Distance Minimization Problems for Multi-factorial Evolutionary Optimization Benchmarking

Abstract

This paper proposes multi-factorial distance minimization problems for benchmarking of multi-factorial optimization. The multi-factorial optimization simultaneously searches for optimal solutions of multiple objective functions in the common variable space and is recently a popular issue regarding evolutionary optimization. The conventional multi-factorial benchmark problems combine multiple existing single-objective benchmark problems. However, the correlation degree among their objectives is unclear and there is a lack of scalability in the number of objectives and visual analyzability of the search behavior. In the multi-objective optimization field, the distance minimization problem has been employed due to the scalability in the number of objectives and visual analyzability. In this work, we apply their benefits to the multi-factorial optimization field. We show the search performances and behaviors of the representative multi-factorial evolutionary algorithms on the multi-factorial distance minimization problems when the correlation among objectives and the number of objectives are varied.