RM-MEDA: A Regularity Model-Based Multiobjective Estimation of Distribution Algorithm

Abstract

Under mild conditions, it can be induced from the Karush-Kuhn-Tucker condition that the Pareto set, in the decision space, of a continuous multiobjective optimization problem is a piecewise continuous (m - 1)-D manifold, where m is the number of objectives. Based on this regularity property, we propose a regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for continuous multiobjective optimization problems with variable linkages. At each generation, the proposed algorithm models a promising area in the decision space by a probability distribution whose centroid is a (m - 1)-D piecewise continuous manifold. The local principal component analysis algorithm is used for building such a model. New trial solutions are sampled from the model thus built. A nondominated sorting-based selection is used for choosing solutions for the next generation. Systematic experiments have shown that, overall, RM-MEDA outperforms three other state-of-the-art algorithms, namely, GDE3, PCX-NSGA-II, and MIDEA, on a set of test instances with variable linkages. We have demonstrated that, compared with GDE3, RM-MEDA is not sensitive to algorithmic parameters, and has good scalability to the number of decision variables in the case of nonlinear variable linkages. A few shortcomings of RM-MEDA have also been identified and discussed in this paper.