.331 -0.832 0.595 -0.190 -0.156 -0.194 -0.163 -0.072 0.355 -0.456 -0.290 0.386 -0.269 -0.447 -0.217 -0.192 -0.139 -0.217 -0.169 -0.430 -0.186 -0.229 -0.121 -0.159 -0.188 -0.188 -0.432 0.347 -1.000 -0.186
82
150.000 149.098 80.338 134.527 127.605 61.051 50.048 50.048 136.698 149.120 150.000 150.000 150.000 56.660 150.000 134.191 132.597 149.958 149.987 143.668 129.579 132.566 150.000 85.511 55.606 57.611 57.420 146.442 134.191 149.255 87.813 52.659 57.829 149.787 131.196 129.290 149.984 149.787 77.343 146.300 53.469 101.241 146.300 80.614 150.000 146.301 131.258 149.958 150.000 149.979 149.983 133.138 149.986 150.000 85.922 149.987 149.987 105.607 50.751 50.000 103.529
0.633 0.815 0.607 0.656 0.640 0.773 0.710 0.710 0.620 0.715 0.607 0.707 0.759 0.637 0.601 0.635 0.605 0.600 0.751 0.766 0.720 0.615 0.708 0.781 0.605 0.697 0.607 0.608 0.635 0.713 0.609 0.605 0.703 0.626 0.707 0.758 0.763 0.633 0.600 0.755 0.635 0.608 0.755 0.702 0.606 0.622 0.708 0.600 0.611 0.752 0.769 0.716 0.765 0.706 0.656 0.751 0.751 0.630 0.720 0.600 0.709
281.982 137.546 284.434 281.082 293.087 298.829 244.878 244.217 288.460 286.004 293.001 284.761 281.865 111.713 292.027 284.614 284.662 299.942 284.468 126.416 284.563 263.988 284.563 285.770 249.144 290.937 115.724 284.813 281.898 284.835 298.811 284.662 142.137 281.884 292.285 299.830 286.283 292.003 299.306 284.813 281.898 284.813 284.816 291.842 287.940 295.051 286.913 300.000 286.658 90.000 291.469 286.006 291.469 284.761 299.811 284.564 284.564 91.670 126.334 90.000 91.579
3.293 5.005 5.062 3.401 3.632 4.507 3.297 3.378 2.667 4.521 3.713 3.481 3.201 3.732 5.088 4.398 4.329 3.065 4.521 5.011 4.416 3.458 4.416 5.245 3.458 5.078 2.667 2.461 3.293 3.538 2.214 3.672 4.276 3.499 4.202 2.999 5.033 3.507 3.733 4.726 3.293 2.461 4.745 3.632 4.369 4.719 4.416 3.065 2.283 4.521 4.721 4.552 4.525 3.493 5.084 4.521 4.521 4.448 4.514 4.361 2.958
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design 2 2 3 2 2 3 2 2 2 3 2 3 2 2 2 2 2 3 3 2 2 2 3 2 2 3 2 3 2 3 2 2 2 2 2 2 2 3 2 3 2 3 2 3 2 2 3 3 2 2 3 3 3 3 2 3 3 2 2 2 2
0.632 0.674 0.889 0.636 0.611 0.649 0.645 0.645 0.635 0.681 0.857 0.753 0.644 0.727 0.643 0.645 0.861 0.619 0.673 0.604 0.679 0.886 0.638 0.655 0.660 0.636 0.604 0.613 0.645 0.610 0.621 0.861 0.670 0.744 0.639 0.623 0.679 0.616 0.638 0.611 0.645 0.613 0.611 0.753 0.600 0.618 0.638 0.661 0.621 0.679 0.632 0.643 0.754 0.755 0.760 0.676 0.676 0.635 0.605 0.867 0.675
1,820,294,751.444 1,509,117,394.968 950,934,918.008 939,180,074.851 1,807,381,520.788 284,446,249.400 539,778,557.899 264,430,547.088 1,458,669,085.562 2,466,979,612.834 903,527,538.368 753,499,093.956 1,349,501,378.970 171,423,470.449 1,904,081,075.931 1,394,471,367.068 968,872,892.835 2,284,788,818.683 2,481,051,920.762 417,699,538.953 1,928,620,990.250 1,476,149,861.208 2,394,141,984.069 657,619,265.988 329,136,981.951 464,122,916.541 559,953,162.499 2,189,580,896.263 1,228,757,064.679 2,147,184,973.840 679,778,301.669 636,000,415.057 738,369,913.362 1,733,425,554.993 1,778,042,057.749 1,440,313,204.247 2,310,363,237.864 2,124,701,273.673 1,108,168,518.756 2,157,101,038.866 355,191,348.852 997,284,159.104 1,968,615,200.168 1,246,192,283.264 1,876,542,138.811 1,071,599,349.426 2,010,361,493.911 2,326,805,006.518 1,578,939,002.561 1,635,688,985.394 2,254,924,237.401 2,196,458,925.742 2,365,939,568.576 1,272,824,750.084 1,320,264,654.807 2,522,738,274.107 2,526,584,736.190 1,135,079,569.783 153,934,036.484 152,466,047.595 1,132,252,138.309
0.0003397 0.0019569 0.0020495 0.0007451 0.0003067 0.0014855 0.0044793 0.0024912 0.0004675 0.0002245 0.0004571 0.0005537 0.0003573 0.0027261 0.0003355 0.0013853 0.0006696 0.0002501 0.0002242 0.0012275 0.0003206 0.0018223 0.0002300 0.0010950 0.0015330 0.0014803 0.0018203 0.0002618 0.0015997 0.0002765 0.0010922 0.0011518 0.0013285 0.0004235 0.0003631 0.0014508 0.0002760 0.0002411 0.0005126 0.0002832 0.0018971 0.0004238 0.0003418 0.0005163 0.0003499 0.0005884 0.0003066 0.0002516 0.0012281 0.0009362 0.0002889 0.0002616 0.0003055 0.0005027 0.0004904 0.0002229 0.0002232 0.0324650 0.0033742 0.0036659 0.0274445
