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Scaling Up estimation of distribution algorithms for Continuous Optimization

IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2013年第6期17卷 797-822页

作者： Dong, Weishan Chen, Tianshi Tino, Peter Yao, Xin Chinese Acad Sci Inst Automat Key Lab Complex Syst & Intelligence Sci Beijing 100190 Peoples R China Chinese Acad Sci Inst Comp Technol Beijing 100190 Peoples R China Univ Birmingham Sch Comp Sci Ctr Excellence Res Computat Intelligence & Applic Birmingham B15 2TT W Midlands England

Since estimation of distribution algorithms (EDAs) were proposed, many attempts have been made to improve EDAs' performance in the context of global optimization. So far, the studies or applications of multivariate probabilistic model-based EDAs in continuous domain are still mostly restricted to low-dimensional problems. Traditional EDAs have difficulties in solving higher dimensional problems because of the curse of dimensionality and rapidly increasing computational costs. However, scaling up continuous EDAs for large-scale optimization is still necessary, which is supported by the distinctive feature of EDAs: because a probabilistic model is explicitly estimated, from the learned model one can discover useful properties of the problem. Besides obtaining a good solution, understanding of the problem structure can be of great benefit, especially for black box optimization. We propose a novel EDA framework with model complexity control (EDA-MCC) to scale up continuous EDAs. By employing weakly dependent variable identification and subspace modeling, EDA-MCC shows significantly better performance than traditional EDAs on high-dimensional problems. Moreover, the computational cost and the requirement of large population sizes can be reduced in EDA-MCC. In addition to being able to find a good solution, EDA-MCC can also provide useful problem structure characterizations. EDA-MCC is the first successful instance of multivariate model-based EDAs that can be effectively applied to a general class of up to 500-D problems. It also outperforms some newly developed algorithms designed specifically for large-scale optimization. In order to understand the strengths and weaknesses of EDA-MCC, we have carried out extensive computational studies. Our results have revealed when EDA-MCC is likely to outperform others and on what kind of benchmark functions.

关键词： estimation of distribution algorithm large-scale optimization model complexity control

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Feature subset selection by genetic algorithms and estimation of distribution algorithms -: A case study in the survival of cirrhotic patients treated with TIPS

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ARTIFICIAL INTELLIGENCE IN MEDICINE 2001年第2期23卷 187-205页

作者： Inza, I Merino, M Larrañaga, P Quiroga, J Sierra, B Girala, M Univ Basque Country Dept Comp Sci & Artificial Intelligence E-20080 San Sebastian Spain Basque Hlth Serv E-20013 San Sebastian Spain Univ Navarra Clin Fac Med E-31080 Pamplona Spain

The transjugular intrahepatic portosystemic shunt (TIPS) is an interventional treatment for cirrhotic patients with portal hypertension. In the light of our medical staff's experience, the consequences of TIPS are not homogeneous for all the patients and a subgroup dies in the first 6 months after TIPS placement. Actually, there is no risk indicator to identify this subgroup of patients before treatment. An investigation for predicting the survival of cirrhotic patients treated with TIPS is carried out using a clinical database with 107 cases and 77 attributes. Four supervised machine learning classifiers are applied to discriminate between both subgroups of patients. The application of several feature subset selection (FSS) techniques has significantly improved the predictive accuracy of these classifiers and considerably reduced the amount of attributes in the classification models. Among FSS techniques, FSS-TREE, a new randomized algorithm inspired on the new EDA (estimation of distribution algorithm) paradigm has obtained the best average accuracy results for each classifier. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： feature subset selection transjugular intrahepatic portosystemic shunt estimation of distribution algorithm indications survival

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Quality Analysis of Discretization Methods for estimation of distribution algorithms

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IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS 2014年第5期E97D卷 1312-1323页

