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univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints

INFORMATION SCIENCES 2011年第11期181卷 2340-2355页

作者： Lozada-Chang, Li-Vang Santana, Roberto Univ Basque Country Intelligent Syst Grp Dept Comp Sci & Artificial Intelligence San Sebastian Spain Univ Politecn Madrid E-28660 Madrid Spain Univ Havana Fac Math & Computat Havana Cuba

In this paper, we introduce a mathematical model for analyzing the dynamics of the univariate marginal distribution algorithm (UMDA) for a class of parametric functions with isolated global optima. We prove a number of results that are used to model the evolution of UMDA probability distributions for this class of functions. We show that a theoretical analysis can assess the effect of the function parameters on the convergence and rate of convergence of UMDA. We also introduce for the first time a long string limit analysis of UMDA. Finally, we relate the results to ongoing research on the application of the estimation of distribution algorithms for problems with unitation constraints. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Estimation of distribution algorithms univariate marginal distribution algorithm Convergence analysis Evolutionary algorithms Long string limit analysis

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univariate marginal distribution algorithm in Combination with Extremal Optimization (EO, GEO)

Univariate Marginal Distribution Algorithm in Combination wi...

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18th International Conference on Neural Information Processing (ICONIP)

作者： Hashemi, Mitra Meybodi, Mohammad Reza Islamic Azad Univ Dept Comp Engn & Informat Technol Qazvin Branch Qazvin Iran Amirkabir Univ Technol Dept Comp Engn & Informat Technol Tehran Iran

ISBN: (纸本)9783642249570;9783642249587

The UMDA algorithm is a type of Estimation of distribution algorithms. This algorithm has better performance compared to others such as genetic algorithm in terms of speed, memory consumption and accuracy of solutions. It can explore unknown parts of search space well. It uses a probability vector and individuals of the population are created through the sampling. Furthermore. EO algorithm is suitable for local search of near global best solution in search space. and it dose not stuck in local optimum. Hence, combining these two algorithms is able to create interaction between two fundamental concepts in evolutionary algorithms, exploration and exploitation. and achieve better results of this paper represent the performance of the proposed algorithm on two NP-hard problems, multi processor scheduling problem and graph hi-partitioning problem.

关键词： univariate marginal distribution algorithm Extremal Optimization Generalized Extremal Optimization Estimation of distribution algorithm

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A univariate marginal distribution algorithm based on extreme elitism and its application to the robotic inverse displacement problem

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GENETIC PROGRAMMING AND EVOLVABLE MACHINES 2017年第3期18卷 283-312页

作者： Gao, Shujun de Silva, Clarence W. Univ British Columbia Dept Mech Engn Ind Automat Lab 6250 Appl Sci Lane Vancouver BC V6T 1Z4 Canada

In this paper, a univariate marginal distribution algorithm in continuous domain (UMDA (C) ) based on extreme elitism (EEUMDA (C) ) is proposed for solving the inverse displacement problem (IDP) of robotic manipulators. This algorithm highlights the effect of a few top best solutions to form a primary evolution direction and obtains a fast convergence rate. Then it is implemented to determine the IDP of a 4-degree-of-freedom (DOF) Barrett WAM robotic arm. After that, the algorithm is combined with differential evolution (EEUMDA (C) -DE) to solve the IDP of a 7-DOF Barrett WAM robotic arm. In addition, three other heuristic optimization algorithms (enhanced leader particle swarm optimization, intersect mutation differential evolution, and evolution strategies) are applied to find the IDP solution of the 7-DOF arm and their performance is compared with that of EEUMDA (C) -DE.

