Multi-objective differential evolution with dynamic covariance matrix learning for multi-objective optimization problems with variable linkages

Recently, many multi-objective differential evolution versions (MODEs) have been developed by incorporating the search engine of differential evolution (DE) and multi-objective processing mechanisms. However, most existing MODEs perform poorly in solving multi-objective optimization problems (MOPs) with variable linkages. The cause of this poor performance is the rotational variability of binomial crossover operator (BCO), which is not conducive to making simultaneous progress across all variables within a solution vector in the search for such MOPs. To alleviate the limitation, dynamic covariance matrix learning (DCML) based on the information distribution of the entire or a portion of the population is proposed to establish a proper coordinate system for the BCO by eigen decomposition. In this method, the rotational invariance of DE can be enhanced to a certain extent by releasing the interactions among the variables; thus, it is useful for MODEs to better balance their exploration and exploitation abilities. By integrating the DCML into existing MODEs, a class of new MODEs, which are called MODEs + DCML for short, are presented in this study. For comparison purposes, the proposed DCML strategy is applied to four commonly used MODEs. Twenty-nine benchmark problems with variable linkages are selected as the test suite to evaluate the performance of the proposed MODEs + DCML. The experimental results show that the proposed DCML can significantly improve the performance of the state-of-the-art MODEs in most test functions.