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

翻译：箱约束限制了决策变量的取值范围，并常见于现实世界优化问题中，例如由物理、自然或空间限制所致。因此，违反箱约束的解可能无法被评估。这一假设在文献中常被忽略，例如现有基准测试套件（如COCO/BBOB）允许优化器评估不可行解。本文针对严格箱约束基准测试框架（SBOX-COST）展开初步研究，该框架是著名BBOB基准测试套件的变体，通过为不可行解返回无效评估值来强制执行箱约束。具体而言，我们旨在理解BBOB与SBOX-COST之间的性能差异，其取决于两种初始化方法和六种约束处理策略——所有测试均采用模组化CMA-ES。研究发现，与预期相反，通过饱和方式处理箱约束并非始终优于完全不处理约束。然而，在所有BBOB函数上，饱和处理优于不处理，且这种优势随维度增加而扩大。严格强制执行箱约束还会对经典CMA-ES（采用均匀随机初始化且无约束处理）的性能产生明显的负面影响，尤其当问题维度增加时更为显著。