Evaluating MAP-elites on constrained optimization problems

Constrained optimization problems are often characterized by multiple constraints that, in the practice, must be satisfied with different tolerance levels. Here, we evaluate the applicability of MAP-Elites to “illuminate” constrained search spaces by mapping them into feature spaces where each feature corresponds to a different constraint. We demonstrate the feasibility of this approach on a large set of benchmark problems, in various dimensionalities, and with different algorithmic configurations. As expected, numerical results show that a basic version of MAP-Elites cannot compete with state-of-the-art algorithms that use gradient information or constraint handling techniques. Nevertheless, it can find constraint violations vs. objectives trade-offs and thus provide new problem information. As such, it could be used in the future as an effective building-block for designing new constrained optimization algorithms.