1.017 0.670 0.735 1.099 0.883 2.215 0.792 1.716 0.856 0.889 1.406 1.435 1.482 2.361 0.830 0.704 1.079 0.879 0.908 2.330 0.879 0.660 0.904 1.080 1.910 1.242 0.878 0.890 0.799 0.848 0.994 1.008 0.884 0.795 0.823 0.679 0.859 0.972 1.019 0.846 1.317 1.535 0.828 0.980 0.829 1.030 0.959 0.875 0.682 0.763 0.843 0.899 0.835 1.018 0.954 0.890 0.889 0.598 2.512 2.363 0.597
50,697,795.549 31,187,572.819 23,554,612.192 24,548,483.692 51,022,311.556 11,873,449.226 12,473,895.520 8,310,528.661 36,844,945.901 78,129,579.936 33,282,316.480 29,129,032.163 49,819,509.003 6,388,302.899 50,063,237.268 30,856,761.457 25,585,575.271 67,972,210.881 79,708,219.532 14,734,477.289 56,950,383.817 32,866,947.522 75,345,510.560 17,648,087.282 11,716,525.588 13,544,912.308 12,867,946.118 64,777,674.805 26,749,325.420 62,900,899.728 17,043,542.238 17,092,687.550 19,280,741.305 43,599,319.590 48,931,653.372 33,314,160.199 69,544,413.231 66,958,295.831 31,529,650.765 64,236,831.877 9,545,283.746 38,185,307.058 54,304,554.275 38,238,481.532 47,753,361.722 26,802,076.903 61,329,562.426 70,177,000.329 33,861,384.530 33,873,162.508 68,080,039.629 69,254,946.642 73,643,463.552 36,409,175.471 39,463,921.291 80,789,741.944 80,991,924.134 22,045,889.290 5,700,859.602 5,528,315.799 22,629,808.417
83
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7,134,835.977 7,205,974.138 7,289,878.533 7,395,128.153 7,428,856.004 7,447,811.718 7,450,664.117 7,458,294.415 7,548,087.692 7,564,068.591 7,567,544.129 7,568,840.801 7,584,790.702 7,588,071.235 7,626,180.595 7,633,643.931 7,713,306.869 7,733,603.092 7,748,703.600 7,781,318.561 7,937,895.168 8,215,508.353 8,223,865.745 8,332,668.692 8,457,895.198 8,460,113.019 8,484,437.385 8,665,119.605 8,686,861.231 8,826,758.663 9,180,549.272 9,228,609.364 9,471,224.572 10,396,284.206 10,437,484.756 10,665,487.852 10,734,560.381 10,767,282.274 10,800,999.228 11,068,174.375 11,070,269.414 11,180,396.435 11,254,586.459 11,256,092.436 11,274,951.591 11,579,759.354 13,708,754.771 14,115,599.447 14,623,210.818 15,148,035.149 15,489,277.666 16,701,928.687 17,741,153.945 18,658,094.519 19,210,157.715 -
Ioannis Chatzikonstantinou
A4 / Appendix: 3rd Model Test Results Population 100
Rel. Angle
Adaptive? 8 No
S
Crossover P. 0.90
-
nc
Progress Graphs. X: Cost, Y: Retail Suitability (generation indexing is zero-based)
84
10
Mutation P. 0.05
nm 30
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
85
Ioannis Chatzikonstantinou
Result Graphs after 34 generations X: Cost, Y: Retail Suitability
86
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
X: Retail Suitability, Y: Cooling Load
87
Ioannis Chatzikonstantinou 4130483 9182117 7775897 7770179 8713140 9794316 4833747 6963096 5071544 9026497 1601046 5579917 4668826 8376277 4726073 8318444 6398064 8875748 9482343 3636695 4398599 5417990 5300149 2559651 7243080 1801841 8365995 7070004 3410371 9480789 7039366 3779542 9652436 5932982 9491538 5036019 5316659 5851310 2747814 8584740 4660591 1644517 9895753 5930612 2399963 6382486 8143165 6203161 2243353 6959715 6015403 8783359 6865781 8744314 1274622 5041034 3920935 4522594 1623428 8203896 3916184 5113276 9315169 7031754 7929094 4431933 1096285 4157144 3212732 8942500 3051358 1127996 8444573 5358611 9879934 4045693 9883548 7629584 9352746 5280593 3410527 2436813 8667224 2511837 3249070 1536605 2375093 3271147 4840176 5145966 1285197 6968164 4960521 9003165 6795910 4544413 9249514 2068675 2766988 3669755