关键词： univariate marginal distribution algorithm Inverse displacement problem Top best solutions Gaussian model Differential evolution algorithm

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A hybrid univariate marginal distribution algorithm for dynamic economic dispatch of units considering valve-point effects and ramp rates

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2015年第2期25卷 374-392页

作者： Gu, Wei Wu, Yonggang Zhang, GuoYong Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Peoples R China

This paper presents a new approach for dynamic economic dispatch (DED) problem in power system by using a hybrid univariate marginal distribution algorithm (HUMDA). The DED problem with valve-point effects and ramp rate limits is a nonliner constrained optimization problem with non-convex and non-smooth characteristics. In the proposed method, a two-stage adaptive mechanism is devised to control parameters of the univariate marginal distribution algorithm in continuous domains (UMDAc) dynamically and lead the algorithm with better search efficiency;a chaotic local search operator is integrated with UMDAc to effectively avoid premature convergence. Moreover, a constraint handle according to the two-stage adaptive mechanism is proposed, and the results show that the strategy can handle constraints effectively. Finally, the efficiency of the proposed method is validated on two test systems consisting of 5, 10 and 30 thermal units. The results show the superiority of the proposed method while it is compared with other works in the area. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： dynamic economic dispatch univariate marginal distribution algorithm two-stage adaptive mechanism chaotic local search operator constraint handle

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The univariate marginal distribution algorithm Copes Well with Deception and Epistasis

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EVOLUTIONARY COMPUTATION 2021年第4期29卷 543-563页

作者： Doerr, Benjamin Krejca, Martin S. Inst Polytech Paris Ecole Polytech CNRS Lab Informat LIX Palaiseau France Sorbonne Univ CNRS LIP6 Paris France

In their recent work, Lehre and Nguyen (2019) show that the univariate marginal distribution algorithm (UMDA) needs time exponential in the parent populations size to optimize the DeceptiveLeadingBlocks (DLB) problem. They conclude from this result that univariate EDAs have difficulties with deception and epistasis. In this work, we show that this negative finding is caused by the choice of the parameters of the UMDA. When the population sizes are chosen large enough to prevent genetic drift, then the UMDA optimizes the DLB problem with high probability with at most lambda(n/2+2e ln n) fitness evaluations. Since an offspring population size lambda of order nlogn can prevent genetic drift, the UMDA can solve the DLB problem with O(n(2) log n) fitness evaluations. In contrast, for classic evolutionary algorithms no better runtime guarantee than O(n(3)) is known (which we prove to be tight for the (1+1) EA), so our result rather suggests that the UMDA can cope well with deception and epistatis. From a broader perspective, our result shows that the UMDA can cope better with local optima than many classic evolutionary algorithms;such a result was previously known only for the compact genetic algorithm. Together with the lower bound of Lehre and Nguyen, our result for the first time rigorously proves that running EDAs in the regime with genetic drift can lead to drastic performance losses.

关键词： Estimation-of-distribution algorithm univariate marginal distribution algorithm runtime analysis epistasis theory

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An application of univariate marginal distribution algorithm in MIMO communication systems

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INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS 2010年第1期23卷 109-124页

作者： Bashir, Sajid Naeem, Muhammad Khan, Adnan Ahmed Shah, Syed Ismail CASE Dept Comp Engn Islamabad Pakistan Simon Fraser Univ Burnaby BC V5A 1S6 Canada NUST Islamabad Pakistan Iqra Univ Dept Comp Islamabad Pakistan

The paper discusses a sequence detector based on univariate marginal distribution algorithm (UMDA) that jointly estimates the symbols transmitted in a multiple input multiple output (MIMO) communication system. While an optimal maximum likelihood detection using an exhaustive search method is prohibitively complex, it has been shown that sphere decoder (SD) achieves the optimal bit error rate (BER) performance with polynomial time complexity for smaller array sizes. However, the worst-case complexity of SD is exponential in the problem dimensions, this brings in question its practical implementation for larger number of spatial layers and for higher-order signal constellation. The proposed detector shows promising results for this overly difficult and complicated operating environment, confirmed through simulation results. A performance comparison of the UMDA detector with SD is presented for higher-order complex MIMO architectures with limited average transmit power. The proposed detector achieves substantial performance gain for higher-order systems attaining a near optimal BER performance with reduced computational complexity as compared with SD. Copyright (C) 2009 John Wiley & Sons, Ltd.

关键词： computational complexity maximum likelihood detection multiple input multiple output systems sphere decoder univariate marginal distribution algorithm vertical bell labs layered space time architecture

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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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Identification of combination of SNPs associated with Crohn's Disease using a Balanced univariate marginal distribution algorithm 4

Identification of combination of SNPs associated with Crohn'...

