Abstract This paper proposes a novel covariance matrix adaptation evolution strategy (CMA-ES) variant, named AEALSCE, for single-objective numerical optimization problems in the continuous domain. To avoid premature convergence and strengthen the exploration capacity of the basic CMA-ES, AEALSCE is obtained by integrating the CMA-ES with two strategies that can adjust the evolutionary directions and enrich the population diversity. The first strategy is named the anisotropic eigenvalue adaptation (AEA) technique, which adapts the search scope towards the optimal evolutionary directions. It scales the eigenvalues of the covariance matrix anisotropically based on local fitness landscape detection. The other strategy is named the local search (LS) strategy, which is executed under the eigen coordinate system and can be subdivided into two parts. In the first part, the new candidates of superior solutions are sampled around the best solution to perform local exploration. In the other part, the new candidates of inferior solutions are generated using a modified mean point along the fitness descent direction. The proposed AEALSCE algorithm is compared with other top competitors, including the CEC 2014 champion, L-SHADE, and the promising NBIPOP-aCMA-ES, by benchmarking the CEC 2014 testbed. Moreover, AEALSCE is applied in solving three constrained engineering design problems and parameter estimation of photovoltaic (PV) models. According to the statistical results of the experiments, our proposed AEALSCE is competitive with other algorithms in convergence efficiency and accuracy. AEALSCE benefits from a good balance of exploration and exploitation, and it exhibits a potential to address real-world optimization problems.
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A covariance matrix adaptation evolution strategy variant and its engineering application
Semantic Scholar · Engineering · 2019
Abstract
Abstract This paper proposes a novel covariance matrix adaptation evolution strategy (CMA-ES) variant, named AEALSCE, for single-objective numerical optimization problems in the continuous domain. To avoid premature convergence and strengthen the exploration capacity of the basic CMA-ES, AEALSCE is obtained by integrating the CMA-ES with two strategies that can adjust the evolutionary directions and enrich the population diversity. The first strategy is named the anisotropic eigenvalue adaptation (AEA) technique, which adapts the search scope towards the optimal evolutionary directions. It scales the eigenvalues of the covariance matrix anisotropically based on local fitness landscape detection. The other strategy is named the local search (LS) strategy, which is executed under the eigen coordinate system and can be subdivided into two parts. In the first part, the new candidates of superior solutions are sampled around the best solution to perform local exploration. In the other part, the new candidates of inferior solutions are generated using a modified mean point along the fitness descent direction. The proposed AEALSCE algorithm is compared with other top competitors, including the CEC 2014 champion, L-SHADE, and the promising NBIPOP-aCMA-ES, by benchmarking the CEC 2014 testbed. Moreover, AEALSCE is applied in solving three constrained engineering design problems and parameter estimation of photovoltaic (PV) models. According to the statistical results of the experiments, our proposed AEALSCE is competitive with other algorithms in convergence efficiency and accuracy. AEALSCE benefits from a good balance of exploration and exploitation, and it exhibits a potential to address real-world optimization problems.