Selection Hyper-heuristics Can Provably Be Helpful in Evolutionary Multi-objective Optimization

Selection hyper-heuristics are automated methodologies for selecting existing low-level heuristics to solve hard computational problems. They have been found very useful for evolutionary algorithms when solving both single and multi-objective real-world optimization problems. Previous work mainly focuses on empirical study, while theoretical study, particularly in multi-objective optimization, is largely insufficient. In this paper, we use three main components of multi-objective evolutionary algorithms (selection mechanisms, mutation operators, acceptance strategies) as low-level heuristics, respectively, and prove that using heuristic selection (i.e., mixing low-level heuristics) can be exponentially faster than using only one low-level heuristic. Our result provides theoretical support for multi-objective selection hyper-heuristics, and might be helpful for designing efficient heuristic selection methods in practice.