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4th International Conference on Information Science and Control Engineering (ICISCE)

作者： Wei Bin Zhong Weidong Zhao Jing APF Engn Coll Key Lab Network & Informat Secur Xian Shaanxi Peoples R China Xijing Univ Coll Sci Xian Shaanxi Peoples R China

ISBN: (纸本)9781538630136

Detecting diseases associated SNPs is the central goal of genetics and molecular biology. However, high throughput techniques often provide long lists of disease SNPs candidates, and the identification of disease SNPs among the candidates set remains timeconsuming and expensive. In addition, contrasting to the number of SNPs involved, the available datasets (samples) generally have fairly small sample size and the datasets used in these studies are often imbalanced (the number of cases and controls are not equal). Therefore, it is necessary to develop a robust tool to identify the disease associated SNPs. In this paper, we proposed a modified univariate marginal distribution algorithm (MUMDA) taking into account the imbalanced ratios of case/control for selecting the associated SNPs. In addition, the sparse vector encoding method was used in this paper. We illustrated the effectiveness of our algorithm using Crohn's disease (CD) dataset which includes 144 cases and 243 controls (each one has 103 SNPs). Our observations suggested that the proposed method could capture important features of the genetic architecture of CD and our algorithm outperformed other current methods.

关键词： Single nucleotide polymorphisms disease association studies feature selection support vector machine univariate marginal distribution algorithm

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Runtime Analysis of the univariate marginal distribution algorithm under Low Selective Pressure and Prior Noise

Runtime Analysis of the Univariate Marginal Distribution Alg...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Lehre, Per Kristian Phan Trung Hai Nguyen Univ Birmingham Sch Comp Sci Birmingham B15 2TT W Midlands England

ISBN: (纸本)9781450361118

We perform a rigorous runtime analysis for the univariate marginal distribution algorithm on the LEADINGONES function, a wellknown benchmark function in the theory community of evolutionary computation with a high correlation between decision variables. For a problem instance of size n, the currently best known upper bound on the expected runtime is O (n lambda log lambda + n(2)) (Dang and Lehre, GECCO 2015), while a lower bound necessary to understand how the algorithm copes with variable dependencies is still missing. Motivated by this, we show that the algorithm requires a e(Omega(mu)) runtime with high probability and in expectation if the selective pressure is low;otherwise, we obtain a lower bound of Omega/(n lambda/log(lambda-mu) on the expected runtime. Furthermore, we for the first time consider the algorithm on the function under a prior noise model and obtain an O (n(2)) expected runtime for the optimal parameter settings. In the end, our theoretical results are accompanied by empirical findings, not only matching with rigorous analyses but also providing new insights into the behaviour of the algorithm.

关键词： univariate marginal distribution algorithm leadingones noisy optimisation running time analysis theory

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Application of Chaotic univariate marginal distribution algorithm to economic dispatch control of Cascade Hydropower Plants

Application of Chaotic Univariate Marginal Distribution Algo...

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1st International Conference on Energy and Environmental Protection (ICEEP 2012)

作者： Gu, Wei Wu, Yonggang Wu, Jincheng Huazhong Univ Sci & Technol Sch Hydropower & Informat Engn Wuhan 430074 Peoples R China

ISBN: (纸本)9783037854150

The economic dispatch control of cascade hydropower plants is a large scale non-linear constrained optimization problem, which plays an important role in cascade reservoirs daily optimal. This paper proposes a chaotic univariate marginal distribution algorithm (CUMDA) to solve the economic dispatch problem of cascade hydropower plants. In the proposed method, a chaotic search is integrated with univariate marginal distribution algorithm (UMDA) to effectively avoid premature convergence, chaotic sequences combine with adaptive approach are applied to help algorithm escape from local optimal trap. The feasibility of the proposed method is demonstrated for economic dispatch control of a test cascade hydro system. The simulation results show that the proposed method can obtain higher quality solution.

关键词： Economic dispatch control cascade hydropower plants univariate marginal distribution algorithm Chaotic

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