Self-adaptation via multi-objectivisation: a theoretical study

Per Kristian Lehre, Xiaoyu Qin

Abstract: The exploration vs exploitation dilemma is to balance exploring new but potentially less fit regions of the fitness landscape while also focusing on regions near the fittest individuals. For the tunable problem class SparseLocalOpt, a non-elitist EA with tournament selection can limit the percentage of "sparse" local optimal individuals in the population using a sufficiently high mutation rate (Dang et al., 2021). However, the performance of the EA depends critically on choosing the "right" mutation rate, which is problem instance-specific. A promising approach is self-adaptation, where parameter settings are encoded in chromosomes and evolved. We propose a new self-adaptive EA for single-objective optimisation, which treats parameter control from the perspective of multiobjective optimisation: The algorithm simultaneously maximises the fitness and the mutation rates. Since individuals in "dense" fitness valleys survive high mutation rates, and individuals on "sparse" local optima only survive with lower mutation rates, they can coexist on a non-dominated Pareto front. Runtime analyses show that this new algorithm (MOSA-EA) can efficiently escape a local optimum with unknown sparsity, where some fixed mutation rate EAs become trapped. Complementary experimental results show that the MOSA-EA outperforms a range of EAs on random NK-Landscape and k-Sat instances.