Non-elitist evolutionary algorithms excel in fitness landscapes with sparse deceptive regions and dense valleys

Dang, Duc Cuong, Eremeev, Anton and Lehre, Per Kristian (2021) Non-elitist evolutionary algorithms excel in fitness landscapes with sparse deceptive regions and dense valleys. In GECCO 2021 - Proceedings of the 2021 Genetic and Evolutionary Computation Conference. Association for Computing Machinery. pp. 1133-1141 . (doi:10.1145/3449639.3459398).

Abstract

It is largely unknown how the runtime of evolutionary algorithms depends on fitness landscape characteristics for broad classes of problems. Runtime guarantees for complex and multi-modal problems where EAs are typically applied are rarely available. We present a parameterised problem class SparseLocalOptα,ϵ where the class with parameters α, μ ∈ [0, 1] contains all fitness landscapes with deceptive regions of sparsity ϵ and fitness valleys of density α. We study how the runtime of EAs depends on these fitness landscape parameters. We find that for any constant density and sparsity α, ϵ ∈ (0, 1), SparseLocalOptα,ϵ has exponential elitist (μ + λ) black-box complexity, implying that a wide range of elitist EAs fail even for mildly deceptive and multi-modal landscapes. In contrast, we derive a set of sufficient conditions for non-elitist EAs to optimise any problem in SparseLocalOptα,ϵ in expected polynomial time for broad values of α and ϵ. These conditions can be satisfied for tournament selection and linear ranking selection, but not for (μ, λ)-selection.

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