A Computational Intelligence Approach to Alleviate Complexity Issues in Design1 ¨ zer Ciftcioglu Michael S. Bittermann, I. Sevil Sariyildiz, and O

Abstract An approach to handle complexity issues in design is presented, where computation is used to reach the most suitable solutions. The approach is based on a novel concept of the objects forming a design. This concept is termed intelligent design objects. Such objects exhibit intelligent behaviour in the sense that they approach the most desirable solutions for conflicting, vague goals put forward by a designer. That is, the objects know ‘themselves’ what to do to satisfy the designer’s goals. This is accomplished by using fuzzy information processing to deal with the vagueness of objectives, and multi-objective evolutionary algorithm to deal with the conflicts among the objectives. The result of this approach is that designers and decision makers have great certainty about the satisfaction of their goals and are able to concentrate on second order aspects they could not consider with great awareness prior to the computation. The effectiveness of the approach is demonstrated through implementation in two applications from the domain of architecture. Keywords Architectural design • Computational intelligence • Fuzzy neural tree • Genetic algorithm • Multi-objective optimization

1 This paper is taken from M.S Bittermann’s PhD thesis: Intelligent Design Objects (IDO) - A cognitive approach for performance-based design. Department of Building Technology, Delft University of Technology, Delft, The Netherlands (2009) 235.

M.S. Bittermann (*) Delft University of Technology, Delft, The Netherlands e-mail: [email protected] ¨ . Ciftcioglu I. Sariyildiz • O Chair of Design Informatics, Department of Building Technology, Delft University of Technology, Delft, The Netherlands J. Portugali et al. (eds.), Complexity Theories of Cities Have Come of Age, DOI 10.1007/978-3-642-24544-2_19, # Springer-Verlag Berlin Heidelberg 2012

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1 Introduction Design is complex. This is because it involves conflicting goals that are often vague. For example, a design is demanded to be functional, look appealing and have moderate costs. The vagueness of these objectives makes it problematic to remain ‘fair’ when comparing alternative solutions during design, and the conflicts among the objectives make it problematic to reach optimality. The fairness refers to high precision in performance evaluations. This is particularly challenging to achieve, when performance aspects like visual perception are involved, due to their soft nature. Another source of complexity is that the number of possible solutions is excessively large in general. A design consists of many parameters, where every parameter may take different values, so that the total amount of possible combinations forming a solution is enormous. This is referred to as combinatorial explosion in the parameter domain. It makes it problematic to ensure one did not miss a superior solution during the design process. A final source of complexity, which is in fact a consequence of the ones named already, is that prior to the design it is generally not clear how important goals are relative to each other. For example it is difficult to tell exactly how important the functionality of a design is compared to perception aspects prior to knowing what the meaning and implication of such a statement is. That is, before finding the most suitable solutions for the goals, and thereby becoming aware of the nature of the inevitable trade-offs, it is premature to commit to a relative importance among the soft goals. Every one of these complexity issues is a challenging issue in itself and in combination they are the reason why it is difficult to accomplish scientific means for design enhancement. The enhancement is meant to support designers, so that they can be more certain their designs are most suitable for the intended purpose. There have been a number of works addressing this issue since the emergence of computers. A number of them are using methods of classical artificial intelligence (AI) (Eastman 1973; Gero 1987; Flemming and Woodbury 1995; Koile 2004). The classical AI approach is severely limited, in particular due to unnatural rigidity in the reasoning mechanism employed that cannot deal with the complexity inherent to design. Therefore this approach did not flourish, in particular for design purposes. Recent approaches to computational design are based on an emerging information processing paradigm known as computational intelligence (CI), consisting of the methodologies known as fuzzy logic, evolutionary computation, artificial neural networks, and other, bio-inspired, computational systems (Zadeh 1994; Engelbrecht 2005). CI methodologies are superior to the classical AI methodologies in particular with respect to dealing with vagueness and combinatorial explosion, e.g. see (Caldas 2006; Deb and Srinivasan 2006; Shea et al. 2006; Bandaru and Deb 2010). It is particularly interesting to consider the role that fuzzy sets of fuzzy logic are playing in dealing with complexity. A shortcoming of the classical AI approach in treating complexity in design stems from a certain simplification that is ramified by using fuzzy sets. This simplification is that classical AI approaches generally

