Comparing Boundary Handling Techniques of CMA-ES on the bbob and sbox-cost Test Suites

Bound constraints on the variables are the most basic constraints in an optimization problem formulation and, thus, among the most common. It is therefore essential to understand the impact of different boundary handling techniques on algorithm performance. Equally, it is important to understand the practical impact of using bound constraint handling in an algorithm on principally unbounded problems but where the user has a good indication of the domain of the (sought) optimum. Both questions will be investigated in this paper on the newly introduced box-constrained version sbox-cost of the well-known, unconstrained test suite bbob and for the example of the two boundary handling techniques, implemented in the CMA-ES python module pycma. The numerical experiments performed with the COCO platform show that there is (i) only a minor difference in performance between the two test suites and (ii) a slight performance reduction for the (default) BoundTransform boundary handling compared to the BoundPenalty version of CMA-ES.