A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms

Globally multimodal problem optimization via an estimation of distribution algorithm based on unsupervised learning of Bayesian networks

Many optimization problems are what can be called globally multimodal, i.e., they present several global optima. Unfortunately, this is a major source of difficulties for most estimation of distribution algorithms, making their effectiveness and efficiency degrade, due to genetic drift. With the aim of overcoming these drawbacks for discrete globally multimodal problem optimization, this paper introduces and evaluates a new estimation of distribution algorithm based on unsupervised learning of Bayesian networks. We report the satisfactory results of our experiments with symmetrical binary optimization problems

An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics

[EN] The optimization methods and, in particular, metaheuristics must be constantly improved to reduce execution times, improve the results, and thus be able to address broader instances. In particular, addressing combinatorial optimization problems is critical in the areas of operational research and engineering. In this work, a perturbation operator is proposed which uses the k-nearest neighbors technique, and this is studied with the aim of improving the diversification and intensification properties of metaheuristic algorithms in their binary version. Random operators are designed to study the contribution of the perturbation operator. To verify the proposal, large instances of the well-known set covering problem are studied. Box plots, convergence charts, and the Wilcoxon statistical test are used to determine the operator contribution. Furthermore, a comparison is made using metaheuristic techniques that use general binarization mechanisms such as transfer functions or db-scan as binarization methods. The results obtained indicate that the KNN perturbation operator improves significantly the results.The first author was supported by the Grant CONICYT/FONDECYT/INICIACION/11180056.García, J.; Astorga, G.; Yepes, V. (2021). An Analysis of a KNN Perturbation Operator: An Application to the Binarization of Continuous Metaheuristics. Mathematics. 9(3):1-20. https://doi.org/10.3390/math9030225S12093Al-Madi, N., Faris, H., & Mirjalili, S. (2019). Binary multi-verse optimization algorithm for global optimization and discrete problems. International Journal of Machine Learning and Cybernetics, 10(12), 3445-3465. doi:10.1007/s13042-019-00931-8García, J., Moraga, P., Valenzuela, M., Crawford, B., Soto, R., Pinto, H., … Astorga, G. (2019). A Db-Scan Binarization Algorithm Applied to Matrix Covering Problems. 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Regularized model learning in EDAs for continuous and multi-objective optimization

Probabilistic modeling is the de�ning characteristic of estimation of distribution algorithms (EDAs) which determines their behavior and performance in optimization. Regularization is a well-known statistical technique used for obtaining an improved model by reducing the generalization error of estimation, especially in high-dimensional problems. `1-regularization is a type of this technique with the appealing variable selection property which results in sparse model estimations. In this thesis, we study the use of regularization techniques for model learning in EDAs. Several methods for regularized model estimation in continuous domains based on a Gaussian distribution assumption are presented, and analyzed from di�erent aspects when used for optimization in a high-dimensional setting, where the population size of EDA has a logarithmic scale with respect to the number of variables. The optimization results obtained for a number of continuous problems with an increasing number of variables show that the proposed EDA based on regularized model estimation performs a more robust optimization, and is able to achieve signi�cantly better results for larger dimensions than other Gaussian-based EDAs. We also propose a method for learning a marginally factorized Gaussian Markov random �eld model using regularization techniques and a clustering algorithm. The experimental results show notable optimization performance on continuous additively decomposable problems when using this model estimation method. Our study also covers multi-objective optimization and we propose joint probabilistic modeling of variables and objectives in EDAs based on Bayesian networks, speci�cally models inspired from multi-dimensional Bayesian network classi�ers. It is shown that with this approach to modeling, two new types of relationships are encoded in the estimated models in addition to the variable relationships captured in other EDAs: objectivevariable and objective-objective relationships. An extensive experimental study shows the e�ectiveness of this approach for multi- and many-objective optimization. With the proposed joint variable-objective modeling, in addition to the Pareto set approximation, the algorithm is also able to obtain an estimation of the multi-objective problem structure. Finally, the study of multi-objective optimization based on joint probabilistic modeling is extended to noisy domains, where the noise in objective values is represented by intervals. A new version of the Pareto dominance relation for ordering the solutions in these problems, namely �-degree Pareto dominance, is introduced and its properties are analyzed. We show that the ranking methods based on this dominance relation can result in competitive performance of EDAs with respect to the quality of the approximated Pareto sets. This dominance relation is then used together with a method for joint probabilistic modeling based on `1-regularization for multi-objective feature subset selection in classi�cation, where six di�erent measures of accuracy are considered as objectives with interval values. The individual assessment of the proposed joint probabilistic modeling and solution ranking methods on datasets with small-medium dimensionality, when using two di�erent Bayesian classi�ers, shows that comparable or better Pareto sets of feature subsets are approximated in comparison to standard methods

Multi-objective Bayesian Artificial Immune System: Empirical Evaluation And Comparative Analyses

Recently, we have proposed a Multi-Objective Bayesian Artificial Immune System (MOBAIS) to deal effectively with building blocks (high-quality partial solutions coded in the solution vector) in combinatorial multi-objective problems. By replacing the mutation and cloning operators with a probabilistic model, more specifically a Bayesian network representing the joint distribution of promising solutions, MOBAIS takes into account the relationships among the variables of the problem, avoiding the disruption of already obtained high-quality partial solutions. The preliminary results have indicated that our proposal is able to properly build the Pareto front. Motivated by this scenario, this paper better formalizes the proposal and investigates its usefulness on more challenging problems. In addition, an important enhancement regarding the Bayesian network learning was incorporated into the algorithm in order to speed up its execution. To conclude, we compare MOBAIS with state-of-the-art algorithms taking into account quantitative aspects of the Pareto front found by the algorithms. MOBAIS outperforms the contenders in terms of the quality of the obtained solutions and requires an amount of computational resource inferior or compatible with the contenders. © 2009 Springer Science+Business Media B.V.82151173Ada, G.L., Nossal, G.J.V., The clonal selection theory (1987) Sci. Am., 257 (2), pp. 50-57Baluja, S., (1994) Population-based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning, , Technical Report, Carnegie Mellon University, PittsburghBaluja, S., Davies, S., Using optimal dependency-trees for combinational optimization (1997) Proc. of the 14th Int. Conf. on Machine Learning, pp. 30-38. , San FranciscoDe Bonet, J.S., Isbell, C.L., MIMIC: Finding optima by estimating probability densities (1997) Adv. Neural Inf. Process. 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