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involve a logic that is based on premises with sharp ‘truth boundaries’, i.e. they are based on classification using crisp sets. For example, a design is considered expensive if its costs are above a certain threshold value, and it is considered not expensive if the costs are below this value. The sudden shift of the applicability of a label to its non-applicability at a certain parameter value is a simplification of the complexity that is naturally inherent to reality, and in particular design. It entails the omission of a significant amount of information. Therefore the effectiveness of the classical AI approach is generally limited to situations with minimal vagueness in requirements. Fuzzy sets allow the use of the information that is otherwise omitted. This way the natural complexity of design requirements is subject to computational treatment and the possibilities for reaching suitable designs that match the intended purpose are subject to exploration with adequate precision, in contrast with the classical approach. This paper presents a novel system for computational design that addresses the complexity issues mentioned above. It is based on a synergistic combination of several computational intelligence methods. The paper is structured as follows. In Sect. 2 a model of human vision is described that quantifies the perceptual properties of environments. In Sect. 3 a model for evaluating designs is described, in which the outputs of the vision model are used as input. In Sect. 4 multi-objective evolutionary search is described, to deal with the combinatorial explosion and generate optimal designs. The latter is combined with the first two components, yielding an intelligent system with cognitive features. In Sect. 5 the system will be applied to two design tasks to verify its effectiveness. This is followed by conclusions.

2 Modelling Visual Perception 2.1

Introduction

Architects and engineers use different computational models to analyze the properties of a design. For example, computational methods are used for structural analysis, wind analysis, or cost analysis. The motivation behind the modelling effort is to obtain precise information for the evaluation of a design. Perception is an essential aspect of architecture and often a major factor determining the success of a design. It is therefore important to develop means to analyze the visual perception properties of built environment. Modelling visual perception is challenging mainly because it involves not only the eye, but also the brain (Levine and Sheffner 1981; Gibson 1986; Palmer 1999; Foster 2000; Bittermann and Ciftcioglu 2008). The final “seeing” event occurs due to brain processes. The biological vision system is complex, involving many involuntary processes such as eye saccades, retinal sampling, cortical mapping etc. This complexity is responsible for a common phenomenon we encounter at practically every moment, while it may remain unnoticed. We overlook items in our environment, although they are visible to

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us. This overlooking refers to the inability to remember visual information, although the information was processed by the visual system (O’Regan et al. 2000). This phenomenon may also be referred to as uncertainty of human vision or graded objectawareness. It is a characteristic property of human vision, occurring presumably due to the way the human memory is built up and facilitates consciousness dealing with ample environmental information. In this respect, the human vision system clearly differs from an optical system like that of a camera, although the analogy may be suitable to some extend as well (Marr 1982; Pentland 1987).

2.2

A Probabilistic Approach

In the present approach the components involved in human vision are modelled as a whole system instead of modelling each component individually, thereby bridging between the environmental stimulus and its mental realization. At this point the definition of the concepts involved in vision put forward in this approach is not elaborated further. This will be established naturally as a result of the vision model, which is described in the next paragraph. The work concentrates on the influence of geometry on the human vision process, where an observer builds up an unbiased understanding of the environment. This means that an observer has no a-priori preference for an object in the environment. Such a bias may be due to a task the person is about to accomplish, or a general personal preference, or other conditioning. In many instances we expect some degree of bias in visual perception, which is problematic to discern without a model of the unbiased case. Explicitly, the model gives two advantages: • The perception and related phenomena in early vision are understood in greater detail, and some common reflections about them are substantiated. • The model can be effectively introduced into architectural design, since perception is quantified by a probability. We start modelling the perception process using a simple, yet fundamental, geometry. This is shown in Fig. 1. For the sake of simplicity of explanation we consider perception in a two-dimensional space. That is, the vision of an observer is considered in the x-y plane in Fig. 1. In Fig. 1 an observer is facing and viewing a vertical plane from the point denoted by P. Through vision, the observer is able to receive visual information from all directions within his/her vision scope. In the present case we model unbiased human vision. This means the observer has no preference for any direction in the scope. In other words he/she pays attention equally in all directions. In mathematical terms this is modelled by associating an equal probability with any differential angle portion in the visual scope as given by Eq. 1 (Ciftcioglu et al. 2006).