A-Pier Length 3,307,411.000 9,583,438.000 2,605,189.000 9,831,192.000 2,815,288.000 6,076,434.000 5,014,990.000 6,718,440.000 9,259,488.000 2,783,100.000 9,958,866.000 9,267,602.000 2,008,522.000 4,610,793.000 4,995,305.000 4,541,591.000 6,434,082.000 3,146,492.000 5,986,571.000 6,759,383.000 9,886,710.000 4,696,898.000 7,568,350.000 5,245,359.000 5,513,857.000 5,057,278.000 1,578,097.000 7,549,688.000 9,611,730.000 3,258,878.000 3,306,729.000 7,483,859.000 7,059,389.000 7,406,093.000 3,716,702.000 8,836,201.000 9,271,468.000 6,365,971.000 8,315,802.000 1,602,041.000 8,692,834.000 6,772,764.000 2,577,710.000 7,138,363.000 1,971,776.000 8,428,000.000 2,708,817.000 5,507,599.000 8,771,245.000 5,468,675.000 1,666,892.000 5,259,087.000 4,535,499.000 8,074,349.000 4,726,346.000 3,452,250.000 9,883,799.000 8,391,798.000 4,416,690.000 4,707,922.000 3,851,031.000 3,908,411.000 9,470,937.000 1,651,058.000 1,630,227.000 8,760,111.000 3,824,401.000 5,498,087.000 6,724,227.000 7,220,710.000 8,048,885.000 6,472,313.000 1,217,046.000 6,134,164.000 7,254,758.000 1,249,890.000 9,932,680.000 7,301,017.000 5,138,803.000 3,043,793.000 8,203,591.000 8,836,858.000 8,949,240.000 9,717,399.000 9,740,001.000 2,573,793.000 2,375,688.000 3,281,530.000 3,343,010.000 7,509,396.000 8,971,017.000 1,851,821.000 2,468,539.000 8,467,803.000 3,749,383.000 2,256,327.000 9,111,611.000 4,961,992.000 1,947,641.000 8,718,317.000
Radius 245.888 227.782 227.466 400.000 246.405 245.888 400.000 225.579 242.211 244.812 227.504 242.148 234.566 246.498 226.368 241.581 390.092 225.935 226.368 389.296 226.368 226.351 231.186 234.502 225.746 246.498 400.000 224.082 389.296 227.125 245.888 235.308 245.553 225.935 241.069 244.959 242.247 245.094 400.000 242.247 400.000 234.502 226.376 225.443 391.582 242.247 234.995 228.950 231.248 233.407 226.329 254.316 357.567 230.723 245.888 226.351 226.351 245.210 244.797 230.826 399.361 393.052 241.042 245.888 242.249 399.361 232.600 244.904 234.370 246.153 245.924 234.893 246.930 230.723 245.881 233.898 233.898 227.126 242.247 226.063 227.590 240.169 244.798 244.798 244.797 245.226 235.101 244.798 234.502 244.797 226.189 227.590 100.000 226.826 389.296 245.901 227.125 100.000 400.000 226.356
No. Sides 716 1,802 1,802 2,000 654 799 1,843 753 767 809 2,000 1,482 1,649 654 566 547 1,954 757 1,999 2,000 1,999 716 1,580 1,849 1,543 2,000 1,977 1,999 1,975 500 927 799 1,354 679 2,000 531 579 1,483 1,978 579 1,953 738 1,801 1,543 2,000 720 1,682 715 1,390 1,664 1,243 882 2,000 1,976 799 2,000 715 507 517 1,920 2,000 579 1,991 716 767 2,000 1,580 1,477 838 705 611 584 1,249 2,000 1,415 2,000 2,000 1,970 579 1,337 739 603 1,477 1,399 1,472 799 847 1,477 806 1,472 854 754 500 524 1,987 1,543 500 500 1,911 2,000
Angle 0.005 0.098 0.182 3.004 0.252 0.005 0.772 0.154 0.005 0.126 0.173 0.094 0.090 0.252 0.681 0.115 2.959 0.218 0.681 0.600 0.684 0.211 0.061 0.068 0.215 0.252 3.003 0.605 0.629 0.136 0.005 0.085 0.219 0.218 0.189 0.153 0.502 0.185 0.204 0.502 0.772 0.098 0.185 0.215 0.675 0.215 0.086 0.156 0.161 0.093 0.183 0.013 0.646 0.372 0.005 0.169 0.169 0.010 0.005 0.681 0.629 0.222 0.189 0.005 0.005 0.629 0.061 0.428 0.359 0.183 0.502 0.169 0.013 0.372 0.019 0.230 0.232 0.169 0.215 0.005 0.005 0.698 0.010 0.010 0.005 0.089 0.355 0.010 0.085 0.005 0.006 0.005 0.128 0.006 0.629 0.005 3.500 0.005 3.500 0.159
Rel. Pier Rotate -0.038 -0.041 -0.037 0.257 -0.038 -0.038 -0.040 -0.038 -0.037 -0.040 -0.036 -0.043 -0.041 -0.037 -0.052 0.044 -0.043 -0.015 -0.051 0.498 -0.037 -0.038 -0.040 -0.050 -0.041 -0.037 -0.037 -0.051 0.498 0.042 -0.042 -0.041 -0.038 -0.015 0.252 -0.023 -0.041 -0.040 -0.040 -0.041 -0.040 -0.050 -0.040 -0.049 0.498 -0.038 -0.041 -0.037 -0.041 -0.041 -0.038 -0.037 0.037 -0.041 -0.038 -0.036 -0.038 -0.024 -0.024 -0.050 0.537 -0.041 0.281 -0.038 -0.037 0.498 -0.040 0.026 -0.037 -0.038 -0.041 -0.041 -0.037 -0.041 -0.038 0.257 0.257 -0.036 -0.040 -0.038 -0.034 -0.039 0.252 0.252 0.259 -0.041 -0.037 0.252 -0.041 0.259 -0.037 -0.034 -1.000 -0.023 0.498 -0.038 0.042 -0.038 -0.034 0.026
88
Main Width 50.421 50.141 50.096 100.067 50.687 50.147 149.509 50.145 50.274 50.002 63.668 50.030 50.093 50.150 52.482 50.031 161.319 50.439 52.537 167.676 52.408 51.239 51.374 50.345 51.261 50.205 172.042 165.225 50.466 50.007 50.280 50.353 50.142 50.439 148.844 50.181 50.257 50.339 98.874 50.262 162.508 50.345 51.219 50.326 54.989 50.262 51.954 51.374 51.990 50.030 50.142 50.985 81.189 50.383 50.145 52.027 50.020 50.153 50.000 79.633 59.534 50.262 147.353 50.421 50.282 169.303 51.565 50.259 50.145 50.142 50.133 50.134 50.206 57.191 50.310 55.394 99.615 50.142 50.262 50.145 50.000 50.565 50.259 50.251 50.000 50.156 51.572 50.251 50.345 50.000 50.157 50.000 50.000 50.154 180.000 50.437 50.007 50.000 172.022 162.565
