When Hillclimbers Beat Genetic Algorithms in Multimodal Optimization

It has been shown in the past that a multistart hillclimbing strategy compares favourably to a standard genetic algorithm with respect to solving instances of the multimodal problem generator. We extend that work and verify if the utilization of diversity preservation techniques in the genetic algorithm changes the outcome of the comparison. We do so under two scenarios: (1) when the goal is to find the global optimum, (2) when the goal is to find all optima. A mathematical analysis is performed for the multistart hillclimbing algorithm and a through empirical study is conducted for solving instances of the multimodal problem generator with increasing number of optima, both with the hillclimbing strategy as well as with genetic algorithms with niching. Although niching improves the performance of the genetic algorithm, it is still inferior to the multistart hillclimbing strategy on this class of problems. An idealized niching strategy is also presented and it is argued that its performance should be close to a lower bound of what any evolutionary algorithm can do on this class of problems

When hillclimbers beat genetic algorithms in multimodal optimization

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.info:eu-repo/semantics/publishedVersio

When Hillclimbers Beat Genetic Algorithms in Multimodal Optimization.

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 bitstring domain 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 averagecase runtime analysis for multistart next ascent hillclimbing 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