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Fast Solutions Enhancing using a Copula-based EDA and SVM for many-objective problems

IFAC-PapersOnLine 2016年第12期49卷 781-786页

作者： Cheriet, Abdelhakim Cherif, Foudil Taleb-Ahmed, Abdelmalik LESIA Laboraroty University of Biskra Algeria LAMIH Electrical Engineering Department Valenciennes United States

In this paper we propose a new Copula-based estimation of distribution Algorithm, to solve Many-objective optimization problem and to get new optimal solutions in very court time. Our algorithm uses the proprieties of Copula and exploits their statistical properties to make new solutions using the founded optimal solutions through the estimation of their distribution. The first step of the proposed Copula-based estimation of distribution Algorithm (CEDA-SVM) is taking initial solutions offered by any MOEA (Multi Objective Evolutionary Algorithm), and then creates Copulas to estimate their distribution, and we use Support Vector Machine (SVM) to learn the Pareto solutions model; those Copulas will be used to generate new solutions and SVM to avoid the expensive function evaluations. The idea of using the estimated distribution of the optimal solutions helps CEDA-SVM to avoid running the optimizer ( MOEA ) every time we need new alternatives solutions when the founded ones are not satisfactory. We tested CEDA-SVM on a set of many-objective benchmark problems traditionally used by the community, namely DTLZ (1, 2, 3, and 4) with different dimensions (3, 5, 8, 10, and 15). We used CEDA along with MOEA/D-Schy and MOEA/D-BI as two examples of MOEA thus resulting in two variants CEDA-MOAE/D-Scy and CEDA-MOEA/D-BI and compare them with MOEA/D-Schy and MOEA/D-BI. The results of our experiments show that, with both variants of CEDA-SVM, new solutions can be obtained in a very small time compared to the other algorithms. © 2016

关键词： Evolutionary algorithms distribution functions Multiobjective optimization Optimal systems Support vector machines Bench mark problems Copula estimation of distribution algorithms Initial solution Many objective optimizations Multi objective evolutionary algorithms Optimal solutions Statistical properties

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Novel dynamic diversity controlling EAs for coevolving optimal negotiation strategies

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INFORMATION SCIENCES 2014年 273卷 1-32页

作者： Gwak, Jeonghwan Sim, Kwang Mong Jeon, Moongu Gwangju Inst Sci & Technol Sch Informat & Commun Kwangju 500712 South Korea Univ Kent Sch Comp Chatham ME4 4AG Kent England

Finding optimal strategies for negotiation with incomplete information is a challenging issue in agent-based automated negotiation research. Although there are some previous works on finding the strategies through coevolutionary learning using evolutionary algorithms (EAs), their coevolving strategies tend to converge to non-global optima (which bring about ineffective negotiation outcomes for participating agents) due to biased coevolution and failures in coevolution. To cope with these drawbacks, this work introduces and compares novel genetic algorithms (GAs) and estimation of distribution algorithms (EDAs) that have additional capability of dynamic diversity control: (1) the dynamic diversity controlling GA ((DC)-C-2-GA), (2) the dynamic diversity controlling EDA ((DC)-C-2-EDA), (3) the improved (DC)-C-2-GA ((IDC)-C-2-GA) and (4) the improved (DC)-C-2-EDA ((IDC)-C-2-EDA). While (DC)-C-2-GA and (DC)-C-2-EDA adopt the novel diversification and refinement (DR) procedure, (IDC)-C-2-GA and (IDC)-C-2-EDA adopt the modified and enhanced DR (mDR) procedure with two additional local heuristics population repair and local neighborhood search. An extensive series of experiments were carried out to compare and evaluate the performance of the simple GA (S-GA), the simple EDA (S-EDA), and the novel GAs and EDAs in coevolving effective negotiation strategies of two self-interested negotiation agents for their various deadline combinations. Favorable empirical results showed that (i) (IDC)-C-2-EDA could coevolve (near-)optimal negotiation strategies for all the considered cases due to its good generalization performance and (ii) it also generally 'outperformed S-GA, S-EDA, (DC)-C-2-GA, (DC)-C-2-EDA and (IDC)-C-2-GA in terms of solution accuracy, coevolutionary search capability and average coevolution restart ratio. Interestingly, it was also found that the coevolution performance of (IDC)-C-2-GA and (IDC)-C-2-EDA is complementary in that (IDC)-C-2-GA and (IDC)-C-2-EDA generall

