Non-dominated Sorting and Crowding Distance Based Multi-objective Chaotic Evolution

Abstract

We propose a new evolutionary multi-objective optimization (EMO) algorithm based on chaotic evolution optimization framework, which is called as multi-objective chaotic evolution (MOCE). It extends the optimization application of chaotic evolution algorithm to multi-objective optimization field. The non-dominated sorting and tournament selection using crowding distance are two techniques to ensure Pareto dominance and solution diversity in EMO algorithm. However, the search capability of multi-objective optimization algorithm is a serious issue for its practical application. Chaotic evolution algorithm presents a strong search capability for single objective optimization due to the ergodicity of chaotic system. Proposed algorithm is a promising multi-objective optimization algorithm that composes a search algorithm with strong search capability, dominant sort for keeping Pareto dominance, and tournament selection using crowding distance for increasing the solution diversity. We evaluate our proposed MOCE by comparing with NSGA-II and an algorithm using the basic framework of chaotic evolution but different mutation strategy. From the evaluation results, the MOCE presents a strong optimization performance for multi-objective optimization problems, especially in the condition of higher dimensional problems. We also analyse, discuss, and present some research subjects, open topics, and future works on the MOCE.