A Novel Two-Stage Hybrid Multi-Objective Differential Evolution with Opposition Based-Learning

Abstract

Evolutionary algorithms have been shown to be powerful for solving multi-objective optimization problems, where non-dominated sorting is a widely adopted selection method. Differential Evolution (DE) is a simple and efficient population-based EA that has been reported in several studies for its high robustness, fast convergence speed, and good solution quality, making it a very popular EA in the evolutionary computing community. In this paper, a new two stage hybridized multi-objective differential evolution algorithm MODE based on opposition learning OBL is proposed, which balances exploration and exploitation capabilities as found in the original differential evolution DE, as well as OBL that brings higher selection pressure. in this developed approach, two stage are evolved. Firstly, MODE based on ranking mutation is applied using non-dominated sorting and crowding distance. Secondly, jumping probability is used in second stage in order to meet the objective of balancing the precision of the solution and the rate of convergence while maintaining the diversity of the population by opposition-based learning technique. Through the validation of MODE-OBL using a suite of carefully selected test reference problems for continuous multi-objective optimization, it is observed that MODE-OBL achieves overall better performance in terms of convergence and diversity compared to other algorithms of literature. In addition, MODE-OBL can be recommended to solve large portfolio optimization problems as well as problems with complex Pareto sets, as evidenced by its superior optimization performance in these types of problems.