Section Frac. 0.629 0.622 0.625 0.636 0.601 0.629 0.790 0.629 0.629 0.602 0.624 0.623 0.724 0.601 0.629 0.627 0.636 0.643 0.628 0.684 0.627 0.624 0.611 0.629 0.625 0.600 0.620 0.628 0.683 0.644 0.629 0.602 0.600 0.643 0.638 0.602 0.625 0.667 0.624 0.625 0.790 0.629 0.667 0.625 0.684 0.624 0.602 0.624 0.600 0.624 0.600 0.620 0.722 0.672 0.629 0.624 0.624 0.602 0.602 0.628 0.619 0.625 0.638 0.629 0.629 0.619 0.611 0.600 0.607 0.602 0.625 0.725 0.629 0.672 0.619 0.620 0.636 0.627 0.625 0.627 0.627 0.677 0.600 0.600 0.602 0.602 0.607 0.600 0.602 0.637 0.625 0.632 0.600 0.625 0.684 0.629 0.627 0.619 0.601 0.627
B-Pier Length 90.258 90.230 111.917 278.115 90.181 90.258 288.038 90.258 90.258 90.000 90.268 92.445 106.756 90.181 223.517 91.161 292.278 108.726 223.517 106.577 291.902 90.096 90.366 90.258 90.235 90.181 291.519 223.517 96.243 91.161 90.258 90.258 111.796 91.574 92.051 90.820 92.513 91.511 91.117 90.256 291.955 90.258 111.917 90.231 106.577 90.084 90.817 90.291 90.182 91.948 111.796 291.519 228.718 100.579 90.258 90.096 90.096 106.679 106.679 228.681 292.272 90.795 92.051 90.258 90.197 292.272 90.366 92.401 113.641 91.832 90.256 90.768 90.090 100.579 90.777 91.942 91.942 90.096 90.274 110.222 90.000 90.291 91.619 92.973 106.799 90.258 110.049 110.125 90.258 90.241 90.258 108.087 90.257 90.280 283.404 90.258 91.161 90.000 286.474 90.801
Angle 5.912 4.890 5.144 4.895 5.565 5.069 4.986 5.542 5.569 5.626 2.095 5.108 2.136 5.565 5.437 5.114 3.663 5.078 2.082 5.111 2.082 2.408 5.064 4.901 5.021 2.209 4.907 2.049 5.111 5.115 5.569 5.566 5.053 5.076 5.021 5.561 5.569 5.120 4.699 5.569 4.986 4.901 5.120 5.021 5.144 5.126 5.733 4.933 4.919 5.109 5.053 4.906 2.012 5.108 5.569 2.095 5.066 5.116 5.109 2.001 5.105 5.569 5.021 5.912 5.569 5.082 4.721 4.943 5.026 5.562 5.569 5.120 5.691 4.928 5.574 5.102 5.102 5.046 5.126 5.060 4.927 5.565 5.022 5.021 2.381 5.633 5.025 5.022 5.569 2.359 5.812 4.708 2.000 5.812 5.111 5.944 5.115 5.574 4.906 5.021
No. Branches 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2
Section Frac. 0.603 0.606 0.607 0.793 0.623 0.602 0.618 0.603 0.603 0.601 0.601 0.606 0.623 0.606 0.607 0.636 0.788 0.606 0.623 0.797 0.624 0.601 0.601 0.606 0.601 0.622 0.731 0.801 0.786 0.608 0.603 0.600 0.600 0.606 0.608 0.600 0.607 0.601 0.634 0.601 0.624 0.616 0.623 0.601 0.619 0.601 0.600 0.601 0.601 0.626 0.600 0.607 0.796 0.629 0.603 0.601 0.601 0.766 0.766 0.604 0.788 0.601 0.608 0.603 0.603 0.729 0.601 0.601 0.600 0.600 0.601 0.602 0.603 0.624 0.601 0.780 0.793 0.601 0.600 0.603 0.604 0.601 0.601 0.601 0.768 0.600 0.600 0.601 0.600 0.768 0.606 0.601 0.600 0.606 0.797 0.603 0.636 0.604 0.736 0.624
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design Cost 222.804 487.879 491.973 866.078 213.371 241.186 1,646.411 233.909 233.673 247.803 670.470 411.880 462.426 210.970 222.807 186.857 1,372.854 241.061 580.037 1,823.624 593.322 229.162 443.272 502.241 433.586 537.208 1,440.120 1,788.337 562.410 173.840 271.556 245.503 384.612 218.548 1,540.428 181.363 193.670 417.827 1,062.564 193.107 1,874.018 232.821 505.334 426.198 612.429 228.539 473.647 230.153 400.121 454.925 355.045 311.575 946.628 536.923 241.099 554.026 224.201 181.073 180.539 830.037 712.490 217.059 1,519.285 222.804 233.700 1,936.187 445.011 409.279 258.463 223.720 200.941 200.874 353.672 611.007 394.935 593.184 1,044.932 528.596 194.210 367.790 223.683 201.982 404.939 386.658 402.763 246.105 266.889 408.689 247.035 401.281 252.046 231.470 143.723 174.770 2,093.284 416.870 120.919 139.945 1,234.208 1,672.497
