CES-485 Approximating the Set of Pareto Optimal Solutions in Both the Decision and Objective Spaces by an Estimation of Distribution Algorithm

Most existing multiobjective evolutionary algorithms aim at approximating the PF, the distribution of the Pareto optimal solutions in the objective space. In many real-life applications, however, a good approximation to the PS, the distribution of the Pareto optimal solutions in the decision space, is also required by a decision maker. This paper considers a class of MOPs, in which the dimensionalities of the PS and PF are different so that a good approximation to the PF might not approximate the PS very well. It proposes a probabilistic model based multiobjective evolutionary algorithm, called MMEA, for approximating the PS and the PF simultaneously for a MOP in this class. In the modelling phase of MMEA, the population is clustered into a number of subpopulations based on their distribution in the objective space, the PCA technique is used to detect the dimensionality of the centroid of each subpopulation, and then a probabilistic model is built for modelling the distribution of the Pareto optimal solutions in the decision space. Such modelling procedure could promote the population diversity in both the decision and objective spaces. To ease the burden of setting the number of subpopulations, a dynamic strategy for periodically adjusting it has been adopted in MMEA. The experimental comparison between MMEA and the two other methods, KP1 and Omni-Optimizer on a set of test instances, some of which are proposed in this paper, have been made in this paper. It is clear from the experiments that MMEA has a big advantage over the two other methods in approximating both the PS and the PF of a MOP when the PS is a nonlinear manifold, although it might not be able to perform significantly better in the case when the PS is a linear manifold.