When Hillclimbers Beat Genetic Algorithms in Multimodal Optimization

TL;DR

This paper compares hillclimbing and evolutionary algorithms on multimodal problems, showing hillclimbers often outperform genetic algorithms due to the lack of exploitable structure in the problem landscape.

Contribution

It provides an average-case runtime analysis of multistart hillclimbing on a generalized multimodal problem generator and empirically demonstrates its superiority over certain evolutionary strategies.

Findings

Hillclimbers outperform genetic algorithms on the tested multimodal instances.

Lack of structure in local optima space hinders evolutionary algorithms' effectiveness.

Brute-force strategies may be optimal when no exploitable landscape structure exists.

Abstract

This paper investigates the performance of multistart next ascent hillclimbing and well-known evolutionary algorithms incorporating diversity preservation techniques on instances of the multimodal problem generator. This generator induces a class of problems in the bitstringdomain which is interesting to study from a theoretical perspective in the context of multimodal optimization, as it is a generalization of the classical OneMax and TwoMax functions for an arbitrary number of peaks. An average-case runtime analysis for multistart next ascent hill-climbing is presented for uniformly distributed equal-height instances of this class of problems. It is shown empirically that conventional niching and mating restriction techniques incorporated in an evolutionary algorithm are not sufficient to make them competitive with the hillclimbing strategy. We conjecture the reason for this behaviour is the lack of structure in the space of local optima on instances of this problem class, which makes an optimization algorithm unable to exploit information from one optimum to infer where another optimum might be. When no such structure exist, it seems that the best strategy for discovering all optima is a brute-force one. Overall, our study gives insights with respect to the adequacy of hillclimbers and evolutionary algorithms for multimodal optimization, depending on properties of the fitness landscape.