Estimation-of-distribution algorithms for multi-valued decision variables

The majority of research on estimation-of-distribution algorithms (EDAs) concentrates on pseudo-Boolean optimization and permutation problems, leaving the domain of EDAs for problems in which the decision variables can take more than two values, but which are not permutation problems, mostly unexplo...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1003; pp. 114622 - 114622:16
Main Authors: Ben Jedidia, Firas, Doerr, Benjamin, Krejca, Martin S.
Format: Journal Article
Language:English
Published: Elsevier B.V 01.07.2024
Elsevier
Subjects:
Computer Science
Estimation-of-distribution algorithms
Evolutionary algorithms
Genetic drift
LeadingOnes benchmark
Neural and Evolutionary Computing
Univariate marginal distribution algorithm
LeadingOnes benchmark
Genetic drift
Estimation-of-distribution algorithms
Evolutionary algorithms
Univariate marginal distribution algorithm
univariate marginal distribution algorithm
estimation-of-distribution algorithms
genetic drift
evolutionary algorithms
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:The majority of research on estimation-of-distribution algorithms (EDAs) concentrates on pseudo-Boolean optimization and permutation problems, leaving the domain of EDAs for problems in which the decision variables can take more than two values, but which are not permutation problems, mostly unexplored. To render this domain more accessible, we propose a natural way to extend the known univariate EDAs to this setting. Different from a naïve reduction to the binary case, our approach avoids additional constraints. Since understanding genetic drift is crucial for an optimal parameter choice, we extend the known quantitative analysis of genetic drift to EDAs for multi-valued, categorical variables. Roughly speaking, when the variables take r different values, the time for genetic drift to become significant is r times shorter than in the binary case. Consequently, the update strength of the probabilistic model has to be chosen r times lower now. To investigate how desired model updates take place in this framework, we undertake a mathematical runtime analysis on the r-valued LeadingOnes problem. We prove that with the right parameters, the multi-valued UMDA solves this problem efficiently in O(rln⁡(r)2n2ln⁡(n)) function evaluations. This bound is nearly tight as our lower bound Ω(rln⁡(r)n2ln⁡(n)) shows. Overall, our work shows that our good understanding of binary EDAs naturally extends to the multi-valued setting, and it gives advice on how to set the main parameters of multi-values EDAs.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2024.114622