关键词： Automated negotiation Negotiation agents Coevolutionary learning Genetic algorithms estimation of distribution algorithms Adaptive diversity control

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An evolutionary algorithm with guided mutation for the maximum clique problem

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2005年第2期9卷 192-200页

作者： Zhang, QF Sun, JY Tsang, E Univ Essex Dept Comp Sci Colchester CO4 3SQ Essex England

estimation of distribution algorithms sample new solutions (offspring) from a probability model which characterizes the distribution of promising solutions in the search space at each generation. The location information of solutions found so far (i.e., the actual positions of these solutions in the search space) is not directly used for generating offspring in most existing estimation of distribution algorithms. This paper introduces a new operator, called guided mutation. Guided mutation generates offspring through combination of global statistical information and the location information of solutions found so far. An evolutionary algorithm with guided mutation (EA/G) for the maximum clique problem is proposed in this paper. Besides guided mutation, EA/G adopts a strategy for searching different search areas in different search phases. Marchiori's heuristic is applied to each new solution to produce a maximal clique in EA/G. Experimental results show that EA/G outperforms the heuristic genetic algorithm of Marchiori (the best evolutionary algorithm reported so far) and a MIMIC algorithm on DIMACS benchmark graphs.

关键词： estimation of distribution algorithms evolutionary algorithm guided mutation heuristics hybrid genetic algorithm maximum clique problem (MCP)

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Learning and Searching Pseudo-Boolean Surrogate Functions from Small Samples

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EVOLUTIONARY COMPUTATION 2020年第2期28卷 317-338页

作者： Swingler, Kevin Univ Stirling Comp Sci & Math Stirling FK9 4LA Scotland

When searching for input configurations that optimise the output of a system, it can be useful to build a statistical model of the system being optimised. This is done in approaches such as surrogate model-based optimisation, estimation of distribution algorithms, and linkage learning algorithms. This article presents a method for modelling pseudo-Boolean fitness functions using Walsh bases and an algorithm designed to discover the non-zero coefficients while attempting to minimise the number of fitness function evaluations required. The resulting models reveal linkage structure that can be used to guide a search of the model efficiently. It presents experimental results solving benchmark problems in fewer fitness function evaluations than those reported in the literature for other search methods such as EDAs and linkage learners.

关键词： Fitness function modelling estimation of distribution algorithms pseudo-Boolean functions linkage learning Walsh decomposition mixed order hyper networks statistical machine learning

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Scalability of using Restricted Boltzmann Machines for combinatorial optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第2期256卷 368-383页

作者： Probst, Malte Rothlauf, Franz Grahl, Joern Johannes Gutenberg Univ Mainz Dept Informat Syst & Business Adm Jakob Welder Weg 9 D-55128 Mainz Germany Univ Cologne Dept Management Econ & Social Sci Univ Str 91 D-50969 Cologne Germany

estimation of distribution algorithms (EDAs) require flexible probability models that can be efficiently learned and sampled. Restricted Boltzmann Machines (RBMs) are generative neural networks with these desired properties. We integrate an RBM into an EDA and evaluate the performance of this system in solving combinatorial optimization problems with a single objective. We assess how the number of fitness evaluations and the CPU time scale with problem size and complexity. The results are compared to the Bayesian Optimization Algorithm (BOA), a state-of-the-art multivariate EDA, and the Dependency Tree Algorithm (DTA), which uses a simpler probability model requiring less computational effort for training the model. Although RBM-EDA requires larger population sizes and a larger number of fitness evaluations than BOA, it outperforms BOA in terms of CPU times, in particular if the problem is large or complex. This is because RBM-EDA requires less time for model building than BOA. DTA with its restricted model is a good choice for small problems but fails for larger and more difficult problems. These results highlight the potential of using generative neural networks for combinatorial optimization. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Combinatorial optimization Heuristics Evolutionary computation estimation of distribution algorithms Neural Networks

