We present a novel approach for constructing discrete optimization benchmarks that enables fine-grained control over problem properties, and such benchmarks can facilitate analyzing discrete algorithm behaviors. We build benchmark problems based on a set of block functions, where each block function maps a subset of variables to a real value. Problems are instantiated through a set of block functions, weight factors, and an adjacency graph representing the dependency among the block functions. Through analyzing intermediate block values, our framework allows to analyze algorithm behavior not only in the objective space but also at the level of variable representations in the obtained solutions. This capacity is particularly useful for analyzing discrete heuristics in large-scale multi-modal problems, thereby enhancing the practical relevance of benchmark studies. We demonstrate how the proposed approach can inspire the related work in self-adaptation and diversity control in evolutionary algorithms. Moreover, we explain that the proposed benchmark design enables explicit control over problem properties, supporting research in broader domains such as dynamic algorithm configuration and multi-objective optimization.

翻译：我们提出了一种构建离散优化基准测试的新方法，该方法能够对问题属性进行细粒度控制，且此类基准测试有助于分析离散算法的行为。我们基于一组块函数构建基准问题，其中每个块函数将变量的一个子集映射到一个实数值。问题通过一组块函数、权重因子以及表示块函数间依赖关系的邻接图来实例化。通过分析中间块值，我们的框架不仅能在目标空间分析算法行为，还能在所得解中变量表示的层面进行分析。这种能力对于分析大规模多模态问题中的离散启发式算法尤为有用，从而增强了基准研究的实际相关性。我们展示了所提方法如何能够启发进化算法中自适应和多样性控制的相关工作。此外，我们解释了所提出的基准设计能够显式控制问题属性，支持更广泛领域的研究，例如动态算法配置和多目标优化。