A mathematical analysis of EDAs with distance-based exponential models
Estimation of Distribution Algorithms have been successfully used to solve permutation-based Combinatorial Optimization Problems. In this case, the algorithms use probabilistic models specifically designed for codifying probability distributions over permutation spaces. One class of these probabilit...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/57921 |
| Acesso em linha: | http://hdl.handle.net/10810/57921 |
| Access Level: | acceso abierto |
| Palavra-chave: | estimation of distribution algorithms permutation based combinatorial optimization problems mathematical modeling dynamical systems mallows model |
| Resumo: | Estimation of Distribution Algorithms have been successfully used to solve permutation-based Combinatorial Optimization Problems. In this case, the algorithms use probabilistic models specifically designed for codifying probability distributions over permutation spaces. One class of these probability models are distance-based exponential models, and one example of this class is the Mallows model. In spite of its practical success, the theoretical analysis of Estimation of Distribution Algorithms for permutation-based Combinatorial Optimization Problems has not been developed as extensively as it has been for binary problems. With this motivation, this paper presents a first mathematical analysis of the convergence behavior of Estimation of Distribution Algorithms based on Mallows models. The model removes the randomness of the algorithm in order to associate a dynamical system to it. Several scenarios of increasing complexity with different fitness functions and initial probability distributions are analyzed. The obtained results show: a) the strong dependence of the final results on the initial population, and b) the possibility to converge to non-degenerate distributions even in very simple scenarios, which has not been reported before in the literature. |
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