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A Self-guided Genetic Algorithm for permutation flowshop scheduling problems

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COMPUTERS & OPERATIONS RESEARCH 2012年第7期39卷 1450-1457页

作者： Chen, Shih-Hsin Chang, Pei-Chann Cheng, T. C. E. Zhang, Qingfu Yuan Ze Univ Dept Informat Management Tao Yuan Taiwan Nanhua Univ Dept Elect Commerce Management Chiayi Taiwan Hong Kong Polytech Univ Dept Logist & Maritime Studies Kowloon Hong Kong Peoples R China Univ Essex Sch Comp Sci & Elect Engn Colchester CO4 3SQ Essex England

In this paper we develop a Self-guided Genetic Algorithm (Self-guided GA), which belongs to the category of estimation of distribution algorithms (EDAs). Most EDAs explicitly use the probabilistic model to sample new solutions without using traditional genetic operators. EDAs make good use of the global statistical information collected from previous searches but they do not efficiently use the location information about individual solutions. It is recently realized that global statistical information and location information should complement each other during the evolution process. In view of this, we design the Self-guided GA based on a novel strategy to combine these two kinds of information. The Self-guided GA does not sample new solutions from the probabilistic model. Instead, it estimates the quality of a candidate offspring based on the probabilistic model used in its crossover and mutation operations. In such a way, the mutation and crossover operations are able to generate fitter solutions, thus improving the performance of the algorithm. We tested the proposed algorithm by applying it to deal with the NP-complete flowshop scheduling problem to minimize the makespan. The experimental results show that the Self-guided GA is very promising. We also demonstrate that the Self-guided GA can be easily extended to treat other intractable combinatorial problems. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： estimation of distribution algorithms Permutation flowshop scheduling Self-guided crossover Self-guided mutation

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Toward Large-Scale Continuous EDA: A Random Matrix Theory Perspective

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EVOLUTIONARY COMPUTATION 2016年第2期24卷 255-291页

作者： Kaban, A. Bootkrajang, J. Durrant, R. J. Univ Birmingham Sch Comp Sci Birmingham B15 2TT W Midlands England Chiang Mai Univ Dept Comp Sci Chiang Mai 50200 Thailand Univ Waikato Dept Stat Private Bag 3105 Hamilton 3240 New Zealand

estimations of distribution algorithms (EDAs) are a major branch of evolutionary algorithms (EA) with some unique advantages in principle. They are able to take advantage of correlation structure to drive the search more efficiently, and they are able to provide insights about the structure of the search space. However, model building in high dimensions is extremely challenging, and as a result existing EDAs may become less attractive in large-scale problems because of the associated large computational requirements. Large-scale continuous global optimisation is key to many modern-day real-world problems. Scaling up EAs to large-scale problems has become one of the biggest challenges of the field. This paper pins down some fundamental roots of the problem and makes a start at developing a new and generic framework to yield effective and efficient EDA-type algorithms for large-scale continuous global optimisation problems. Our concept is to introduce an ensemble of random projections to low dimensions of the set of fittest search points as a basis for developing a new and generic divide-and-conquer methodology. Our ideas are rooted in the theory of random projections developed in theoretical computer science, and in developing and analysing our framework we exploit some recent results in nonasymptotic random matrix theory.