作者： Chen, Chao-Hong Chen, Ying-ping Natl Chiao Tung Univ Dept Comp Sci Hsinchu Taiwan

estimation of distribution algorithms (EDAs). since they were introduced, have been successfully used to solve discrete optimization problems and hence proven to be an effective methodology for discrete optimization. To enhance the applicability of EDAs, researchers started to integrate EDAs with discretization methods such that the EDAs designed for discrete variables can be made capable of solving continuous optimization problems. In order to further our understandings of the collaboration between EDAs and discretization methods, in this paper, we propose a quality measure of discretization methods for EDAs. We then utilize the proposed quality measure to analyze three discretization methods: fixed-width histogram (FWH). fixed-height histogram (FHH), and greedy random split (GRS). Analytical measurements are obtained for FHH and FWH, and sampling measurements are conducted for FHH. FWH, and GRS. Furthermore, we integrate Bayesian optimization algorithm (BOA), a representative EDA, with the three discretization methods to conduct experiments and to observe the performance difference. A good agreement is reached between the discretization quality measurements and the numerical optimization results. The empirical results show that the proposed quality measure can be considered as an indicator of the suitability for a discretization method to work with EDAs.

关键词： quality analysis discretization distortion fixed-width histogram fixed-height histogram greedy random split estimation of distribution algorithm Bayesian optimization algorithm

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Environment identification-based memory scheme for estimation of distribution algorithms in dynamic environments

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SOFT COMPUTING 2011年第2期15卷 311-326页

作者： Peng, Xingguang Gao, Xiaoguang Yang, Shengxiang Northwestern Polytech Univ Sch Elect & Informat Xian 710129 Shaanxi Peoples R China Univ Leicester Dept Comp Sci Leicester LE1 7RH Leics England

In estimation of distribution algorithms (EDAs), the joint probability distribution of high-performance solutions is presented by a probability model. This means that the priority search areas of the solution space are characterized by the probability model. From this point of view, an environment identification-based memory management scheme (EI-MMS) is proposed to adapt binary-coded EDAs to solve dynamic optimization problems (DOPs). Within this scheme, the probability models that characterize the search space of the changing environment are stored and retrieved to adapt EDAs according to environmental changes. A diversity loss correction scheme and a boundary correction scheme are combined to counteract the diversity loss during the static evolutionary process of each environment. Experimental results show the validity of the EI-MMS and indicate that the EI-MMS can be applied to any binary-coded EDAs. In comparison with three state-of-the-art algorithms, the univariate marginal distribution algorithm (UMDA) using the EI-MMS performs better when solving three decomposable DOPs. In order to understand the EI-MMS more deeply, the sensitivity analysis of parameters is also carried out in this paper.

关键词： estimation of distribution algorithm Dynamic optimization problem Environment identification Memory scheme Diversity compensation

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A roadmap for solving optimization problems with estimation of distribution algorithms

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NATURAL COMPUTING 2024年第1期23卷 99-113页

作者： Ceberio, Josu Mendiburu, Alexander Lozano, Jose A. Univ Basque Country Dept Comp Sci & Artificial Intelligence UPV EHU Manuel Lardizabal Pasealekua 1 Donostia San Sebastian 20018 Spain Univ Basque Country Dept Comp Architecture & Technol UPV EHU Manuel Lardizabal Pasealekua 1 Donostia San Sebastian 20018 Spain

In recent decades, estimation of distribution algorithms (EDAs) have gained much popularity in the evolutionary computation community for solving optimization problems. Characterized by the use of probabilistic models to represent the solutions and the interactions between the variables of the problem, EDAs can be applied to either discrete, continuous or mixed domain problems. Due to this robustness, these algorithms have been used to solve a diverse set of real-world and academic optimization problems. However, a straightforward application is only limited to a few cases, and for the general case, an efficient application requires intuition from the problem as well as notable understanding in probabilistic modeling. In this paper, we provide a roadmap for solving optimization problems via EDAs. It is not the aim of the paper to provide a thorough review of EDAs, but to present a guide for those practitioners interested in using the potential of EDAs when solving optimization problems. In order to present a roadmap which is as useful as possible, we address the key aspects involved in the design and application of EDAs, in a sequence of stages: (1) the choice of the codification, (2) the choice of the probability model, (3) strategies to incorporate knowledge about the problem to the model, and (4) balancing the diversification-intensification behavior of the EDA. At each stage, first, the contents are presented together with common practices and advice to follow. Then, an illustration is given with an example which shows different alternatives. In addition to the roadmap, the paper presents current open challenges when developing EDAs, and revises paths for future research advances in the context of EDAs.