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Fig. 1 Plan view of the basic geometric situation of perception (a). Perspective view of the same situation (b)

fy ¼

1 p=2

(1)

where fy is the probability density (pdf) associated to the vision angle, where the vision scope is taken to range from p/4  y  p/4. The probability density function models the visual attention an observer pays to the vision angle in early vision and any differential angle dy receives equal attention, reflecting the unbiased case. Any point of an environment existing in the visual scope receives a particular degree of the visual attention. In case of the basic geometry shown in Fig. 1, this degree is given by Eq. 2 for the interval  lo  x  lo (Ciftcioglu et al. 2006). The pdf fx(x) in Eq. 2 models visual attention along the x dimension. fx ðxÞ ¼

2 lo ; p ðl2o þ x2 Þ

(2)

Integration of visual attention in a finite small interval, where fx(x) is approximately constant, gives unbiased perception as probability P ð P¼

Dx

fx ðxÞ dx ffi fx ðxÞ Dx;

(3)

The implications of these results are seen in Fig. 2. Namely, when the distance between observer and object is short, the visual attention is strongly focused on a relatively small area in the frontal part of the object, and strongly diminishes towards the side parts of the wall, whereas when the distance is far, the attention is ‘smeared out’ almost homogenously over the object, so that the peak attention is also less. This means that for the nearby wall an unbiased observer will be strongly aware of the details in frontal direction and hardly aware of the side parts of the

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Fig. 2 Unbiased attention for an object at a near distance (a). At a far distance (b)

wall. Another result is that the integral of pdf fx(x) along the wall object is greater in Fig. 2a than in 2b. This means that when the wall is nearer it yields a higher perception, i.e. an unbiased observer will be more aware of the wall than in the distant case. These results coincide with our common experience of vision, indicating the validity of the model. The benefit of the computations is the precise quantification of perception. This way a systematic search for optimal architectural designs, satisfying requirements that are expressed in terms of perception, may be executed. This will be explained in the following sections. One exemplary application of the probabilistic model for spatial analysis is shown in Fig. 3, where it is used to measure unbiased perception during a walk through a retail environment. Figure 4 shows the resulting perception of every object as a virtual observer is moving through the space, where the distance is given as the number of 30 cm intervals from the starting location. During the first part of the walk, until interval 20, the observer is most aware of Object O1, which is the cart of yellow shopping bags. During the second part, from interval 20 until 36, the observer becomes most aware of objects O8, which are the exhibited furniture

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Fig. 3 Perceptual analysis along a trajectory in the space

Fig. 4 Resulting perception of the respective objects along the trajectory

pieces. This second part is less strongly dominated, so that relatively more attention is paid to the other objects than at the beginning of the trajectory. The final part of the trajectory increasingly accentuates the escalators (object O6). In the meanwhile O7, the advertisement signage indicating prices at the restaurant of the store, is also receiving significant attention. In the intervals 42–47 the unbiased observer is even slightly more aware of the signage than of the escalators. Relocation of the objects in the scene would clearly change the observer’s experience.

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3 Evaluating Design Performance The model presented in the previous section delivers, as its output, information on the perceptual properties of a space. Such a piece of information is one of many characterizing a design, such as sizes of spaces, distances among objects, stress resistance of elements, etc. However, in design it is not only necessary to observe the direct physical features of the objects, but to interpret these with respect to the goals pursued. For example, in a space the stairs may be desired to be hardly perceived, for instance in order to organize the people flow efficiently, although sufficiently perceived to be easily located if needed. It is noted that this requirement entails a certain low amount of perception for the stairs, and deviation from this amount means that the requirement will not be totally fulfilled. Many requirements have this character, i.e. they do not pinpoint a single acceptable parameter value for a solution, but a range of values that are more or less satisfactory. Design also involves conflicting requirements, so many requirements are bound to be only partially fulfilled. Such requirements are characterized as soft, and they can be modelled using fuzzy sets and fuzzy logic (Zadeh 1975). These concepts were introduced by Zadeh as generalizations of classical crisp sets and traditional logic. In contrast to a crisp set, a fuzzy set has no sharp set boundary, instead the boundary is ‘smeared out’ over a range in the universe of discourse. A fuzzy set is characterized through a function called membership function. That is, whereas classic sets permit an object only to belong to a set or not belong to it, through a fuzzy set an object is associated to the set by means of a membership degree m, which can be any rational number between zero and one. This allows the modelling of partial truth. In our case this refers the partial truth that a design object possesses a desired feature. This means that we interpret the membership degree as a degree of satisfaction of a requirement, the latter being expressed through a membership function. Two examples of fuzzy sets used to model elemental design requirements are shown in Fig. 5. From the figure we note that a hall with a certain size a0 partly satisfies the requirement R1: large hall by 65%. Stairs with a perception of degree p0 satisfy the requirement R2: low perception of the stairs, but not too low by 86%.

