Individuals redistribution based on differential evolution for covariance matrix adaptation evolution strategy

Zhe Chen,Yuanxing Liu

doi:10.1038/s41598-021-04549-1

Abstract

Among population-based metaheuristics, both Differential Evolution (DE) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) perform outstanding for real parameter single objective optimization. Compared with DE, CMA-ES stagnates much earlier in many occasions. In this paper, we propose CMA-ES with individuals redistribution based on DE, IR-CMA-ES, to address stagnation in CMA-ES. We execute experiments based on two benchmark test suites to compare our algorithm with nine peers. Experimental results show that our IR-CMA-ES is competitive in the field of real parameter single objective optimization.

Highlights

Among population-based metaheuristics, both Differential Evolution (DE) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) perform outstanding for real parameter single objective optimization
Our IR-CMA-ES is compared with nine population-based metaheuristics, L-SHADE5, UMOEAs-II7, jSO15, L-PalmDE16, HS-ES4, HARDDE17, NDE18, PaDE19, and CSDE20
Among the above competitors selected by us, UMOEAs-II is based on both CMA-ES and DE, while HS-ES is based on CMA-ES

Summary

Introduction

Among population-based metaheuristics, both Differential Evolution (DE) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) perform outstanding for real parameter single objective optimization. Among types of population-based metaheuristic for real parameter single objective optimization, both Differential Evolution (DE) and Covariance Matrix Adaptation Evolution Strategy (CMA-ES) perform outstanding. In the six competitions on real parameter single objective optimization among population-based metaheuristics held by Congress of Evolutionary Computation (CEC), there are seven winners, including two joint winners in 2016. In execution of population-based metaheuristics, two phenomena, early convergence and stagnation, which both lead to the fact that no further improvement on solution can be made, are very common. For non-trivial instance of real parameter single objective optimization, stagnation occurs much more often than early convergence in execution of types of populationbased metaheuristics, including DE and CMA-ES. DE may be a good choice for improving CMA-ES on resisting stagnation

Methods

Results

Discussion

Conclusion