关键词： estimation of distribution algorithm Optimization Problem Probabilistic model Domain

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Harmless Overfitting: Using Denoising Autoencoders in estimation of distribution algorithms

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JOURNAL OF MACHINE LEARNING RESEARCH 2020年第1期21卷 1-31页

作者： Probst, Malte Rothlauf, Franz Honda Res Inst EU Carl Legien Str 30 D-63073 Offenbach Germany Johannes Gutenberg Univ Mainz Informat Syst & Business Adm Jakob Welder Weg 9 D-55128 Mainz Germany Johannes Gutenberg Univ Mainz Mainz Germany

estimation of distribution algorithms (EDAs) are metaheuristics where learning a model and sampling new solutions replaces the variation operators recombination and mutation used in standard Genetic algorithms. The choice of these models as well as the corresponding training processes are subject to the bias/variance tradeoff, also known as under- and overfitting: simple models cannot capture complex interactions between problem variables, whereas complex models are susceptible to modeling random noise. This paper suggests using Denoising Autoencoders (DAEs) as generative models within EDAs (DAE-EDA). The resulting DAE-EDA is able to model complex probability distributions. Furthermore, overfitting is less harmful, since DAEs overfit by learning the identity function. This overfitting behavior introduces unbiased random noise into the samples, which is no major problem for the EDA but just leads to higher population diversity. As a result, DAE-EDA runs for more generations before convergence and searches promising parts of the solution space more thoroughly. We study the performance of DAE-EDA on several combinatorial single-objective optimization problems. In comparison to the Bayesian Optimization algorithm, DAE-EDA requires a similar number of evaluations of the objective function but is much faster and can be parallelized efficiently, making it the preferred choice especially for large and difficult optimization problems.

关键词： denoising autoencoder estimation of distribution algorithm overfitting combinatorial optimization neural networks

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Effective search for Pittsburgh learning classifier systems via estimation of distribution algorithms

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INFORMATION SCIENCES 2012年 198卷 100-117页

作者： Yang, Jiadong Xu, Hua Jia, Peifa Tsinghua Univ State Key Lab Intelligent Technol & Syst Tsinghua Natl Lab Informat Sci & Technol Dept Comp Sci & Technol Beijing 100084 Peoples R China

Pittsburgh-style learning classifier systems (LCSs), in which an entire candidate solution is represented as a set of variable number of rules, combine supervised learning with genetic algorithms (GAS) to evolve rule-based classification models. It has been shown that standard crossover operators in GAs do not guarantee an effective evolutionary search in many sophisticated problems that contain strong interactions between features. In this paper, we propose a Pittsburgh-style learning classifier system based on the Bayesian optimization algorithm with the aim of improving the effectiveness and efficiency of the rule structure exploration. In the proposed method, classifiers are generated and recombined at two levels. At the lower level, single rules contained in classifiers are produced by sampling Bayesian networks which characterize the global statistical information extracted from the current promising rules in the search space. At the higher level, classifiers are recombined by rule-wise uniform crossover operators to keep the semantics of rules in each classifier. Experimental studies on both artificial and real world binary classification problems show that the proposed method converges faster while achieving solutions with the same or even higher accuracy compared with the original Pittsburgh-style LCSs. (C) 2012 Elsevier Inc. All rights reserved.