关键词： Large-scale optimisation estimation of distribution algorithms random projections random matrix theory

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Using Previous Models to Bias Structural Learning in the Hierarchical BOA

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EVOLUTIONARY COMPUTATION 2012年第1期20卷 135-160页

作者： Hauschild, M. W. Pelikan, M. Sastry, K. Goldberg, D. E. Univ Missouri Dept Comp Sci MEDAL St Louis MO 63121 USA Univ Illinois Dept Ind & Enterprise Syst Engn Illinois Genet Algorithms Lab IlliGAL Urbana IL 61801 USA

estimation of distribution algorithms (EDAs) are stochastic optimization techniques that explore the space of potential solutions by building and sampling explicit probabilistic models of promising candidate solutions. While the primary goal of applying EDAs is to discover the global optimum or at least its accurate approximation, besides this, any EDA provides us with a sequence of probabilistic models, which in most cases hold a great deal of information about the problem. Although using problem-specific knowledge has been shown to significantly improve performance of EDAs and other evolutionary algorithms, this readily available source of problem-specific information has been practically ignored by the EDA community. This paper takes the first step toward the use of probabilistic models obtained by EDAs to speed up the solution of similar problems in the future. More specifically, we propose two approaches to biasing model building in the hierarchical Bayesian optimization algorithm (hBOA) based on knowledge automatically learned from previous hBOA runs on similar problems. We show that the proposed methods lead to substantial speedups and argue that the methods should work well in other applications that require solving a large number of problems with similar structure.

关键词： Hierarchical BOA efficiency enhancement learning from experience probabilistic model model structure model complexity estimation of distribution algorithms

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Maximum spanning tree based linkage learner

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AI COMMUNICATIONS 2014年第3期27卷 263-274页

作者： Helmi, B. Hoda Rahmani, Adel T. Iran Univ Sci & Technol Dept Comp Sci Tehran *** Iran

Linkage learning in evolutionary algorithms is identifying the structure of the dependencies between variables of a problem in order to find the optimum solution of the problem. It is a necessary process for optimizing the hard problems that can not be optimized randomly via common recombination operators of simple genetic algorithm. This paper presents a simple yet effective linkage learner that works based on graph theory. A graph is used as the structure to keep the pairwise dependencies between variables of the problem. We call this graph 'the underlying dependency graph of the problem' (UDGP). Maximum spanning tree (MST) of the UDGP is then found. It is shown that MST contains all the necessary linkages if the dependency graph is built upon sufficient population. In this approach, pairwise dependencies that are mutual information between each pair of variables, are used to find linkage information. The proposed approach has the advantage of being capable of learning the linkage without the need for the costly fit-to-data evaluations of model search. It is parameter free and the algorithm description is straight forward. The proposed technique is tested on several benchmark problems and it is shown to be able to compete with similar approaches. Based on the experimental results it can successfully find the linkage groups in a polynomial number of fitness evaluations.

关键词： Linkage learning graph theory maximum spanning tree estimation of distribution algorithms optimization problems decomposable functions mutual information AI

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Regularized logistic regression without a penalty term: An application to cancer classification with microarray data

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EXPERT SYSTEMS WITH APPLICATIONS 2011年第5期38卷 5110-5118页

作者： Bielza, Concha Robles, Victor Larranaga, Pedro Tech Univ Madrid Dept Artificial Intelligence Madrid Spain Tech Univ Madrid Dept Comp Architecture & Technol Madrid Spain

Regularized logistic regression is a useful classification method for problems with few samples and a huge number of variables. This regression needs to determine the regularization term, which amounts to searching for the optimal penalty parameter and the norm of the regression coefficient vector. This paper presents a new regularized logistic regression method based on the evolution of the regression coefficients using estimation of distribution algorithms. The main novelty is that it avoids the determination of the regularization term. The chosen simulation method of new coefficients at each step of the evolutionary process guarantees their shrinkage as an intrinsic regularization. Experimental results comparing the behavior of the proposed method with Lasso and ridge logistic regression in three cancer classification problems with microarray data are shown. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Logistic regression Regularization estimation of distribution algorithms Cancer classification Microarray data

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