Retail 11,037.8483 6,018.2280 3,740.2283 100.7933 4,392.1207 10,914.2845 219.2549 6,148.8126 11,301.6862 6,514.9741 3,519.2053 6,945.1987 6,122.5131 4,436.9469 1,133.7155 6,440.4195 59.0270 3,992.9699 917.4204 354.8154 798.5223 4,801.8465 7,739.8933 7,320.6122 3,817.6194 3,238.7964 55.8784 335.9654 1,180.5207 6,004.1915 12,313.8823 7,860.8219 3,485.4097 4,521.0884 1,318.9918 5,896.1511 2,929.5475 4,602.0416 1,516.3199 2,929.2644 202.6135 6,644.5469 3,621.7732 3,883.8462 954.8219 4,848.6421 6,843.1634 5,235.8445 4,690.1767 6,761.6063 4,025.5425 5,356.8252 562.4955 2,206.8109 11,723.1574 4,315.4276 5,156.3607 7,077.4522 7,255.0530 617.8909 682.1964 3,369.8020 1,280.5641 11,037.8483 11,300.1109 238.2221 7,715.0880 2,259.2163 2,658.8710 5,470.9036 2,746.7555 5,672.0611 12,266.7210 1,881.9433 11,674.0423 3,104.4569 1,761.8508 4,177.6417 4,998.7683 10,859.4239 10,606.6654 2,032.3033 12,070.6011 11,912.8023 11,438.2232 7,477.7680 2,481.7607 10,531.0125 7,899.0736 13,197.9498 12,368.2269 8,637.4526 8,830.3319 10,001.5005 229.2209 13,569.7601 529.1915 13,205.6662 49.0877 1,406.7979
Accessibility 174.362 66.285 67.725 90.738 182.706 158.054 69.066 162.321 164.235 150.992 58.258 81.264 73.630 182.697 190.353 210.444 91.282 161.414 67.566 60.960 71.681 170.042 75.866 64.560 77.621 59.476 91.090 62.470 65.023 227.134 137.282 153.167 90.889 178.342 58.407 214.386 202.758 81.156 60.648 203.083 65.273 164.995 67.513 77.686 64.216 168.189 70.758 169.962 86.818 71.768 99.072 141.702 63.558 61.052 158.053 58.817 170.133 219.948 220.026 65.942 70.535 178.657 58.687 174.362 164.235 63.252 75.870 82.299 147.026 171.026 194.302 201.354 98.705 59.586 86.061 58.897 58.351 60.518 201.833 95.412 170.793 198.549 83.222 88.170 86.293 152.799 145.580 84.639 151.940 85.089 148.221 167.142 241.736 224.726 63.667 80.866 300.244 251.000 105.686 58.171
Cooling Load 58.261 96.895 99.117 218.448 56.359 60.924 385.158 58.725 59.641 61.086 126.331 86.350 97.536 55.729 67.552 52.828 343.143 61.595 121.439 366.676 128.553 58.180 90.235 99.636 88.806 104.893 353.783 356.138 121.592 50.279 65.515 60.333 83.126 56.991 276.951 51.259 53.751 88.527 209.899 53.459 431.196 59.210 102.605 87.515 130.162 58.713 94.876 58.518 83.570 92.521 77.657 86.250 212.516 106.775 60.921 107.020 57.126 53.831 53.678 168.338 165.125 65.365 273.507 58.261 59.645 420.678 90.607 85.515 63.889 57.707 54.791 56.802 77.860 119.171 83.796 115.534 193.958 103.087 53.617 80.204 57.206 56.117 84.800 82.138 87.069 60.902 65.316 86.638 60.517 86.466 61.401 59.735 34.793 49.889 470.187 87.367 42.175 34.453 319.750 296.731
Rank 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Cr. Distance 32.970 33.482 33.573 33.749 33.987 34.300 34.690 35.003 35.047 35.221 35.250 35.890 36.324 36.433 36.739 37.342 38.278 38.717 38.908 39.309 39.797 40.108 40.148 40.307 40.384 40.391 40.436 40.492 40.663 40.808 40.911 41.426 42.514 43.860 43.977 44.236 44.425 44.770 46.586 47.052 47.399 47.530 48.371 48.861 50.153 51.010 51.057 51.239 52.174 52.352 52.550 55.258 59.114 59.472 59.728 60.274 60.585 61.710 63.594 63.800 64.044 64.086 64.641 66.430 66.520 66.716 68.233 69.646 69.721 69.844 70.399 72.848 73.174 73.931 75.017 75.622 76.264 76.533 79.137 81.392 82.700 85.645 90.976 91.152 94.375 99.266 104.047 152.994 185.070 210.396 224.282 234.345 350.515 429.476 -
89
Ioannis Chatzikonstantinou
A5 / Appendix: 4th Model Test Results Population 100
Rel. Angle
Adaptive? 10 Yes
S 5
Crossover P. 0.90
nc
Progress Graphs. X: Cost, Y: Retail Suitability (generation indexing is zero-based)
90
10
Mutation P. 0.05
nm 30
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
91
Ioannis Chatzikonstantinou
Result Graphs after 34 generations X: Cost, Y: Retail Suitability
X: Cost, Y: Accessibility
92
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design
X: Retail Suitability, Y: Cooling Load
X: Accessibility, Y: Cooling Load
93
Ioannis Chatzikonstantinou 4130483 9182117 7775897 7770179 8713140 9794316 4833747 6963096 5071544 9026497 1601046 5579917 4668826 8376277 4726073 8318444 6398064 8875748 9482343 3636695 4398599 5417990 5300149 2559651 7243080 1801841 8365995 7070004 3410371 9480789 7039366 3779542 9652436 5932982 9491538 5036019 5316659 5851310 2747814 8584740 4660591 1644517 9895753 5930612 2399963 6382486 8143165 6203161 2243353 6959715 6015403 8783359 6865781 8744314 1274622 5041034 3920935 4522594 1623428 8203896 3916184 5113276 9315169 7031754 7929094 4431933 1096285 4157144 3212732 8942500 3051358 1127996 8444573 5358611 9879934 4045693 9883548 7629584 9352746 5280593 3410527 2436813 8667224 2511837 3249070 1536605 2375093 3271147 4840176 5145966 1285197 6968164 4960521 9003165 6795910 4544413 9249514 2068675 2766988 3669755
