An introduction and survey of estimation of distribution algorithms

Abstract 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. This explicit use of probabilistic models in optimization offers some significant advantages over other types of metaheuristics. This paper discusses these advantages and outlines many of the different types of EDAs. In addition, some of the most powerful efficiency enhancement techniques applied to EDAs are discussed and some of the key theoretical results relevant to EDAs are outlined.

[1]  Martin Pelikan,et al.  Intelligent bias of network structures in the hierarchical BOA , 2009, GECCO.

[2]  Kalyanmoy Deb,et al.  Analyzing Deception in Trap Functions , 1992, FOGA.

[3]  David E. Goldberg,et al.  Let's Get Ready to Rumble: Crossover Versus Mutation Head to Head , 2004, GECCO.

[4]  Thomas G. Dietterich What is machine learning? , 2020, Archives of Disease in Childhood.

[5]  David H. Ackley,et al.  An empirical study of bit vector function optimization , 1987 .

[6]  David E. Goldberg,et al.  Real-Coded Bayesian Optimization Algorithm: Bringing the Strength of BOA into the Continuous World , 2004, GECCO.

[7]  Pedro Larrañaga,et al.  Solving the Traveling Salesman Problem with EDAs , 2002, Estimation of Distribution Algorithms.

[8]  Rajkumar Roy,et al.  Advances in Soft Computing: Engineering Design and Manufacturing , 1998 .

[9]  Max Henrion,et al.  Propagating uncertainty in bayesian networks by probabilistic logic sampling , 1986, UAI.

[10]  David E. Goldberg,et al.  Scalability of the Bayesian optimization algorithm , 2002, Int. J. Approx. Reason..

[11]  John H. Holland,et al.  Genetic Algorithms and the Optimal Allocation of Trials , 1973, SIAM J. Comput..

[12]  Martin Pelikan,et al.  Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications (Studies in Computational Intelligence) , 2006 .

[13]  Cláudio F. Lima,et al.  Towards automated selection of estimation of distribution algorithms , 2010, GECCO '10.

[14]  Petros Koumoutsakos,et al.  A Mixed Bayesian Optimization Algorithm with Variance Adaptation , 2004, PPSN.

[15]  Tian-Li Yu,et al.  Difficulty of linkage learning in estimation of distribution algorithms , 2009, GECCO.

[16]  A. K. Hartmann,et al.  Cluster-exact approximation of spin glass groundstates , 1995 .

[17]  Pedro Larrañaga,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

[18]  David E. Goldberg,et al.  iBOA: the incremental bayesian optimization algorithm , 2008, GECCO '08.

[19]  David E. Goldberg,et al.  Getting the best of both worlds: Discrete and continuous genetic and evolutionary algorithms in concert , 2003, Inf. Sci..

[20]  David Maxwell Chickering,et al.  Learning Bayesian Networks: The Combination of Knowledge and Statistical Data , 1994, Machine Learning.

[21]  Endika Bengoetxea,et al.  A parallel framework for loopy belief propagation , 2007, GECCO '07.

[22]  Marcus Gallagher,et al.  Multi-layer Perceptron Error Surfaces: Visualization, Structure and Modelling , 2000 .

[23]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

[24]  David E. Goldberg,et al.  Model accuracy in the Bayesian optimization algorithm , 2011, Soft Comput..

[25]  Dirk Thierens,et al.  Crossing the road to efficient IDEAs for permutation problems , 2001 .

[26]  John A. Hartigan,et al.  Clustering Algorithms , 1975 .

[27]  Siddhartha Shakya,et al.  Optimising cancer chemotherapy using an estimation of distribution algorithm and genetic algorithms , 2006, GECCO '06.

[28]  Hisashi Handa The effectiveness of mutation operation in the case of Estimation of Distribution Algorithms , 2007, Biosyst..

[29]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[30]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

[31]  Piotr Lipinski ECGA vs. BOA in discovering stock market trading experts , 2007, GECCO '07.

[32]  David E. Goldberg,et al.  Node Histogram vs . Edge Histogram : A Comparison of PMBGAs in Permutation Domains , 2006 .

[33]  S. Baluja,et al.  Using Optimal Dependency-Trees for Combinatorial Optimization: Learning the Structure of the Search Space , 1997 .

[34]  H. Mühlenbein Convergence of Estimation of Distribution Algorithms for Finite Samples , 2007 .

[35]  Qingfu Zhang,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 1 RM-MEDA: A Regularity Model-Based Multiobjective Estimation of , 2022 .

