Evolutionary Multi-Factorial Optimization Using Estimated Objective Function Similarities

Abstract

This paper proposes an evolutionary algorithm named MFEA/OS (Multi-Factorial Evolutionary Algorithm based on Objective Similarity) for multi-factorial optimization that aims to optimize multiple objective functions simultaneously. In evolutionary multi-factorial optimization, each solution in the population is associated with an objective function to be optimized. Evolutionary variation such as crossover is applied to two solutions, even if they are associated with different objective functions. This interaction is expected to enhance the simultaneous optimization of multiple objective functions. However, generating new offspring solutions from parent solutions associated with dissimilar objective functions would actually be harmful to their simultaneous optimization. For each pair of objective functions, the proposed MFEA/OS calculates the difference in the distributions of their associated solutions in the variable space as the objective similarity. The proposed MFEA/OS then encourages evolutionary variation between two solutions associated with similar objective functions. To verify the effects of the proposed MFEA/OS, this work uses continuous and discrete test problems that can adjust the similarities among multiple objective functions. Experimental results show that the proposed MFEA/OS can estimate the objective similarities in continuous and discrete test problems and achieves higher multi-factorial optimization performance than conventional algorithms in both test problems with correlated objective functions.