Fig. 5 Two fuzzy sets expressing two elemental design requirements

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Fig. 6 The structure of a neural tree

By means of fuzzy membership functions a physical property of a design is interpreted as a degree of satisfaction of an elemental requirement. The requirements considered here are relatively simple, whereas the ultimate requirement for a design, namely a high design performance, is complex. The latter is influenced by satisfaction of a number of such elemental requirements at the same time. For instance, several requirements should be highly satisfied for a high design performance. In this work, the performance is computed using a fuzzy neural tree (Ciftcioglu et al. 2007a). This is particularly suitable for dealing with a complex linguistic concept like design performance. A neural tree is composed of one or several model output units, referred to as root nodes, that are connected to input units called terminal nodes, and the connections are via logic processors termed internal nodes. An example of a neural tree is shown in Fig. 6. The neural tree is used for performance evaluation by structuring the relationships between aspects of performance. The root node takes the meaning of high design performance and the inner nodes one level below are the aspects of the performance. The meaning of each of these aspects may vary from design project to design project and it is determined by experts. The model inputs shown as squares in Fig. 6 are fuzzy sets, such as those given in Fig. 5. Figure 7 shows details of the nodal connections of a neural tree, like the one shown in Fig. 6. In Fig. 7 wij is the weight assigned to the connection between terminal node i and inner node j. The weights are given by domain experts, and express the relative significance of the nodes. The centres of the basis functions are set to be the same as the weights of the connections arriving at that node. Therefore, for a terminal node connected to an inner node, the inner node output denoted by Oj, is obtained by the equation

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Fig. 7 Details of a neural tree structure showing the different type of node connections

Oj ¼ expð

 n  wij ðwi  1Þ 2 1 X Þ 2 i sj

(4)

where j is the number of the node; i denotes consecutive numbers associated to each input of the inner node; n denotes the highest number of the inputs arriving at node j; wi denotes the degree of membership being the output of the i-th terminal node; wij is the weight associated with the connection between the i-th terminal node and the inner node j; and sj denotes the width of the Gaussian of node j (Ciftcioglu et al. 2007b). One notes that the fuzzy logic operation performed at each node is an AND operation among the input components Xi coming to the node. This means for instance that if all the elemental requirements are fulfilled, then the design performance is high. For any other pattern of satisfaction on the elemental level, the performance is computed and obtained at the root node output. It is also noted that the model requires the establishment of the width parameter sj at every node. This is accomplished by imposing a consistency condition on the model. This condition ensures that when all inputs take a certain value, the model output yields the very same value (Ciftcioglu et al. 2007b). The consistency is ensured by means of gradient adaptive optimization identifying optimal sj values for each node.

4 Generating Solutions with Maximal Performance The information obtained from the performance evaluation is useful to search for designs that have superior performance. However, this process is not straight forward. Assuming we know that the performance of our design is moderate overall, how to increase its performance remains a difficult question. As a design consists of many design objects, such as several spaces, walls, floors, ceilings, etc., and each object has several parameters characterizing it, the amount of possible solutions to consider is enormous. This is termed combinatorial explosion. To deal with combinatorial explosion, advanced search methodologies emerged in the last decades in order to identify the most suitable solutions among the excessive amount of possible ones. The most prominent methodology is

