MEMOTS : a Memetic Algorithm Integrating Tabu Search for Multiobjective Optimization Thibaut Lust and Jacques Teghem Laboratory of Mathematics & Operational Research, Facult´e Polytechnique de Mons 9, rue de Houdain B-7000 Mons, Belgium [email protected]

Abstract In multiobjective optimization problems, several criteria are defined correspondent to various functions to be minimized or maximized. Compared to single optimization, an additional difficulty appears, since the criteria considered are generally contradictory what leads to situations where to improve a criterion can be done only to the detriment of the others. Consequently, the aim is not to find the optimal solution of the problem, but a sufficiently broad set of solutions known as efficient or Pareto. An efficient solution, is a non-dominated solution, i.e. there is not a solution at least also good on all the criteria and better on at least a criterion. The decision maker will then select one of the efficient solutions that adequately reflects his preferences. To generate the set of efficient solutions of difficult optimization problems, exacts methods are inefficient, and this is why the metaheuristics were quite recently adapted to multiobjective problems [1]. We present a new metaheuristic, called MEMOTS, to find a good approximation of the set of efficient solutions of multiobjective problems. The MEMOTS method is based on a memetic algorithm, also called genetic local search [5]. At each offspring generated by MEMOTS, we apply a local search method, which is an original multiobjective Tabu Search. The role of the Tabu Search in MEMOTS is to intensify the research, while diversification is ensured by a population of solutions among which the individuals of low density are selected. MEMOTS, contrary to a great number of other methods [2, 3, 4, 6], has the advantage of not using an aggregation function employing weight sets, which clear up the problem of their determination and the normalization of the values taken by the criteria. We experiment the MEMOTS method on the multidimensional multiobjective knapsack 1

problem, and show that the performances of MEMOTS are greater than MOGLS [4], a famous multiobjective method.

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