An adaptive penalty based covariance matrix adaptation-evolution strategy

Although most of unconstrained optimization problems with moderate to high dimensions can be easily handled with Evolutionary Computation (EC) techniques, constraint optimization problems (COPs) with inequality and equality constraints are very hard to deal with. Despite the fact that only equality constraints can be used to eliminate a certain variable, both types of constraints implicitly enforce a relation between problem variables. Most conventional constraint handling methods in EC do not consider the correlations between problem variables imposed by the problem constraints. This paper relies on the idea that a proper genetic operator, which captures mentioned implicit correlations, can improve performance of evolutionary constrained optimization algorithms. With this in mind, we employ a (μ+λ)-Evolution Strategy with a simplified variant of Covariance Matrix Adaptation based mutation operator along an adaptive weight adjustment scheme. The proposed algorithm is tested on two test sets. The outperformance of the algorithm is significant on the first benchmark when compared with five conventional methods. The results on the second test set show that algorithm is highly competitive when benchmarked with three state-of-art algorithms. The main drawback of the algorithm is its slightly lower speed of convergence for problems with high dimension and/or large search domain.