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evolutionary computation (EC), due to its established effectiveness (Goldberg 1989; Coello 1999). Evolutionary computation has an inherent mechanism leading it towards suitable solutions that is inspired by biological evolution. This mechanism breeds better solutions through the combination of successful individuals. That is, the method generates a number of random possible solutions, evaluates their fitness, and then exchanges portions of the ‘genetic code’ that characterizes these between fit solutions. This is schematically shown in Fig. 8. Evolutionary computation is especially convenient for addressing problems where multiple objectives should be satisfied at the same time, like minimal cost and maximal functionality. In the multi-objective case the grading of fitness of solutions is based on a criterion referred to as Pareto non-dominance. A solution is termed Pareto non-dominated when there is no other solution that outperforms it for every objective involved. In other words, when compared to any other solution, a non-dominated solution is superior for at least one criterion. Evolutionary computation has been used for optimization in many engineering applications (Deb 2001). However, for use in design there are still two major drawbacks to using EC. The first is that EC conventionally uses crisp functions to evaluate the fitness of solutions. However, as pointed out in Sect. 3, many design requirements are soft, so that EC needs to be combined with other methods to handle this issue. The second issue concerns the effectiveness of EC in addressing problems with multiple objectives. Its effectiveness diminishes drastically if the amount of objectives exceeds about four or five. Therefore the solutions found may be of inferior quality and the diversity among solutions is too low for confident decision-making. This is a topical concern in evolutionary multi-objective optimization (Zitzler et al. 2003; Hughes 2005).

Fig. 8 Flowchart of a genetic algorithm

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4.1

An Approach Based on Synergy Among Different CI Methods

In this work both bottlenecks are addressed. The first issue concerning the softness of criteria is handled by coupling the neuro-fuzzy performance evaluation model described in Sect. 3 with a multi-objective evolutionary algorithm. The resulting system is shown in Fig. 9. In this case the fuzzy model plays the role of the fitness function. This means that the search process makes use of human-like reasoning as it strives for optimality. The second issue, concerning the effectiveness of multiobjectivity, is alleviated by applying a relaxed Pareto ranking concept during the search (Bittermann and Ciftcioglu 2009). From Fig. 9 we note that the computational design system starts its processing by generating a population of random solutions within the boundaries put forward by the designer in advance and instantiates them in virtual reality. Several properties of these solutions are then measured, such as sizes, distances, and perceptual properties. These are interpreted with respect to the elemental design requirements at the input layer of a fuzzy neural tree. This information is propagated through the tree, yielding the degree of satisfaction of the solution at the penultimate level right below the root node. That is, the evaluation using the fuzzy model is able to express the features of a solution in abstract, linguistic terms. For example it provides the performance regarding functionality, perception and cost effectiveness. These outputs are then used to compare the randomly generated solutions regarding their respective Pareto non-dominance. Relatively non-dominated solutions are then favoured for reproduction and the genetic operations, so that the next generation is more likely to contain non-dominated solutions. This generation-evaluation-loop is executed for a number of generations, finally resulting in a set of solutions that are all non-dominated. This set approximates a surface in objective space that is referred to as Pareto optimal front. A designer or decision-maker is then able to compare these solutions in order to select his favourite design among the apparently equally valid solutions. If the favourite solution completely satisfies the designer’s preferences, the design solution is

Fig. 9 System based on evolutionary computation, perception and fuzzy modelling

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Fig. 10 Cognitive design approach based on the CI system intelligent

found. Otherwise the designer may change the criteria of the computational design process and re-run the algorithm. This process iterates as shown in Fig. 10, where the box containing the term IDO represents the system shown in Fig. 9.

4.2

Cognitive Features of the System

The solutions on the Pareto front are not completely equivalent. As they should be, they are all non-dominated; however some solutions still have an advantage over the others in the following sense: At the root node of the neural tree, the performance score is computed by the defuzzification process given by w1 ð1Þf1 þ w2 ð1Þf2 þ ::: þ wn ð1Þfn ¼ p;

(5)

where w1+w2+. . .+wn ¼ 1; f1fn are the outputs at the penultimate nodes; p is the design performance, which is naturally requested to be maximized. The vector w containing the weights on the penultimate level is termed priority vector. The node outputs f1fn can be considered as the design feature vector f. The reflection of these features in the design performance is maximized if the weights w1wn define the same direction as that of the feature vector. Normalising the components and equating them to the weights yields f1 ; f1 þ f2 þ ::: þ fn fn ¼ f1 þ f2 þ ::: þ fn

w1 ¼

w2 ¼

f2 ; f1 þ f2 þ ::: þ fn

Due to Eq. 6 the performance given by Eq. 5 becomes

::: ; wn (6)