关键词： Learning classifier system Genetics-based machine learning estimation of distribution algorithm Bayesian optimization algorithm Evolutionary computation

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Unified eigen analysis on multivariate Gaussian based estimation of distribution algorithms

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INFORMATION SCIENCES 2008年第15期178卷 3000-3023页

作者： Dong, Weishan Yao, Xin Chinese Acad Sci Inst Automat Key Lab Complex Syst & Intelligence Sci Beijing 100190 Peoples R China Univ Birmingham Sch Comp Sci CERCIA Birmingham B15 2TT W Midlands England

Multivariate Gaussian models are widely adopted in continuous estimation of distribution algorithms (EDAs), and covariance matrix plays the essential role in guiding the evolution. In this paper, we propose a new framework for multivariate Gaussian based EDAs (MGEDAs), named eigen decomposition EDA (ED-EDA). Unlike classical EDAs, ED-EDA focuses on eigen analysis of the covariance matrix, and it explicitly tunes the eigenvalues. All existing MGEDAs can be unified within our ED-EDA framework by applying three different eigenvalue tuning strategies. The effects of eigenvalue on influencing the evolution are investigated through combining maximum likelihood estimates of Gaussian model with each of the eigenvalue tuning strategies in ED-EDA. In our experiments, proper eigenvalue tunings show high efficiency in solving problems with small population sizes, which are difficult for classical MGEDA adopting maximum likelihood estimates alone. Previously developed covariance matrix repairing (CMR) methods focusing on repairing computational errors of covariance matrix can be seen as a special eigenvalue tuning strategy. By using the ED-EDA framework, the computational time of CMR methods can be reduced from cubic to linear. Two new efficient CMR methods are proposed. Through explicitly tuning eigenvalues, ED-EDA provides a new approach to develop more efficient Gaussian based EDAs. (c) 2008 Elsevier Inc. All rights reserved.

关键词： estimation of distribution algorithm eigen analysis multivariate Gaussian distribution covariance matrix scaling eigenvalue tuning

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MB-GNG: Addressing drawbacks in multi-objective optimization estimation of distribution algorithms

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OPERATIONS RESEARCH LETTERS 2011年第2期39卷 150-154页

作者： Marti, Luis Garcia, Jesus Berlanga, Antonio Coello Coello, Carlos A. Molina, Jose M. Univ Carlos III Madrid Dept Informat Grp Appl Artificial Intelligence Madrid 28270 Spain IPN CINVESTAV Dept Comp Sci Mexico City 07360 DF Mexico

We examine the model-building issue related to multi-objective estimation of distribution algorithms (MOEDAs) and show that some of their, as yet overlooked, characteristics render most current MOEDAs unviable when addressing optimization problems with many objectives. We propose a novel model-building growing neural gas (MB-GNG) network that is specially devised for properly dealing with that issue and therefore yields a better performance. Experiments are conducted in order to show from an empirical point of view the advantages of the new algorithm. (c) 2011 Elsevier B.V. All rights reserved.

关键词： Multi-objective optimization estimation of distribution algorithm Model building Growing neural gas

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Hybrid estimation of distribution algorithms for solving a keyboard layout problem

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JOURNAL OF INDUSTRIAL AND PRODUCTION ENGINEERING 2018年第6期35卷 352-367页

作者： Pradeepmon, T. G. Panicker, Vinay V. Sridharan, R. Natl Inst Technol Dept Mech Engn Calicut Kerala India

The use of smartphones and handheld devices in our daily activities has sharply increased. The added features of wireless technology and related applications on these devices make it possible to write emails, notes, and long text. Even though the most commonly used electronic input device is a keyboard, very little work has been dedicated for finding an optimal layout for this device. In this research, the aim is to propose a better layout for the single-finger keyboard in terms of rapid typing. The keyboard layout problem can be formulated as a quadratic assignment problem, which is one of the hardest combinatorial optimization problems. Some well-known literary works in English are chosen for estimating the keying-in-time. A variant of genetic algorithm, namely, the estimation of distribution algorithms is used to find a better layout. The new layout is found to be efficient compared with some of the existing prominent keyboard layouts.

关键词： Single-finger keyboard estimation of distribution algorithm quadratic assignment problem keyboard layout problem population based incremental learning univariate marginal distribution algorithm

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