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A new real-coded Bayesian optimization algorithm based on a team of learning automata for continuous optimization

GENETIC PROGRAMMING AND EVOLVABLE MACHINES 2014年第2期15卷 169-193页

作者： Moradabadi, Behnaz Beigy, Hamid Sharif Univ Technol Dept Comp Engn Tehran Iran

estimation of distribution algorithms have evolved as a technique for estimating population distribution in evolutionary algorithms. They estimate the distribution of the candidate solutions and then sample the next generation from the estimated distribution. Bayesian optimization algorithm is an estimation of distribution algorithm, which uses a Bayesian network to estimate the distribution of candidate solutions and then generates the next generation by sampling from the constructed network. The experimental results show that the Bayesian optimization algorithms are capable of identifying correct linkage between the variables of optimization problems. Since the problem of finding the optimal Bayesian network belongs to the class of NP-hard problems, typically Bayesian optimization algorithms use greedy algorithms to build the Bayesian network. This paper proposes a new real-coded Bayesian optimization algorithm for solving continuous optimization problems that uses a team of learning automata to build the Bayesian network. This team of learning automata tries to learn the optimal Bayesian network structure during the execution of the algorithm. The use of learning automaton leads to an algorithm with lower computation time for building the Bayesian network. The experimental results reported here show the preference of the proposed algorithm on both uni-modal and multi-modal optimization problems.

关键词： estimation of distribution algorithms Bayesian optimization algorithm Learning automata

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A Markovianity based optimisation algorithm

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GENETIC PROGRAMMING AND EVOLVABLE MACHINES 2012年第2期13卷 159-195页

作者： Shakya, Siddhartha Santana, Roberto Lozano, Jose A. Univ Politecn Madrid E-28660 Madrid Spain Univ Basque Country Fac Informat San Sebastian 20018 Spain BT Innovate & Design Business Modelling & Operat Transformat Practice Ipswich Suffolk England

Several estimation of distribution algorithms (EDAs) based on Markov networks have been recently proposed. The key idea behind these EDAs was to factorise the joint probability distribution of solution variables in terms of cliques in the undirected graph. As such, they made use of the global Markov property of the Markov network in one form or another. This paper presents a Markov Network based EDA that is based on the use of the local Markov property, the Markovianity, and does not directly model the joint distribution. We call it Markovianity based Optimisation Algorithm. The algorithm combines a novel method for extracting the neighbourhood structure from the mutual information between the variables, with a Gibbs sampler method to generate new points. We present an extensive empirical validation of the algorithm on problems with complex interactions, comparing its performance with other EDAs that use higher order interactions. We extend the analysis to other functions with discrete representation, where EDA results are scarce, comparing the algorithm with state of the art EDAs that use marginal product factorisations.

关键词： estimation of distribution algorithms Markov networks Competent genetic algorithms

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An AI-based system for pricing diverse products and services

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KNOWLEDGE-BASED SYSTEMS 2010年第4期23卷 357-362页

作者： Shakya, S. Chin, C. M. Owusu, G. BT Innovate & Design Intelligent Syst Res Ctr Ipswich IP5 3RE Suffolk England

This paper describes an applied research work that looks at different ways to effectively manage resources Particularly, it describes how revenue management techniques can be used to balance demand against capacity, and describes a system that uses different OR and AI techniques to intelligently price diverse products and services This system can produce pricing policies for wide range of products and services regardless of the model of demand used The system incorporates a model specification layer, which provides flexibility in defining the demand model for different products It also incorporates an optimisation layer, which takes the specified model as an input and produces the pricing and production guidelines for the product The system can be either used as a stand alone system or can be incorporated as a generic modelling and optimisation component within a larger revenue management system (C) 2009 Elsevier B V All rights reserved

关键词： estimation of distribution algorithms Genetic algorithm Evolutionary algorithm Evolutionary computation Probabilistic graphical models Artificial intelligence

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An investigation of the selection strategies impact on MOEDAs: CMA-ES and UMDA

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APPLIED SOFT COMPUTING 2018年 62卷 963-973页

作者： Strickler, Andrei Castro, Olacir, Jr. Pozo, Aurora Santana, Roberto Univ Fed Parana Comp Sci Dept Curitiba Parana Brazil Univ Basque Country UPV EHU Dept Comp Sci & Artificial Intelligence San Sebastian 20080 Spain

Researchers have acknowledged the importance of the selection, replacement, and archiving strategies in the behavior of evolutionary algorithms (EAs). However, these important relationships have not been deeply investigated in terms of estimation of distribution algorithms (EDAs). In a preliminary research, we focused on UMDA, a simple EDA that uses univariate Gaussian factorizations. Experimental results confirm that the choice of the selection method can provoke probabilistic modeling to be more effective for some classes of functions. Motivated by these results, this study is extended by evaluating several variants of selection strategies and probabilistic modeling approaches. The aim is to detect possible interactions between these two important components of evolutionary algorithms. Specifically, we use the selection strategies as defined for NSGA2, SPEA2, and IBEA algorithms, and the probabilistic models implemented as part of UMDA and CMA-ES, and a simple crossover operator (SBX). The recently introduced COCO framework comprising 55 bi-objective functions is used as the benchmark for the analysis. The results show that probabilistic modeling has an advantage over the classical genetic operator regardless of the selection method applied. Nevertheless, the results also show that some selection methods have a better performance when applied together with EDAs. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Multi-objective optimization estimation of distribution algorithms CMAES Selection