A-Pier Length 1,345,921.000 2,322,305.000 4,618,374.000 3,116,767.000 2,827,817.000 7,967,918.000 8,136,239.000 9,641,431.000 3,711,877.000 1,668,471.000 2,178,834.000 9,351,422.000 6,826,218.000 9,108,260.000 1,390,870.000 4,065,911.000 9,619,421.000 7,222,478.000 2,128,756.000 2,680,873.000 4,697,579.000 6,057,408.000 3,208,113.000 6,984,196.000 9,158,493.000 5,833,283.000 1,433,502.000 3,685,733.000 9,863,126.000 3,231,350.000 7,588,102.000 6,222,447.000 7,445,864.000 3,173,616.000 9,861,589.000 7,343,813.000 6,560,547.000 5,629,814.000 6,105,528.000 8,367,209.000 7,473,812.000 2,920,246.000 5,255,923.000 1,510,093.000 8,570,055.000 9,983,246.000 5,074,843.000 3,723,698.000 8,623,302.000 6,170,669.000 5,542,489.000 2,881,170.000 3,813,928.000 3,636,621.000 1,325,152.000 8,852,047.000 5,542,588.000 4,063,118.000 8,404,485.000 8,428,777.000 4,006,488.000 5,154,469.000 4,535,731.000 6,274,615.000 1,602,154.000 2,509,766.000 1,750,676.000 8,000,314.000 9,849,386.000 6,977,761.000 5,811,820.000 4,386,820.000 7,389,648.000 5,055,681.000 6,196,400.000 7,514,138.000 6,082,042.000 8,884,622.000 6,903,429.000 8,807,803.000 5,999,366.000 8,223,199.000 7,543,634.000 1,918,368.000 6,052,612.000 3,810,845.000 7,918,332.000 7,873,075.000 8,386,462.000 9,610,087.000 8,147,924.000 3,021,306.000 8,913,323.000 6,250,548.000 7,723,098.000 8,664,738.000 8,657,379.000 1,986,165.000 8,760,302.000 5,459,276.000
Radius 322.191 374.631 300.253 350.097 370.675 325.343 312.925 380.258 377.814 398.896 325.253 306.389 338.044 353.444 275.202 264.409 304.809 319.151 326.360 232.836 350.786 346.806 374.729 325.534 303.648 396.202 235.634 350.563 374.784 264.409 308.974 395.230 348.921 268.606 353.444 325.683 271.404 351.093 326.052 308.318 294.838 326.052 338.044 377.654 326.052 313.101 302.443 352.038 302.745 304.863 381.713 326.052 374.729 338.044 317.198 323.913 376.465 357.269 264.409 338.044 380.321 326.163 296.048 387.777 325.268 398.957 398.896 374.729 325.253 326.052 395.190 352.994 395.190 380.321 306.342 264.409 306.616 350.372 374.596 374.631 305.458 338.044 325.516 395.190 320.118 319.747 374.729 370.675 326.052 326.052 322.746 399.415 307.951 371.368 400.000 296.048 307.951 303.648 380.547 306.342
No. Sides 1,690 1,835 1,949 1,243 1,947 2,000 1,946 2,000 1,960 1,903 1,944 1,967 1,247 1,262 2,000 2,000 1,911 1,999 725 1,946 1,946 1,967 1,947 1,852 735 1,964 2,000 1,262 1,960 1,991 1,903 1,865 750 1,946 1,435 1,916 2,000 751 1,947 754 1,221 1,909 1,243 1,729 670 1,911 750 1,961 670 1,909 1,967 1,946 2,000 1,247 2,000 1,828 1,964 1,251 2,000 1,250 1,903 670 525 1,963 2,000 1,962 1,915 1,948 1,742 1,913 1,913 2,000 1,984 1,903 1,968 2,000 1,967 1,961 1,947 1,814 1,964 1,293 1,964 1,984 826 1,947 1,943 2,000 1,919 1,909 1,909 1,915 1,915 1,992 1,964 525 1,915 747 2,000 1,974
Angle 2.702 3.395 2.702 3.293 1.679 3.350 2.409 3.387 0.561 1.871 1.940 1.861 2.501 3.290 0.913 3.066 0.744 1.027 3.272 2.420 1.861 1.849 1.661 2.677 3.234 2.691 2.691 3.293 3.214 2.011 3.041 2.442 2.879 2.527 3.410 0.750 2.691 2.890 1.940 3.291 3.214 3.214 2.501 2.703 3.111 0.750 3.234 1.889 3.111 3.290 2.528 2.889 1.993 2.501 1.071 2.969 2.019 3.061 2.011 2.885 1.620 1.901 3.235 1.918 1.956 3.118 1.881 1.661 1.940 1.173 1.889 1.956 3.118 3.041 0.561 3.066 1.889 3.014 1.661 3.350 1.894 2.483 0.860 3.118 2.870 1.039 1.652 2.011 1.173 1.067 1.067 0.005 0.112 1.661 0.913 3.263 0.005 3.245 3.335 0.561
Rel. Pier Rotate 0.832 0.733 0.851 0.572 0.726 0.551 0.948 0.815 0.832 0.594 0.551 -0.496 0.244 0.716 0.234 -0.485 -0.992 -0.666 0.420 0.232 0.232 0.690 0.733 0.810 0.721 0.125 0.137 0.716 0.832 -0.439 0.588 -0.624 0.541 0.232 0.716 0.896 0.137 -1.000 0.559 0.716 -0.488 -0.478 0.575 0.638 0.549 0.896 0.452 -0.492 0.549 -0.651 0.919 0.559 0.737 0.244 -0.666 0.960 0.221 0.411 -0.461 0.185 -0.799 0.549 -0.457 -0.481 0.551 -0.496 -0.910 0.737 0.551 -0.480 -0.910 0.551 -0.514 0.588 -0.424 0.667 -0.496 -0.461 -0.419 0.725 0.180 0.574 0.546 -0.476 0.728 0.790 -0.422 0.726 -0.478 -0.516 -0.478 -0.457 -0.457 -0.535 0.221 -0.482 -0.457 -0.784 0.815 -0.422
