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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| Vydáno v: | Theoretical computer science Ročník 1003; s. 114622 - 114622:16 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.07.2024
Elsevier |
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| ISSN: | 0304-3975, 1879-2294 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 114622 |
| Author | Ben Jedidia, Firas Doerr, Benjamin Krejca, Martin S. |
| Author_xml | – sequence: 1 givenname: Firas surname: Ben Jedidia fullname: Ben Jedidia, Firas organization: École Polytechnique, Institut Polytechnique de Paris, Route de Saclay, Palaiseau, 91120, France – sequence: 2 givenname: Benjamin surname: Doerr fullname: Doerr, Benjamin organization: Laboratoire d'Informatique (LIX), CNRS, École Polytechnique, Institut Polytechnique de Paris, 1 rue Honoré d'Estienne d'Orves, Palaiseau, 91120, France – sequence: 3 givenname: Martin S. orcidid: 0000-0002-1765-1219 surname: Krejca fullname: Krejca, Martin S. email: martin.krejca@polytechnique.edu organization: Laboratoire d'Informatique (LIX), CNRS, École Polytechnique, Institut Polytechnique de Paris, 1 rue Honoré d'Estienne d'Orves, Palaiseau, 91120, France |
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| Keywords | 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 |
| Language | English |
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