An Individual and Model-Based Offspring Generation Strategy for Evolutionary Multiobjective Optimization

Abstract

According to the Karush–Kuhn–Tucker condition, the Pareto set (PS) of a continuous <inline-formula> <tex-math notation= LaTeX >$m$ </tex-math></inline-formula>-objective optimization problem is a continuous (<inline-formula> <tex-math notation= LaTeX >$m-1$ </tex-math></inline-formula>)<inline-formula> <tex-math notation= LaTeX >$-D$ </tex-math></inline-formula> piecewise manifold. Based on this regularity property, the ratio of the sum of the first (<inline-formula> <tex-math notation= LaTeX >$m-1$ </tex-math></inline-formula>) largest eigenvalue of the population’s covariance matrix to the sum of the whole eigenvalue can be employed to illustrate the degree of convergence of the population. This paper proposes a new algorithm, named DE/RM-MEDA, which hybridizes differential evolution (DE) and estimation of distribution algorithm (EDA) for multiobjective optimization problems (MOPs) with the complicated PS. In the proposed algorithm, EDA extracts the population distribution information to sample new trial solutions by establishing a probability model, while DE uses the individual information to create others new individuals through the mutation and crossover operators. At each generation, the number of new solutions generated by the two operators is adjusted by the above-defined ratio. The proposed algorithm is validated on nine tec09 problems. The sensitivity and the scalability have also been experimentally investigated in this paper. The comparison results between DE/RM-MEDA and the other two state-of-the-art evolutionary algorithms, namely NSGA-II-DE and RM-MEDA, show that the proposed algorithm is highly competitive algorithms for solving MOPs with complicated PSs in terms of convergence and diversity metrics.