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pmax ¼

f12 þ f22 þ :::: þ fn2 f1 þ f2 þ :::: þ fn

(7)

Every solution on the Pareto front has an associated pmax value that characterizes it. This value gives the maximum design performance the solution attains, when there is no a-priori preference regarding the objectives. Solutions can be compared regarding their pmax value, and the solution with the highest value is preferable among the Pareto solutions. This solution has a characteristic priority vector w*. This vector implies that the computer advises the decision maker which goal he should make more or less important in the present task, information that was not known prior to the search process. This means that the machine performs an act beyond mere optimization or intelligent information processing. This act is an act of cognition, yielding information about second-order aspects that were not included in the criteria given by the human decision maker. The artificial cognition alleviates decision making in the sense that the designer need not explore the entire Pareto front, but has information on proficient areas on the front. It is noted that the computational search for the Pareto front yields objects with intelligent behaviour. That is, the objects need no explicit instruction to satisfy high-level criteria.

5 Two Applications of the System 5.1

Application 1

In this application, the design of an ensemble of residential housing units is considered. The problem is taken from an actual design case. The task is to find suitable locations of a number of housing units on their respective lots. The site belongs to one of the largest areas in the Netherlands subject to development, named Leidsche Rijn. The site has a size of about 3,600 m2. The streets and lots are provided in advance in this case. The site is shown in Fig. 11. In the figure, 20 houses are shown. Three of them are existing, namely E1, E2, and E3, so that 17 houses are subject to optimal positioning. In this task two main objectives are pursued. The first one is to maximize the visual privacy of the buildings, in particular that of their south facades, where the living rooms are situated. The second one is to maximize the size of the gardens. The visual privacy is computed using the perception model described in Sect. 2. The visual privacy of a fac¸ade is considered to be the reciprocal of the sum of attention “impinging” on the facade. In other words it quantifies how low the integral degree of perception of a fac¸ade is. Explicitly, we calculate the visual privacy of an object O as

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Fig. 11 The neighbourhood subject to design

Fig. 12 Visual privacy computation based on the probabilistic perception model

Ppriv ðOÞ ¼ P n

1

(8)

PðO; Vn Þ

1

where P(O,Vn) is the degree of perception of object O from the n-th viewpoint. Figure 12 illustrates the implementation of the visual privacy computation for the

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houses of the housing complex, where elemental perceptions in the form of vision rays are shown. As to the second criterion in this task, the maximum size of the garden facing south is restricted by the placement boundaries both north and south and the width of the house. This is illustrated in Fig. 13 using house H1 as an example. In the figure, the boundary of the lot is shown as a solid line and the placement boundary is shown as a dashed line. Explicitly, the garden performance G is given by g/gmax. This means the garden performance belonging to a house is calculated by dividing the extent of a garden towards the south by the maximum extent the garden can have, considering the boundary of the house’s plot. Figure 14 shows the requirement of high visual privacy for the various houses. It is noted that as the terminal node output increases with increasing privacy. The fuzzy neural tree used in this application is shown in Fig. 15. The resulting Pareto optimal front after 20 generations is shown in Fig. 16. Pareto optimal solutions 1 and 4 in Fig. 16 are shown in Figs. 17 and 18 for comparison. It is noted that solution 1 outperforms solution 4 as its maximal performance p from Eq. 7 is larger, namely .89 versus .85. This is seen in Fig. 16. In fact, solution 1 is the solution with the greatest maximal performance p among the Pareto solutions. This means that for the present task the computations indicate that privacy is a more significant factor in the design than garden size. This result could not be foreseen prior to executing the computational search process; it is an act of machine cognition. In terms of the parameters of the solutions, both designs differ significantly only in two places, namely house H6 and houses Gb1–Gb4 are located further north in design nr. 4. This is also an interesting result that could not be foreseen, namely that all Pareto solutions have a common optimal location pattern for most of the houses.

5.2

Application 2

This design task concerns the design of an interior space. The space is based on the main hall of the World Trade Centre in Rotterdam in the Netherlands. Figure 19 shows the main entrance hall of the building as seen from its entrance. In the figure, a virtual human observer can be seen viewing the interior space of the entrance hall. The perception of the virtual observer plays a role in the treatment of a number of perception based requirements for the design. An example is that the stairs should not be very noticeable from the entrance of the space. Another example is that the building core should be positioned in such a way that the entrance hall is spacious, while the elevators should be easily perceived at the same time. The task is therefore to optimally place the design objects to satisfy a number of perception and functionality requirements. The objects are a vertical building core containing the elevators, a mezzanine, stairs, and two vertical ducts.

