Self-adaptation Can Help Evolutionary Algorithms Track Dynamic Optima

Per Kristian Lehre, Xiaoyu Qin

Abstract: Real-world optimisation problems often involve dynamics, where objective functions may change over time. Previous studies have shown that evolutionary algorithms (EAs) can solve dynamic optimisation problems. Additionally, the use of diversity mechanisms, populations, and parallelisation can enhance the performance of EAs in dynamic environments if appropriate parameter settings are utilised. Self-adaptation, which encodes parameters in genotypes of individuals and allows them to evolve together with solutions, can help configure parameters of EAs. This parameter control mechanism has been proved to effectively handle a static problem with unknown structure. However, the benefit of self-adaptation on dynamic optimisation problems remains unknown. We consider a tracking dynamic optima problem, the so-called Dynamic Substring Matching (DSM) problem, which requires algorithms to successively track a sequence of structure-changing optima. Our analyses show that mutation-based EAs with a fixed mutation rate have a negligible chance of tracking these dynamic optima, while the self-adaptive EA tracks them with an overwhelmingly high probability. Furthermore, we provide a level-based theorem with tail bounds, which bounds the chance of the algorithm finding the current optima within a given evaluation budget. Overall, self-adaptation is promising for tracking dynamic optima.