MOPED: a Multi-Objective Parzen-based Estimation of Distribution algorithm for continuous problems Mario Costa 1 , Edmondo Minisci 2 1 Department of Electronics, Polytechnic of Turin, C.so Duca degli Abruzzi, 24, 10129 Turin, ITALY mario.costa@polito.it 2 Department of Aerospace Engineering, Polytechnic of Turin, C.so Duca degli Abruzzi, 24, 10129, Turin, ITALY edmondo_minisci@yahoo.it Abstract. An evolutionary multi-objective optimization tool based on an estimation of distribution algorithm is proposed. The algorithm uses the ranking method of non-dominated sorting genetic algorithm-II and the Parzen estimator to approximate the probability density of solutions lying on the Pareto front. The proposed algorithm has been applied to different types of test case problems and results show good performance of the overall optimization procedure in terms of the number of function evaluations. An alternative spreading technique that uses the Parzen estimator in the objective function space is proposed as well. When this technique is used, achieved results appear to be qualitatively equivalent to those previously obtained by adopting the crowding distance described in non-dominated sorting genetic algorithm-II. 1 Introduction The extensive use of evolutionary algorithms in the last decade demonstrated that an optimization process can be obtained by combining effects of interactive operators such as selection - whose task is mainly to identify the best individuals in the current population - and crossover and mutation, which try to generate new and better solutions starting from the selected ones. But, if the mimicking of natural evolution in living species has been a source of inspiration of new strategies, the attempt to copy natural techniques as they are sometimes introduces a great complexity without a corresponding improvement of algorithms performance. Moreover standard evolutionary algorithms can be ineffective when problems exhibit a high level of interaction among variables. This is mainly due to the fact that recombination operators are likely to disrupt promising sub-structures of optimal solutions. Alternatively, in order to make a rational use of the evolutionary metaphor and/or to create optimization tools that are able to handle very hard problems (with several parameters, with difficulties in linkage learning, deceptive), some algorithms have been proposed that automatically learn the structure of the search space. Following this way, several works, based on explicit probabilistic-statistic tools, have been carried out.