Bivariate estimation-of-distribution algorithms can find an exponential number of optima - Archive ouverte HAL
Communication Dans Un Congrès Année : 2020

Bivariate estimation-of-distribution algorithms can find an exponential number of optima

Résumé

Finding a large set of optima in a multimodal optimization landscape is a challenging task. Classical population-based evolutionary algorithms (EAs) typically converge only to a single solution. While this can be counteracted by applying niching strategies, the number of optima is nonetheless trivially bounded by the population size. Estimation-of-distribution algorithms (EDAs) are an alternative, maintaining a probabilistic model of the solution space instead of an explicit population. Such a model is able to implicitly represent a solution set that is far larger than any realistic population size. To support the study of how optimization algorithms handle large sets of optima, we propose the test function EqalBlocks-OneMax (EBOM). It has an easy to optimize fitness landscape, however, with an exponential number of optima. We show that the bivariate EDA mutual-information-maximizing input clustering (MIMIC), without any problem-specific modification, quickly generates a model that behaves very similarly to a theoretically ideal model for that function, which samples each of the exponentially many optima with the same maximal probability.
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Dates et versions

hal-04132943 , version 1 (19-06-2023)

Identifiants

Citer

Benjamin Doerr, Martin S Krejca. Bivariate estimation-of-distribution algorithms can find an exponential number of optima. GECCO '20: Genetic and Evolutionary Computation Conference, Jul 2020, Cancún (on line), Mexico. pp.796-804, ⟨10.1145/3377930.3390177⟩. ⟨hal-04132943⟩
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