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Box-constraints limit the domain of decision variables and are common inreal-world optimization problems, for example, due to physical, natural orspatial limitations. Consequently, solutions violating a box-constraint may notbe evaluable. This assumption is often ignored in the literature, e.g.,existing benchmark suites, such as COCO/BBOB, allow the optimizer to evaluateinfeasible solutions. This paper presents an initial study on thestrict-box-constrained benchmarking suite (SBOX-COST), which is a variant ofthe well-known BBOB benchmark suite that enforces box-constraints by returningan invalid evaluation value for infeasible solutions. Specifically, we want tounderstand the performance difference between BBOB and SBOX-COST as a functionof two initialization methods and six constraint-handling strategies all testedwith modular CMA-ES. We find that, contrary to what may be expected, handlingbox-constraints by saturation is not always better than not handling them atall. However, across all BBOB functions, saturation is better than nothandling, and the difference increases with the number of dimensions. Strictlyenforcing box-constraints also has a clear negative effect on the performanceof classical CMA-ES (with uniform random initialization and no constrainthandling), especially as problem dimensionality increases.

Analysis of modular CMA-ES on strict box-constrained problems in the SBOX-COST benchmarking suite