Multi-objective Optimization with Joint Probabilistic Modeling of Objectives and Variables

Karshenas, Hossein; Santana, Roberto; Bielza, Concha; Larrañaga, Pedro

doi:10.1007/978-3-642-19893-9_21

Cited by 11 publications

(11 citation statements)

References 18 publications

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“…Moreover, although the choice of probabilistic model in an EDA is important, it should be noted that the difference between MBN-EDA and RM-MEDA performance is not only due to the difference in their probabilistic models. We have previously shown [24] that the incorporation of objectives into the same probabilistic model can result in significantly better performance.…”

Section: Resultsmentioning

confidence: 99%

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Multiobjective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

Karshenas

Santana

Bielza

et al. 2014

IEEE Trans. Evol. Computat.

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Abstract-This paper proposes a new multi-objective estimation of distribution algorithm (EDA) based on joint modeling of objectives and variables. This EDA uses the multi-dimensional Bayesian network as its probabilistic model. In this way it can capture the dependencies between objectives, variables and objectives, as well as the dependencies learnt between variables in other Bayesian network-based EDAs. This model leads to a problem decomposition that helps the proposed algorithm to find better trade-off solutions to the multi-objective problem. In addition to Pareto set approximation, the algorithm is also able to estimate the structure of the multi-objective problem. To apply the algorithm to many-objective problems, the algorithm includes four different ranking methods proposed in the literature for this purpose. The algorithm is applied to the set of walking fish group (WFG) problems, and its optimization performance is compared with an evolutionary algorithm and another multi-objective EDA. The experimental results show that the proposed algorithm performs significantly better on many of the problems and for different objective space dimensions, and achieves comparable results on some compared with the other algorithms.

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Section: Resultsmentioning

confidence: 99%

“…A preliminary study of this notion was presented in [24], discussing the incorporation of objectives into EDA model building. In this paper, we extend the study by using a specific probabilistic modeling adapted from a multi-dimensional Bayesian network (MBN), usually used for multi-label classification tasks [25], [26].…”

Section: Introductionmentioning

confidence: 99%

Multiobjective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

Karshenas

Santana

Bielza

et al. 2014

IEEE Trans. Evol. Computat.

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“…Recently EDAs have been successfully implemented on optimizing problems that includes more than one objective, showing a good performance and comparable results with other Multi-objective-implemented Metaheuristics [2][3][4]. Most of these MOEDAs have their basis in single-objective EDAs; the table 1 shows the cases.…”

Section: Multi-objective Estimation Of Distribution Algorithmsmentioning

confidence: 97%

Classification scheme of multi-objective Estimation of Distribution Algorithms

Mendoza-González

Ponce-de-Leon

Diaz-Diaz

2013

2013 IEEE Congress on Evolutionary Computation

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A variety of Estimation of Distribution Algorithms for multi-objective optimization (MOEDAs) has been reported, each of them with its own characteristics and techniques in their optimization process. In this research we present a classification scheme for these algorithms, based on ten characteristics: domain of the variables, relationships between the variables, probabilistic graphical model, estimation approach, restriction support, problem handling, sorting method, individuals' handling, selection approach, and replacement approach. These characteristics were extracted by analyzing all the 24 MOEDAs reported in the literature. The scheme presented here helps to identify the methods and techniques used in each algorithm, also, a useful method for the analysis of the optimization process of an EDA is proposed. This paper includes a brief analysis of the influence in the results of applying different selection/replacement percentages.

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“…EBCOA has also been extended to continuous domains (Miquelez et al 2006) by building Bayesian classifiers that assume Gaussian distributions for the variables given the class variable value. Karshenas et al (2011) proposed learning a joint GBN consisting of both variables and objectives in their JGBN-EDA for multi-objective optimization.…”

Section: Continuous Edasmentioning

confidence: 99%

A review on probabilistic graphical models in evolutionary computation

et al. 2012

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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.

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Multi-objective Optimization with Joint Probabilistic Modeling of Objectives and Variables

Cited by 11 publications

References 18 publications

Multiobjective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

Multiobjective Estimation of Distribution Algorithm Based on Joint Modeling of Objectives and Variables

Classification scheme of multi-objective Estimation of Distribution Algorithms

A review on probabilistic graphical models in evolutionary computation

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