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A new real-coded stochastic Bayesian optimization algorithm for continuous global optimization

GENETIC PROGRAMMING AND EVOLVABLE MACHINES 2016年第2期17卷 145-167页

作者： Moradabadi, Behnaz Ebadzadeh, Mohammad Mahdi Meybodi, Mohammad Reza Amirkabir Univ Technol Dept Comp Engn Tehran Iran

estimation of distribution algorithms are considered to be a new class of evolutionary algorithms which are applied as an alternative to genetic algorithms. Such algorithms sample the new generation from a probabilistic model of promising solutions. The search space of the optimization problem is improved by such probabilistic models. In the Bayesian optimization algorithm (BOA), the set of promising solutions forms a Bayesian network and the new solutions are sampled from the built Bayesian network. This paper proposes a novel real-coded stochastic BOA for continuous global optimization by utilizing a stochastic Bayesian network. In the proposed algorithm, the new Bayesian network takes advantage of using a stochastic structure (that there is a probability distribution function for each edge in the network) and the new generation is sampled from the stochastic structure. In order to generate a new solution, some new structure, and therefore a new Bayesian network is sampled from the current stochastic structure and the new solution will be produced from the sampled Bayesian network. Due to the stochastic structure used in the sampling phase, each sample can be generated based on a different structure. Therefore the different dependency structures can be preserved. Before the new generation is generated, the stochastic network's probability distributions are updated according to the fitness evaluation of the current generation. The proposed method is able to take advantage of using different dependency structures through the sampling phase just by using one stochastic structure. The experimental results reported in this paper show that the proposed algorithm increases the quality of the solutions on the general optimization benchmark problems.

关键词： Evolutionary algorithms estimation of distribution algorithms Bayesian optimization algorithms Bayesian networks

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A graphical model for evolutionary optimization

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EVOLUTIONARY COMPUTATION 2008年第3期16卷 289-313页

作者： Monson, Christopher K. Seppi, Kevin D. Brigham Young Univ Dept Comp Sci Provo UT 84602 USA

We present a statistical model of empirical optimization that admits the creation of algorithms with explicit and intuitively defined desiderata. Because No Free Lunch theorems dictate that no optimization algorithm can be considered more efficient than any other when considering all possible functions, the desired function class plays a prominent role in the model. In particular, this provides a direct way to answer the traditionally difficult question of what algorithm is best matched to a particular class of functions. Among the benefits of the model are the ability to specify the function class in a straightforward manner, a natural way to specify noisy or dynamic functions, and a new source of insight into No Free Lunch theorems for optimization.

关键词： mathematical optimization models evolutionary optimization estimation of distribution algorithms

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ASYNCHRONOUS PARALLEL algorithms FOR STRATEGIC HYBRID SEARCHING BASED ON A MIXTURE GAUSSIAN MODEL

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2014年第2期10卷 459-479页

作者： Said, Said Mohamed Nakamura, Morikazu Univ Ryukyus Dept Informat Engn 1 Senbaru Nishihara Okinawa 9030213 Japan

Technically exploring a solution space in an effective way helps not only to find good quality solutions, but also to reduce computation time. This paper proposes an optimization technique that utilizes hybridization, strategic search, parallelization, and asynchronous cooperation. A master-slave topology has been formulated in which the master strategically sorts out portions of the search space in four phases with the help of a clustering algorithm and assumes the role of an estimation of distribution algorithm to model the solution distribution within the space using a Gaussian mixture model without variable dependency. The new algorithm models a solution distribution by considering not only the mean vector of clustered solutions obtained from previous searches, as per the continuous univariate marginal distribution algorithm, but also by including information about the quality of solutions. With sorted probability distributions assigned by the master, slaves use genetic algorithms to extensively explore the solution space. The effect of our proposal has been experimentally analyzed in continuous domains, and the resultant algorithm shows significant improvements both in finding relatively good solutions and in reducing computation time.

