On the Runtime Analysis of Fitness Sharing Mechanisms
Fitness sharing is a popular diversity mechanism implementing the idea that similar individuals in the population have to share resources and thus, share their fitnesses. Previous runtime analyses of fitness sharing studied a variant where selection was based on populations instead of individuals. We use runtime analysis to highlight the benefits and dangers of the original fitness sharing mechanism on the well-known test problem TwoMax, where diversity is crucial for finding both optima. In contrast to population-based sharing, a (2+1) EA in the original setting does not guarantee finding both optima in polynomial time; however, a (μ+1) EA with μ ≥ 3 always succeeds in expected polynomial time. We further show theoretically and empirically that large offspring populations in (μ + λ) EAs can be detrimental as overpopulation can make clusters of search points go extinct.
KeywordsEvolutionary computation diversity mechanisms fitness sharing runtime analysis
Unable to display preview. Download preview PDF.
- 5.Goldberg, D.E.: Genetic Algorithms for Search, Optimization, and Machine Learning. Addison-Wesley (1989)Google Scholar
- 6.Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multimodalfunction optimization. In: Proc. of ICGA, pp. 41–49. Lawrence Erlbaum Associates (1987)Google Scholar
- 7.Mahfoud, S.W.: Niching methods. In: Bäck, T., Fogel, D.B., Michalewicz, Z., (eds.) Handbook of Evolutionary Computation, pp. C6.1:1–C6.1:4. IOP Publishing and Oxford University Press (1997)Google Scholar
- 9.Oliveto, P.S., Witt, C.: Erratum: Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation. ArXiv e-prints (2012)Google Scholar
- 10.Oliveto, P.S., Zarges, C.: Analysis of diversity mechanisms for optimisation in dynamic environments with low frequencies of change. In: Proc. of GECCO, pp. 837–844. ACM (2013)Google Scholar
- 11.Sudholt, D.: Crossover is provably essential for the Ising model on trees. In: Proc. of GECCO, pp. 1161–1167. ACM Press (2005)Google Scholar