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A modified Covariance Matrix Adaptation Evolution Strategy with adaptive penalty function and restart for constrained optimization

In the last decades, a number of novel meta-heuristics and hybrid algorithms have been proposed to solve a great variety of optimization problems. Among these, constrained optimization problems are considered of particular interest in applications from many different domains. The presence of multiple constraints can make optimization problems particularly hard to solve, thus imposing the use of specific techniques to handle fitness landscapes which generally show complex properties. In this paper, we introduce a modified Covariance Matrix Adaptation Evolution Strategy (CMA-ES) specifically designed for solving constrained optimization problems. The proposed method makes use of the restart mechanism typical of most modern variants of CMA-ES, and handles constraints by means of an adaptive penalty function. This novel CMA-ES scheme presents competitive results on a broad set of benchmark functions and engineering problems, outperforming most state-of-the-art algorithms as for both efficiency and constraint handling.

 

Highlights:

  • We introduce a modified Covariance Matrix Adaptation Evolution Strategy.
  • Our CMA-ES is specifically designed for solving constrained optimization problems.
  • The proposed method makes use of a restart mechanism and adaptive penalty function.
  • This novel CMA-ES presents competitive results on a set of benchmark functions.

Vinícius Veloso De Melo and Giovanni Iacca. 2014. A modified Covariance Matrix Adaptation Evolution Strategy with adaptive penalty function and restart for constrained optimization. Expert Syst. Appl. 41, 16 (November 2014), 7077-7094. DOI=10.1016/j.eswa.2014.06.032 http://dx.doi.org/10.1016/j.eswa.2014.06.032

 

@article{DeMelo:2014:MCM:2658287.2658459,
author = {De Melo, Vin\’{\i}cius Veloso and Iacca, Giovanni},
title = {A Modified Covariance Matrix Adaptation Evolution Strategy with Adaptive Penalty Function and Restart for Constrained Optimization},
journal = {Expert Syst. Appl.},
issue_date = {November, 2014},
volume = {41},
number = {16},
month = nov,
year = {2014},
issn = {0957-4174},
pages = {7077–7094},
numpages = {18},
url = {http://dx.doi.org/10.1016/j.eswa.2014.06.032},
doi = {10.1016/j.eswa.2014.06.032},
acmid = {2658459},
publisher = {Pergamon Press, Inc.},
address = {Tarrytown, NY, USA},
keywords = {Adaptive penalty function, Constrained optimization, Covariance Matrix Adaptation Evolution Strategy},
}

 
Keywords:
Optimització constret. Matriu de covariància adaptació evolució estratègia. Funció adaptativa pena.
约束的优化问题。协方差矩阵适应进化策略。自适应惩罚函数。
約束的優化問題。共變數矩陣適應進化策略。自我調整懲罰函數。
Optimisation contrainte. Stratégie d’évolution Adaptation matrice de covariance. Fonction adaptative de pénalité.
Eingeschränkte Optimierung. Kovarianz Matrix Evolution Anpassungsstrategie. Adaptive Penalty-Funktion.
विवश अनुकूलन। सहप्रसरण मैट्रिक्स अनुकूलन विकास रणनीति। अनुकूली पेनल्टी समारोह।
Dihalang pengoptimuman. Covariance matriks strategi evolusi adaptasi. Fungsi hukuman penyesuaian.
Optimización con restricciones. Covarianza matriz estrategia de evolución de adaptación. Función adaptativa de la pena.