First Improvement Hill Climber with Linkage Learning -- on Introducing Dark Gray-Box Optimization into Statistical Linkage Learning Genetic Algorithms

Abstract

Gray-box optimization requires user-supported information about inter-variable dependencies to propose more effective optimizers for hard combinatorial problems. In Black-box optimization, such information is unavailable. Therefore, the Gray-box operators are only usable in Black-box scenarios if an optimizer can discover the inter-variable dependencies independently. Empirical Linkage Learning (ELL) techniques are guaranteed to discover only the true dependencies, which led to proposing the Dark Gray-box optimizers class. Such optimizers use ELL to construct Empirical Variable Interaction Graph (eVIG), which may miss some dependencies but contains only the true ones. eVIG allows using Gray-box operators in Black-box scenarios. ELL techniques are computationally expensive. Therefore, the recently proposed Local Search with Linkage Learning (LSwLL) is promising because it makes ELL a no-cost technique. However, LSwLL has some disadvantages. First, it can decompose only the problems of additive nature. Second, LSwLL removes ELL costs, but in some optimization scenarios, it may be expensive itself. Therefore, we propose the First Improvement Hill Climber with Linkage Learning (FIHCwLL). FIHCwLL decomposes additive and non-additive problems, and its overall costs are frequently lower than LSwLL (although ELL is not no-cost anymore). We introduce FIHCwLL into two state-of-the-art model-building optimizers, creating two new Dark Gray-box optimizers of significantly improved effectiveness.