[36]  Martin Pelikan,et al.  Spurious dependencies and EDA scalability , 2010, GECCO '10.

[37]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

[38]  R. K. Ursem Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[39]  Heinz Mühlenbein,et al.  The Factorized Distribution Algorithm and the Minimum Relative Entropy Principle , 2006, Scalable Optimization via Probabilistic Modeling.

[40]  Reuven Y. Rubinstein,et al.  Optimization of computer simulation models with rare events , 1997 .

[41]  Saint Louis,et al.  Competent Program Evolution , 2006 .

[42]  Arturo Hernández Aguirre,et al.  Using Copulas in Estimation of Distribution Algorithms , 2009, MICAI.

[43]  Chao-Hong Chen,et al.  Enabling the Extended Compact Genetic Algorithm for Real-Parameter Optimization by Using Adaptive Discretization , 2010, Evolutionary Computation.

[44]  Kalyanmoy Deb,et al.  Genetic Algorithms, Noise, and the Sizing of Populations , 1992, Complex Syst..

[45]  Josef Schwarz,et al.  The Parallel Bayesian Optimization Algorithm , 2000 .

[46]  Daniel E. Goldberg The design of innovation: Lessons from genetic algorithms , 1998 .

[47]  David E. Goldberg,et al.  Multi-objective bayesian optimization algorithm , 2002 .

[48]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[49]  Pedro Larrañaga,et al.  Optimization by Max-Propagation Using Kikuchi Approximations , 2007 .

[50]  Gary B. Lamont,et al.  Applications Of Multi-Objective Evolutionary Algorithms , 2004 .

[51]  C. N. Liu,et al.  Approximating discrete probability distributions with dependence trees , 1968, IEEE Trans. Inf. Theory.

[52]  Pedro Larrañaga,et al.  Towards a New Evolutionary Computation - Advances in the Estimation of Distribution Algorithms , 2006, Towards a New Evolutionary Computation.

[53]  Patrick M. Reed,et al.  The Value of Online Adaptive Search: A Performance Comparison of NSGAII, epsilon-NSGAII and epsilonMOEA , 2005, EMO.

[54]  Dirk Thierens,et al.  Enhancing the Performance of Maximum-Likelihood Gaussian EDAs Using Anticipated Mean Shift , 2008, PPSN.

[55]  Shumeet Baluja,et al.  A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning , 1994 .

[56]  Martin Pelikan,et al.  Fitness Inheritance in the Bayesian Optimization Algorithm , 2004, GECCO.

[57]  Robin Höns,et al.  Estimation of distribution algorithms and minimum relative entropy , 2005 .

[58]  Siddhartha Shakya,et al.  An EDA based on local markov property and gibbs sampling , 2008, GECCO '08.

[59]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[60]  Pedro Larrañaga,et al.  Adaptive Estimation of Distribution Algorithms , 2008, Adaptive and Multilevel Metaheuristics.

[61]  Martin Pelikan,et al.  Hierarchical Bayesian optimization algorithm: toward a new generation of evolutionary algorithms , 2010, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[62]  Thomas D. LaToza,et al.  On the supply of building blocks , 2001 .

[63]  Pedro Larrañaga,et al.  Unsupervised Learning Of Bayesian Networks Via Estimation Of Distribution Algorithms: An Application To Gene Expression Data Clustering , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[64]  Robert Elliott Smith,et al.  Why is parity hard for estimation of distribution algorithms? , 2007, GECCO '07.

[65]  Martin Pelikan,et al.  Scalable Optimization via Probabilistic Modeling , 2006, Studies in Computational Intelligence.

[66]  David E. Goldberg,et al.  Designing Competent Mutation Operators Via Probabilistic Model Building of Neighborhoods , 2004, GECCO.

[67]  Ponnuthurai N. Suganthan,et al.  Guest Editorial Special Issue on Differential Evolution , 2011, IEEE Transactions on Evolutionary Computation.

[68]  Martin Pelikan,et al.  Design of Parallel Estimation of Distribution Algorithms , 2006, Scalable Optimization via Probabilistic Modeling.

[69]  L. A. Marascuilo,et al.  Nonparametric and Distribution-Free Methods for the Social Sciences , 1977 .

[70]  David E. Goldberg Using Time Efficiently: Genetic-Evolutionary Algorithms and the Continuation Problem , 1999, GECCO.

[71]  G. Schwarz Estimating the Dimension of a Model , 1978 .