94
Main Width 93.484 136.726 67.634 139.805 131.089 140.711 124.937 140.046 139.498 108.410 55.180 162.902 54.168 139.805 92.327 112.325 149.160 77.852 148.827 52.255 128.585 167.124 68.673 60.568 53.580 152.984 95.473 139.805 140.682 139.598 133.090 139.123 53.580 124.857 69.758 157.518 93.484 51.231 57.168 137.693 53.580 139.932 150.158 74.908 57.088 149.160 53.580 137.768 57.088 51.814 152.913 55.555 71.155 54.168 153.013 50.000 151.672 92.640 112.325 55.389 69.785 57.088 142.441 142.605 150.748 167.496 105.157 60.951 55.180 60.251 105.157 150.857 167.496 133.090 167.124 112.325 167.124 145.004 68.673 136.726 84.711 150.158 151.827 169.798 60.691 67.524 51.977 141.292 54.226 54.865 57.168 50.000 125.865 154.157 151.827 141.738 51.275 50.327 145.035 161.099
Section Frac. 0.641 0.643 0.641 0.656 0.775 0.732 0.675 0.642 0.695 0.851 0.722 0.694 0.608 0.655 0.814 0.775 0.879 0.604 0.600 0.811 0.695 0.694 0.762 0.613 0.603 0.627 0.627 0.656 0.642 0.775 0.840 0.609 0.603 0.602 0.656 0.651 0.627 0.603 0.762 0.656 0.603 0.600 0.611 0.641 0.600 0.879 0.603 0.693 0.603 0.662 0.858 0.603 0.753 0.608 0.604 0.642 0.813 0.818 0.775 0.608 0.706 0.603 0.744 0.862 0.736 0.705 0.851 0.753 0.736 0.600 0.851 0.723 0.851 0.840 0.696 0.775 0.694 0.696 0.762 0.643 0.814 0.611 0.812 0.851 0.606 0.619 0.761 0.775 0.600 0.600 0.743 0.600 0.636 0.762 0.814 0.744 0.846 0.603 0.642 0.696
B-Pier Length 251.662 297.969 251.652 290.880 122.387 231.609 284.971 292.336 128.231 97.456 129.517 245.889 299.161 132.780 267.915 92.235 172.639 166.526 123.349 167.347 167.347 298.317 295.075 170.841 103.314 299.289 176.394 291.357 292.336 123.515 300.000 298.763 255.606 259.102 132.774 170.042 268.148 256.622 167.418 291.357 270.562 171.531 299.161 295.040 169.210 172.639 120.535 244.800 169.210 185.842 226.179 165.379 295.075 299.161 245.474 297.678 299.040 269.247 92.235 177.632 170.187 169.210 132.155 298.867 129.784 244.783 97.220 295.075 129.517 171.531 252.183 231.609 243.191 274.628 90.000 290.206 245.889 268.502 97.104 294.783 299.040 116.217 294.874 243.191 297.223 167.320 97.104 122.387 171.531 171.531 100.502 90.000 90.000 295.075 299.056 132.769 90.000 103.078 292.336 90.000
Angle 6.014 3.691 6.129 4.478 2.014 5.504 5.139 6.107 6.016 5.860 2.469 4.101 2.507 4.626 6.007 2.000 2.357 2.303 6.016 2.253 4.125 4.104 3.768 2.000 3.107 4.163 5.979 4.636 6.016 2.000 2.378 3.803 3.132 4.125 3.173 2.326 5.979 3.023 2.455 3.161 3.119 4.556 2.590 3.796 4.235 2.357 3.107 6.002 4.260 5.388 2.373 4.222 3.768 2.507 2.330 3.861 4.191 3.680 2.000 2.507 2.913 4.197 4.298 2.308 2.330 4.016 5.860 3.768 2.469 2.941 5.860 5.504 6.002 2.913 2.940 2.000 4.101 2.912 3.845 3.691 3.123 2.632 4.191 4.514 6.051 4.478 5.344 2.014 3.112 5.982 2.382 2.000 4.232 3.763 4.191 4.298 2.360 3.107 6.017 3.112
No. Branches 3 2 3 2 2 2 2 3 3 3 2 2 2 2 2 2 2 3 3 3 3 2 2 1 2 3 3 2 3 2 2 2 2 3 2 2 3 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 2 2 2 2 2 3 3 3 3 2 2 3 2 3 2
Section Frac. 0.816 0.600 0.742 0.729 0.661 0.825 0.701 0.878 0.868 0.745 0.767 0.607 0.710 0.606 0.813 0.879 0.600 0.793 0.600 0.618 0.628 0.870 0.672 0.690 0.611 0.780 0.781 0.729 0.873 0.769 0.792 0.708 0.680 0.618 0.729 0.782 0.781 0.727 0.847 0.729 0.611 0.689 0.709 0.874 0.843 0.689 0.611 0.784 0.848 0.824 0.616 0.776 0.672 0.710 0.781 0.686 0.813 0.658 0.879 0.710 0.793 0.843 0.609 0.778 0.784 0.874 0.745 0.672 0.752 0.691 0.825 0.730 0.658 0.792 0.746 0.671 0.868 0.737 0.879 0.683 0.812 0.612 0.812 0.661 0.728 0.781 0.879 0.661 0.688 0.687 0.688 0.826 0.826 0.672 0.813 0.609 0.826 0.611 0.878 0.743
Evolutionary Computation and Parametric Pattern Generation for Airport Terminal Design Cost
