用沃尔什系数识别噪声干扰的无关变量依赖，提升优化效率
On Revealing the Hidden Problem Structure in Real-World and Theoretical Problems Using Walsh Coefficient Influence
- 通过扩展沃尔什分解，量化变量间依赖强度
- 在含噪声问题中，使优化器效果显著提升
- 适合处理现实世界中存在噪声的复杂优化问题
灰盒优化利用沃尔什分解识别非线性变量依赖，并生成对适应度有联合影响的变量掩码，显著提升变异算子效能。但在某些问题中，所有变量均存在非线性依赖，导致上述掩码失效。我们分析此类问题的真实实例特征，发现许多依赖具有类噪声来源，与优化过程无关，可忽略。为此，提出扩展沃尔什分解，通过测量变量依赖强度构建加权动态变量交互图（wdVIG）。wdVIG能调整混合个体中的依赖强度，过滤无关依赖，重新启用基于依赖的掩码。我们在大规模基准测试中验证了wdVIG潜力：在含噪声问题中，wdVIG掩码显著提升优化器有效性；当所有依赖均相关时（无噪声），wdVIG掩码效果与现有最先进结构相当。
原文摘要 · Abstract (English)
Gray-box optimization employs Walsh decomposition to obtain non-linear variable dependencies and utilize them to propose masks of variables that have a joint non-linear influence on fitness value. These masks significantly improve the effectiveness of variation operators. In some problems, all variables are non-linearly dependent, making the aforementioned masks useless. We analyze the features of the real-world instances of such problems and show that many of their dependencies may have noise-like origins. Such noise-caused dependencies are irrelevant to the optimization process and can be ignored. To identify them, we propose extending the use of Walsh decomposition by measuring variable dependency strength that allows the construction of the weighted dynamic Variable Interaction Graph (wdVIG). wdVIGs adjust the dependency strength to mixed individuals. They allow the filtering of irrelevant dependencies and re-enable using dependency-based masks by variation operators. We verify the wdVIG potential on a large benchmark suite. For problems with noise, the wdVIG masks can improve the optimizer's effectiveness. If all dependencies are relevant for the optimization, i.e., the problem is not noised, the influence of wdVIG masks is similar to that of state-of-the-art structures of this kind.
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