关键词： Evolutionary algorithms Genetic algorithms estimation of distribution algorithms Parallel processing k-means clustering Synchronous/asynchronous algorithms Continuous population-based incremental learning Continuous univariate marginal distribution algorithm

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Linkage identification by fitness difference clustering

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EVOLUTIONARY COMPUTATION 2006年第4期14卷 383-409页

作者： Tsuji, Miwako Munetomo, Masaharu Akama, Kiyoshi Hokkaido Univ Grad Sch Informat Sci & Technol Sapporo Hokkaido 0600811 Japan Hokkaido Univ Informat Initiat Ctr Sapporo Hokkaido 0600811 Japan

Genetic algorithms perform crossovers effectively when linkage sets - sets of variables tightly linked to form building blocks - are identified. Several methods have been proposed to detect the linkage sets. Perturbation methods (PMs) investigate fitness differences by perturbations of gene values and estimation of distribution algorithms (EDAs) estimate the distribution of promising strings. In this paper, we propose a novel approach combining both of them, which detects dependencies of variables by estimating the distribution of strings clustered according to fitness differences. The proposed algorithm, called the Dependency Detection for distribution Derived from fitness Differences (D-5), can detect dependencies of a class of functions that are difficult for EDAs, and requires less computational cost than PMs.

关键词： genetic algorithms estimation of distribution algorithms linkage identification perturbation methods fitness difference clustering building blocks

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A Genetic System Based on Simulated Crossover: Stability Analysis and Relationships with Neural Nets

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EVOLUTIONARY COMPUTATION 2009年第2期17卷 167-201页

作者： Carpentieri, Marco Univ Basilicata Dept Math & Comp Sci I-85100 Potenza Italy

We consider a marginal distribution genetic model based on crossover of sequences of genes and provide relations between the associated infinite population genetic system and the neural networks. A lower bound oil population size is exhibited stating that the behavior of the finite population system, in the case of sufficiently large sizes, can be approximated by the behavior of the corresponding infinite population system. Assumptions on fitness and individual chromosomes are provided implying that the behavior of the finite population genetic system remains consistent with the behavior of the associated infinite population genetic system for suitably long trajectories. The attractors (with binary components) of the infinite Population genetic system are characterized as equilibrium points of a discrete (neural network) system that call be considered as a variant of a Hopfield's network;it is shown that the fitness is a Lyapunov function for the variant of the discrete Hopfield's net. Our main result can be summarized by stating that the relation between marginal distribution genetic systems and neural nets is much more general than that already shown elsewhere for other simpler models.

关键词： Genetic algorithms marginal distribution genetic algorithms estimation of distribution algorithms infinite population genetic modeling Hopfield's neural networks

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A robust optimization hybrid algorithm for solving the direct kinematics of the general Gough-Stewart platform

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REVISTA INTERNACIONAL DE METODOS NUMERICOS PARA CALCULO Y DISENO EN INGENIERIA 2013年第4期29卷 241-247页

作者： Hernandez-Martinez, E. E. Valdez-Pena, S. I. Sanchez-Soto, E. Inst Politecn Nacl ESIME UP Ticoman Mexico City 07340 DF Mexico Ctr Invest Matemat CIMAT AC Guanajuato 36000 Gto Mexico Mexico Univ Papaloapan Oaxaca 68400 Mexico

The direct kinematics problem for parallel robots can be stated as follows: given values of the joint variables, the corresponding Cartesian variable values, the pose of the end-effector, must be found. Most of the times the direct kinematics problem involves the solution of a system of non-linear equations. The most efficient methods to solve such kind of equations assume convexity in a cost function which minimum is the solution of the non-linear system. In consequence, the capacity of such methods depends on the knowledge about an starting point which neighboring region is convex, hence the method can find the global minimum. This article propose a method based on probabilistic learning about an adequate starting point for the Dogleg method which assumes local convexity of the function. The proposed method efficiently avoids the local minima, without need of human intervention or apriori knowledge, thus it shows a more robust performance than the simple Dogleg method or other gradient based methods. To demonstrate the performance of the proposed hybrid method, numerical experiments and the respective discussion are presented. The proposal can be extended to other structures of closed-kinematics chains, to the general solution of systems of non-linear equations, and to the minimization of non-linear functions. (C) 2011 CIMNE (Universitat Politecnica de Catalunya). Published by Elsevier Espana, S.L. All rights reserved.

关键词： Parallel robots Direct kinematics estimation of distribution algorithms Hybrid method Optimization

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Solving Order/Degree Problems by Using EDA-GK with a Novel Sampling Method

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JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS 2018年第2期22卷 236-241页

作者： Hasegawa, Ryoichi Handa, Hisashi Kindai Univ 3-4-1 Kowakae Higashiosaka Osaka 5778502 Japan

The estimation of distribution algorithms with Graph Kernels called EDA-GK is an extension of the estimation of distribution algorithms that can work with graph-related problems. Individuals of the EDA-GK are represented by graphs. In this paper, the EDA-GK is applied to solve for the Order/Degree problems, which are an NP-hard problems and are a benchmark problem in graph theory studies. Moreover, we incorporate a new sampling method for generating offspring. Experimental results on several problem instances of Order/Degree problems show the effectiveness of the EDA-GK.

