A CMA-ES-based 2-stage memetic framework for solving constrained optimization problems

Abstract

Constraint optimization problems play a crucial role in many application domains, ranging from engineering design to finance and logistics. Specific techniques are therefore needed to handle complex fitness landscapes characterized by multiple constraints. In the last decades, a number of novel meta-heuristics have been applied to constraint optimization. Among these, the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) has been attracting lately the most attention of researchers. Recent variants of CMA-ES showed promising results on several benchmarks and practical problems. In this paper, we attempt to improve the performance of an adaptive penalty CMA-ES recently proposed in the literature. We build upon it a 2-stage memetic framework, coupling the CMA-ES scheme with a local optimizer, so that the best solution found by CMA-ES is used as starting point for the local search. We test, separately, the use of three classic local search algorithms (Simplex, BOBYQA, and L-BFGS-B), and we compare the baseline scheme (without local search) and its three memetic variants with some of the state-of-the-art methods for constrained optimization.