Retail Accessibility 791.924 120.7962882 101.537 971.079 67.7675162 106.734 629.376 163.1876127 94.319 803.325 72.2346740 133.117 1,297.058 176.4502294 70.363 1,099.550 79.4280182 102.670 1,150.461 101.7159327 82.699 1,221.231 53.7397899 99.537 1,565.373 437.9394752 63.864 1,082.370 212.6559598 75.100 536.613 394.6262445 75.168 1,592.057 99.3040649 73.558 370.627 240.4229242 131.765 706.608 100.7141033 148.311 1,078.584 384.8911163 64.708 850.836 165.5572069 93.025 1,595.134 315.6676995 65.428 861.336 445.3886682 65.857 521.529 112.3535887 193.269 488.681 335.7197396 86.847 1,274.207 141.8130972 75.051 1,763.629 91.6174340 73.451 751.969 229.7682392 77.336 469.065 257.6070406 90.697 185.191 367.4465496 217.383 1,478.757 66.0603341 85.931 828.651 145.4079511 88.651 811.636 70.2976383 132.079 1,253.841 56.3523008 97.305 1,308.597 157.1424534 72.143 1,160.054 78.8239657 97.774 1,241.512 85.6615013 84.712 244.639 251.8897083 183.096 1,113.472 100.9796133 88.349 392.320 199.1217054 139.410 1,645.280 296.8833292 65.283 878.488 121.8377518 89.546 238.501 266.9213227 184.598 577.275 323.3021776 77.500 584.425 79.4223029 162.028 297.634 216.7494278 153.294 1,030.782 90.2023900 104.537 969.569 90.8979762 118.413 641.026 141.5781823 99.333 218.338 278.9188774 201.058 1,616.065 313.3224784 65.485 191.118 331.1293959 211.508 1,394.091 120.2102300 73.833 215.248 285.1170746 205.492 389.908 263.9697640 108.285 1,515.090 81.4046484 84.293 451.530 243.5960877 95.177 760.235 188.1029859 78.291 370.627 240.4229242 131.765 1,727.985 195.0160449 67.570 413.539 213.7769655 111.966 1,629.614 88.3977579 75.249 656.083 112.4108572 126.265 1,050.011 224.2253556 70.825 325.411 288.5957359 136.272 742.266 289.3508163 75.203 257.962 429.2242298 177.136 425.265 121.6898934 230.216 1,572.345 103.5375618 73.924 1,452.246 144.2354396 71.621 1,407.187 60.3633636 95.276 1,026.027 218.1115951 73.667 670.921 258.6080064 80.374 491.849 415.5170523 83.700 618.929 504.8448938 69.963 1,129.516 155.1474164 75.327 1,526.432 110.5666805 73.133 1,434.659 65.5555584 94.539 1,173.934 80.9835264 95.798 1,741.697 432.9793003 60.861 940.010 102.2559219 95.713 1,689.030 96.6256826 73.905 1,210.666 74.0504666 93.830 694.774 356.5369229 70.063 990.970 64.4215704 106.548 918.104 178.1479936 75.510 885.720 131.8047785 122.529 1,783.519 209.9964347 65.733 1,555.295 58.0357771 94.759 337.929 181.4592509 170.260 712.570 506.3662560 66.576 533.955 472.2314322 72.595 1,365.325 137.4652609 72.408 562.590 527.7117340 72.532 570.846 624.5951677 70.241 604.356 740.9538274 67.642 536.027 11,714.1584648 68.102 1,317.140 2,141.9468698 63.213 1,771.810 94.5123274 72.224 1,822.009 177.3872577 65.580 421.559 121.2370100 230.288 561.935 11,945.7511312 67.067 176.587 390.1445453 216.708 1,278.438 53.2728345 98.318 1,683.903 449.1242008 60.659
Cooling Load 212.946 249.925 160.927 236.881 277.592 280.902 268.118 349.695 339.939 252.933 120.340 342.308 104.420 183.060 248.350 187.002 340.376 186.669 160.492 117.689 284.375 419.214 183.252 102.500 57.104 388.629 188.751 238.227 353.562 270.517 314.275 296.009 81.283 257.522 104.647 336.646 219.717 80.259 135.367 198.259 85.512 245.839 258.340 170.455 73.551 351.704 59.164 318.363 71.941 99.427 392.436 106.022 185.730 104.420 385.499 108.686 410.688 211.994 215.197 88.079 178.520 79.555 145.567 400.358 306.124 364.446 231.341 164.434 114.032 131.730 286.223 344.825 375.309 321.913 333.720 233.482 383.073 300.797 153.987 259.101 228.117 202.876 420.308 433.870 117.017 150.573 121.404 293.712 121.073 122.477 132.891 118.267 261.624 443.346 442.972 144.796 127.894 54.655 363.705 322.684
Rank 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Cr. Distance 6.917 6.925 6.956 7.024 7.047 7.084 7.222 7.356 7.418 7.437 7.510 7.525 7.619 7.718 7.866 7.915 7.935 7.980 8.105 8.123 8.162 8.231 8.291 8.304 8.349 8.381 8.391 8.441 8.506 8.612 8.703 8.750 8.822 8.830 8.905 8.929 9.111 9.153 9.163 9.180 9.313 9.748 9.771 9.986 10.130 10.271 10.549 10.560 10.598 10.600 10.605 10.758 10.792 10.811 11.171 11.276 11.411 11.806 11.871 11.929 11.951 12.036 12.097 12.838 12.848 13.149 13.232 13.449 13.455 13.566 13.670 14.256 14.295 14.326 14.579 14.751 14.771 15.098 15.104 15.895 15.907 15.918 16.100 16.563 16.744 16.984 17.246 22.730 26.143 55.859 385.857 2,452.858 2,756.909 -
95
