An adaptive helper and equivalent objective evolution strategy for constrained optimization

Abstract

The matrix adaptation evolution strategy is a simplified covariance matrix adaptation evolution strategy with reduced computational cost. Using it as a search engine, several algorithms have been recently proposed for constrained optimization and have shown excellent performance. However, these algorithms require the simultaneous application of multiple techniques to handle constraints, and also require gradient information. This makes them inappropriate for handling non-differentiable functions. This paper proposes a new matrix adaption evolutionary strategy for constrained optimization using helper and equivalent objectives. The method optimizes two objectives but with no need for special handling of infeasible solutions and without gradient information. A new mechanism is designed to adaptively adjust the weights of the two objectives according to the convergence rate. The efficacy of the proposed algorithm is evaluated using computational experiments on the IEEE CEC 2017 Constrained Optimization Competition benchmarks. Experimental results demonstrate that it outperforms current state-of-the-art evolutionary algorithms. Furthermore, this paper provides sufficient conditions for the convergence of helper and equivalent objective evolutionary algorithms and proves that using helper objectives can reduce the likelihood of premature convergence.