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Fig. 13 Calculation of the garden performance

Fig. 14 Elemental requirements of visual privacy expressed via fuzzy membership functions

Fig. 15 Fuzzy neural tree for performance evaluation

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Fig. 16 Resulting Pareto optimal designs in objective space

Fig. 17 Pareto-optimal design marked with number 1 in figure 16

The goals are to maximize the performance of every design object as seen from the fuzzy neural tree structure in Fig. 20. As examples of the requirements at the terminal level, two are shown in Fig. 21. The resulting front of Pareto optimal solutions is shown in Fig. 22. It is noted that the objective space has four dimensions, one for the performance of every design

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Fig. 18 Pareto-optimal design marked with number 4 in figure 16

Fig. 19 The design objects of the task

Fig. 20 Two requirements are involved, concerning the spaciousness of the entrance hall (a) and the perception of the stairs (b)

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Fig. 21 Neural tree structure for assessment of design performance

Fig. 22 Pareto optimal designs with respect to the four objective dimensions

object. The representation is obtained by first categorizing the solutions according to which of the four quadrants they belong to, in the two-dimensional objective space formed by the building core and mezzanine performance, and then

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Fig. 23 Design D2

Fig. 24 Design D4

representing the performance of stairs and ducts with a coordinate system for each quadrant. This way four dimensions are shown on the two-dimensional page. Two Pareto optimal designs are shown in Figs. 23 and 24 for comparison. Design D2 outperforms design D3 with respect to the maximal performance p obtained using Eq. 7. Namely D2 scores .78, whereas D4 scores .71. Regarding the satisfaction of the individual objectives, the greatest absolute difference between D2 and D4 is with respect to the performance of the mezzanine. In D2 the mezzanine is located closer to associated functions, and this turns out to be more important relative to the fact that D4 yields more daylight on the mezzanine. D2 therefore scores higher that D4 regarding the mezzanine. Additionally, D2 slightly outperforms D4 regarding the performance of the ducts. This is because the ducts do not penetrate the mezzanine in D2, whereas in D4 they do. The latter is undesirable according to the requirements. Regarding the building core, D2 is inferior to D4, because D4 is more spacious and also because the elevators are

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more centrally located. Regarding the stairs’ performance, the difference between D2 and D4 is negligible. It is emphasized that D2 is the solution with the greatest maximal performance pmax, so that from an unbiased viewpoint it is the most suitable solution to be selected for construction. This result is an act of machine cognition, as it reveals that in the present task the stairs and ducts are more important than the building core. This information was not known prior to the execution of the computational search process.

6 Conclusions A novel computational system for architectural design is presented, and its effectiveness is demonstrated through two applications. It generates designs that satisfy multiple vague criteria that are conflicting. The application results show that the system is capable of dealing with three complexity issues that are challenging computational design approaches. The system handles the common vagueness of requirements induced by visual perception through using a visual perception model that yields the degree to which an unbiased observer is aware of environmental objects. The special neural structure with embedded fuzzy logic processors of the associated performance model is shown to be suitable for handling the vagueness of requirements, where it deals with both the complexity and vagueness of design objectives at the same time. Multi-objective evolutionary search is demonstrated to be an effective framework for addressing the complexity of the design task, in particular as it is able to take the information provided by the fuzzy model into account during its search process. This combination is particularly effective as it permits the evolutionary search to deal with a large amount of requirements. It is further demonstrated that using the fuzzy model in the evolutionary framework yields a form of computational cognition, so that a preferable preference vector is pinpointed from an unbiased viewpoint. This is a demonstration of an act of computational cognition, as it includes determining second-order preferences that were not known before executing the design. From the perspective of architectural practice, the contribution of this approach is that project solutions can be assessed without any presupposition, increasing designers’ confidence of finding the best solution. It is noted that the computational design process is in a symbiotic partnership with the designer. That is, computation takes care of those aspects of designing which are computationally intensive and sensitive to imprecision, giving a designer advanced means to exercise his/her creative ideas with greater effectiveness.