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Toward Understanding EDAs Based on Bayesian Networks Through a Quantitative Analysis

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2012年第2期16卷 173-189页

作者： Echegoyen, Carlos Mendiburu, Alexander Santana, Roberto Lozano, Jose A. Univ Basque Country Intelligent Syst Grp San Sebastian 20018 Spain Tech Univ Madrid Cajal Blue Brain Project Madrid 28660 Spain

The successful application of estimation of distribution algorithms (EDAs) to solve different kinds of problems has reinforced their candidature as promising black-box optimization tools. However, their internal behavior is still not completely understood and therefore it is necessary to work in this direction in order to advance their development. This paper presents a methodology of analysis which provides new information about the behavior of EDAs by quantitatively analyzing the probabilistic models learned during the search. We particularly focus on calculating the probabilities of the optimal solutions, the most probable solution given by the model and the best individual of the population at each step of the algorithm. We carry out the analysis by optimizing functions of different nature such as Trap5, two variants of Ising spin glass and Max-SAT. By using different structures in the probabilistic models, we also analyze the impact of the structural model accuracy in the quantitative behavior of EDAs. In addition, the objective function values of our analyzed key solutions are contrasted with their probability values in order to study the connection between function and probabilistic models. The results not only show information about the internal behavior of EDAs, but also about the quality of the optimization process and setup of the parameters, the relationship between the probabilistic model and the fitness function, and even about the problem itself. Furthermore, the results allow us to discover common patterns of behavior in EDAs and propose new ideas in the development of this type of algorithms.

关键词： Abductive inference Bayesian networks estimation of Bayesian networks algorithm estimation of distribution algorithms Ising Max-SAT probabilistic model

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Quantum inspired evolutionary algorithms with improved rotation gates for real-coded synthetic and real world optimization problems

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INTEGRATED COMPUTER-AIDED ENGINEERING 2017年第3期24卷 203-223页

作者： Wright, Joe Jordanov, Ivan Univ Portsmouth Sch Comp Lion Terrace Portsmouth PO1 3HE Hants England

We investigate two modified Quantum Evolutionary methods for solving real value problems. The Quantum Inspired Evolutionary algorithms (QIEA) were originally used for solving binary encoded problems and their signature features follow superposition of multiple states on a quantum bit and a rotation gate. In order to apply this paradigm to real value problems, we propose two quantum methods Half Significant Bit (HSB) and Stepwise Real QEA (SRQEA), developed using binary and real encoding respectively, while keeping close to the original quantum computing metaphor. We evaluate our approaches against sets of multimodal mathematical test functions and real world problems, using five performance metrics and include comparisons to published results. We report the issues encountered while implementing some of the published real QIEA techniques. Our methods focus on introducing and implementing new rotation gate operators used for evolution, including a novel mechanism for preventing premature convergence in the binary algorithm. The applied performance metrics show superior results for our quantum methods on most of the test problems (especially for the more complex and challenging ones), demonstrating faster convergence and accuracy.

关键词： Quantum evolutionary methods estimation of distribution algorithms performance metrics global optimization multimodal functions real value problems

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Convergence properties of quantum evolutionary algorithms on high dimension problems

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NEUROCOMPUTING 2019年 326卷 82-99页

作者： Wright, Joe Jordanov, Ivan Univ Portsmouth Sch Comp Lion Terrace Portsmouth PO1 3HE Hants England

We propose and investigate new rotation gates for two modified Quantum Inspired Evolutionary methods for solving high dimension optimisation problems. The Quantum Inspired Evolutionary algorithms (QIEA) were originally used for solving binary encoded problems and their signature features follow superposition of multiple states on a quantum bit and a rotation gate. In order to apply this paradigm to high dimension problems, we propose two quantum methods Half Significant Bit (HSB) and Stepwise Real QEA (SRQEA), developed using binary and real encoding, respectively, while keeping close to the original quantum computing metaphor. We introduce five performance metrics and use them to evaluate the proposed approaches against sets of multimodal mathematical test functions and real world problems of high dimensionality. We report issues found while implementing some of the published real QIEA techniques which were the motivation for developing our real algorithm modifications. Our methods focus on introducing and implementing new rotation gate operators used for evolution, including a novel mechanism for preventing premature convergence in the binary algorithm. The applied performance metrics show superior results for our quantum methods on most of the test problems (particularly with high dimension problems), demonstrating faster convergence and accuracy. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Quantum evolutionary methods estimation of distribution algorithms Performance metrics Multimodal functions High dimension problems Global optimization

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Gene selection for cancer classification using wrapper approaches