关键词： estimation of distribution algorithms graph kernel Order/Degree problems

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Automated global structure extraction for effective local building block processing in XCS

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EVOLUTIONARY COMPUTATION 2006年第3期14卷 345-380页

作者： Butz, Martin V. Pelikan, Martin Llora, Xavier Goldberg, David E. Univ Wurzburg Dept Cognit Psychol D-97070 Wurzburg Germany Univ Missouri Dept Math & Comp Sci St Louis MO 63043 USA Univ Illinois Illinois Genet Algorithms Lab Urbana IL 61801 USA

Learning Classifier Systems (LCSs), such as the accuracy-based XCS, evolve distributed problem solutions represented by a population of rules. During evolution, features are specialized, propagated, and recombined to provide increasingly accurate subsolutions. Recently, it was shown that, as in conventional genetic algorithms (GAs), some problems require efficient processing of subsets of features to find problem solutions efficiently. In such problems, standard variation operators of genetic and evolutionary algorithms used in LCSs suffer from potential disruption of groups of interacting features, resulting in poor performance. This paper introduces efficient crossover operators to XCS by incorporating techniques derived from competent GAs: the extended compact GA (ECGA) and the Bayesian optimization algorithm (BOA). Instead of simple crossover operators such as uniform crossover or one-point crossover, ECGA or BOA-derived mechanisms are used to build a probabilistic model of the global population and to generate offspring classifiers locally using the model. Several offspring generation variations are introduced and evaluated. The results show that it is possible to achieve performance similar to runs with an informed crossover operator that is specifically designed to yield ideal problem-dependent exploration, exploiting provided problem structure information. Thus, we create the first competent LCSs, XCS/ECGA and XCS/BOA, that detect dependency structures online and propagate corresponding lower-level dependency structures effectively without any information about these structures given in advance.

关键词： learning classifier systems XCS online learning building block processing decomposable classification problems estimation of distribution algorithms extended compact GA Bayesian optimization algorithm

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A novel Univariate Marginal distribution Algorithm based discretization algorithm

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STATISTICS & PROBABILITY LETTERS 2012年第11期82卷 2001-2007页

作者： Zhao Jing Han ChongZhao Wei Bin Han DeQiang Xi An Jiao Tong Univ Key Lab Intelligent Networks & Network Secur State Key Lab Mfg Syst EngnMinist Educ Inst Integrated AutomatSch Elect & Informat Engn Xian 710049 Peoples R China Xi An Jiao Tong Univ Inst Syst Engn Sch Elect & Informat Engn Xian 710049 Peoples R China

Many data mining algorithms can only deal with discrete data or have a better performance on discrete data;however, for some technological reasons often we can only obtain the continuous value in the real world. Therefore, discretization has played an important role in data mining. Discretization is defined as the process of mapping the continuous attribute space into the discrete space, namely, using integer values or symbols to represent the continuous spaces. In this paper, we proposed a discretization method on the basis of a Univariate Marginal distribution Algorithm (UMDA). The UMDA is a combination of statistics learning theory and Evolution algorithms. The fitness function of the UMDA not only took the accuracy of the classifier into account, but also the number of breakpoints. Experimental results showed that the algorithm proposed in this paper could effectively reduce the number of breakpoints, and at the same time, improve the accuracy of the classifier. (C) 2012 Published by Elsevier B.V.

关键词： Univariate Marginal distribution Algorithm Breakpoints Discretization estimation of distribution algorithms Data mining

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algorithms for Attribute Selection and Knowledge Discovery 12th

Algorithms for Attribute Selection and Knowledge Discovery

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12th International Conference on Knowledge Management in Organizations (KMO) - Emerging Technology

作者： Rodriguez R, Jorge Enrique Medina Garcia, Victor Hugo Medina Estrada, Lina Maria Dist Univ Francisco Jose de Caldas Bogota Colombia

ISBN: (纸本)9783319626987;9783319626970

The features relevant selection is a task performed prior to the data mining and can be seen as one of the most important problems to solve in the data preprocessing stage an in the machine learning. With the feature selection is mainly intended to improve predictive or descriptive performance of models and implement faster and less expensive algorithms. In this paper an analysis about feature selection methods is made emphasizing on decision trees, entropy measure for ranking features, and estimation of distribution algorithms. Finally, we show the result analysis of execute the three algorithms.

关键词： Features selection Complexity Decision trees Entropy estimation of distribution algorithms Machine learning Data mining

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