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INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE 2004年第8期18卷 1373-1390页

作者： Blanco, R Larrañaga, P Inza, I Sierra, B Univ Basque Country Comp Sci & Artificial Intelligence Dept San Sebastian 20080 Spain

Despite the fact that cancer classification has considerably improved, nowadays a general method that classifies known types of cancer has not yet been developed. In this work, we propose the use of supervised classification techniques, coupled with feature subset selection algorithms, to automatically perform this classification in gene expression datasets. Due to the large number of features of gene expression datasets, the search of a highly accurate combination of features is done by means of the new estimation of distribution algorithms paradigm. In order to assess the accuracy level of the proposed approach, the naive-Bayes classification algorithm is employed in a wrapper form. Promising results are achieved, in addition to a considerable reduction in the number of genes. Stating the optimal selection of genes as a search task, an automatic and robust choice in the genes finally selected is performed, in contrast to previous works that research the same types of problems.

关键词： feature subset selection DNA microarrays supervised classification naive-Bayes estimation of distribution algorithms

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Evolutionary algorithms and elliptical copulas applied to Continuous optimization problems

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INFORMATION SCIENCES 2016年第0期369卷 419-440页

作者： de Mello Junior, Harold Dias Marti, Luis Abs da Cruz, Andre V. Rebuzzi Vellasco, Marley M. B. Univ Estado Rio De Janeiro Dept Elect Engn Rio De Janeiro Brazil Univ Fed Fluminense Inst Comp Rio De Janeiro Brazil State Univ West Side Comp Univ Unit Rio De Janeiro Brazil Pontifical Catholic Univ Rio de Janeiro Dept Elect Engn Rio De Janeiro Brazil

estimation of distribution algorithms (EDAs) constitutes a class of evolutionary algorithms that can extract and exploit knowledge acquired throughout the optimization process. The most critical step in the EDAs is the estimation of the joint probability distribution associated to the variables from the most promising solutions determined by the evaluation function. Recently, a new approach to EDAs has been developed, based on copula theory, to improve the estimation of the joint probability distribution function. However, most copula-based EDAs still present two major drawbacks: focus on copulas with constant parameters, and premature convergence. This paper presents a new copula-based estimation of distribution algorithm for numerical optimization problems, named EDA based on Multivariate Elliptical Copulas (EDA-MEC). This model,uses multivariate copulas to estimate the probability distribution for generating a population of individuals. The EDA-MEC differs from Other copula-based EDAs in several aspects: the copula parameter is dynamically estimated, using dependence measures;it uses a variation of the learned probability distribution to generate individuals that help to avoid premature convergence;and uses a heuristic to reinitialize the population as an additional technique to preserve the diversity of solutions. The paper shows, by means of a set of parametric tests, that this approach improves the overall performance of the optimization process when compared with other copula-based EDAs and with other efficient heuristics such as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). (C) 2016 Elsevier Inc. All rights reserved.

关键词： Continuous numeric optimization Copulas estimation of distribution algorithms Evolutionary computation

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Sporadic model building for efficiency enhancement of the hierarchical BOA

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GENETIC PROGRAMMING AND EVOLVABLE MACHINES 2008年第1期9卷 53-84页

作者： Pelikan, Martin Sastry, Kumara Goldberg, David E. Univ Missouri Dept Math & Comp Sci Missouri Estimat Distribut Algorithm Lab St Louis MO 63121 USA Univ Illinois Dept Ind & Enterprise Syst Engn Illinois Genet Algorithm Lab Urbana IL 61801 USA

Efficiency enhancement techniques - such as parallelization and hybridization - are among the most important ingredients of practical applications of genetic and evolutionary algorithms and that is why this research area represents an important niche of evolutionary computation. This paper describes and analyzes sporadic model building, which can be used to enhance the efficiency of the hierarchical Bayesian optimization algorithm (hBOA) and other estimation of distribution algorithms (EDAs) that use complex multivariate probabilistic models. With sporadic model building, the structure of the probabilistic model is updated once in every few iterations (generations), whereas in the remaining iterations, only model parameters (conditional and marginal probabilities) are updated. Since the time complexity of updating model parameters is much lower than the time complexity of learning the model structure, sporadic model building decreases the overall time complexity of model building. The paper shows that for boundedly difficult nearly decomposable and hierarchical optimization problems, sporadic model building leads to a significant model-building speedup, which decreases the asymptotic time complexity of model building in hBOA by a factor of Theta(n(0.26)) to Theta(n(0.5)) where n is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence;nonetheless, if model building is the bottleneck, the evaluation slowdown is insignificant compared to the gains in the asymptotic complexity of model building. The paper also presents a dimensional model to provide a heuristic for scaling the structure-building period, which is the only parameter of the proposed sporadic model-building approach. The paper then tests the proposed method and the rule for setting the structure-building period on the problem of finding ground states of 2D and 3D Ising spin glasses.

关键词： Bayesian optimization algorithm hierarchical BOA estimation of distribution algorithms efficiency enhancement sporadic model building

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