[72]  Xavier Llorà,et al.  Towards billion-bit optimization via a parallel estimation of distribution algorithm , 2007, GECCO '07.

[73]  R. Steele Optimization , 2005 .

[74]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[75]  Kumara Sastry,et al.  Efficient Atomic Cluster Optimization Using A Hybrid Extended Compact Genetic Algorithm With Seeded , 2001 .

[76]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[77]  Hussein A. Abbass,et al.  Program Evolution with Explicit Learning: a New Framework for Program Automatic Synthesis , 2003 .

[78]  David E. Goldberg,et al.  Sporadic model building for efficiency enhancement of hierarchical BOA , 2006, GECCO.

[79]  W. Hart Adaptive global optimization with local search , 1994 .

[80]  Chao-Hong Chen,et al.  Real-coded ECGA for economic dispatch , 2007, GECCO '07.

[81]  Els Ducheyne,et al.  Probabilistic Models for Linkage Learning in Forest Management , 2005 .

[82]  Martin Pelikan,et al.  Searching for Ground States of Ising Spin Glasses with Hierarchical BOA and Cluster Exact Approximation , 2006, Scalable Optimization via Probabilistic Modeling.

[83]  Shigeyoshi Tsutsui Probabilistic Model-Building Genetic Algorithms in Permutation Representation Domain Using Edge Histogram , 2002, PPSN.

[84]  Qingfu Zhang,et al.  On the convergence of a class of estimation of distribution algorithms , 2004, IEEE Transactions on Evolutionary Computation.

[85]  Jonathan L. Shapiro,et al.  Drift and Scaling in Estimation of Distribution Algorithms , 2005, Evolutionary Computation.

[86]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[87]  Dirk Thierens,et al.  Multi-objective Optimization with the Naive MIDEA , 2006 .

[88]  Dirk Thierens,et al.  Mixing in Genetic Algorithms , 1993, ICGA.

[89]  David Maxwell Chickering,et al.  A Bayesian Approach to Learning Bayesian Networks with Local Structure , 1997, UAI.

[90]  T. Koopmans,et al.  Assignment Problems and the Location of Economic Activities , 1957 .

[91]  Jiri Ocenasek,et al.  Parallel Estimation of Distribution Algorithms , 2010 .

[92]  David E. Goldberg,et al.  The gambler''s ruin problem , 1997 .

[93]  Jing J. Liang,et al.  Problem Definitions and Evaluation Criteria for the CEC 2005 Special Session on Real-Parameter Optimization , 2005 .

[94]  Shumeet Baluja,et al.  Incorporating a priori Knowledge in Probabilistic-Model Based Optimization , 2006, Scalable Optimization via Probabilistic Modeling.

[95]  Heinz Mühlenbein,et al.  FDA -A Scalable Evolutionary Algorithm for the Optimization of Additively Decomposed Functions , 1999, Evolutionary Computation.

[96]  Yaochu Jin,et al.  Knowledge incorporation in evolutionary computation , 2005 .

[97]  Nir Friedman,et al.  Learning Bayesian Networks with Local Structure , 1996, UAI.

[98]  Martin Pelikan,et al.  Analyzing Probabilistic Models in Hierarchical BOA , 2009, IEEE Transactions on Evolutionary Computation.

[99]  Roberto Santana,et al.  Toward Understanding EDAs Based on Bayesian Networks Through a Quantitative Analysis , 2012, IEEE Transactions on Evolutionary Computation.

[100]  Michèle Sebag,et al.  Extending Population-Based Incremental Learning to Continuous Search Spaces , 1998, PPSN.

[101]  Pedro Larrañaga,et al.  Learning Factorizations in Estimation of Distribution Algorithms Using Affinity Propagation , 2010, Evolutionary Computation.

[102]  Jianchao Zeng,et al.  Estimation of distribution algorithm based on archimedean copulas , 2009, GEC '09.

[103]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .

[104]  Bill Ravens,et al.  An Introduction to Copulas , 2000, Technometrics.

[105]  David E. Goldberg,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1999, Evolutionary Computation.

[106]  David E. Goldberg,et al.  Loopy Substructural Local Search for the Bayesian Optimization Algorithm , 2009, SLS.

[107]  J. Periaux,et al.  Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems , 2001 .

[108]  Barbara S. Minsker,et al.  Evaluation of Advanced Genetic Algorithms Applied to Groundwater Remediation Design , 2005 .

[109]  Marcus Gallagher,et al.  Real-valued Evolutionary Optimization using a Flexible Probability Density Estimator , 1999, GECCO.

[110]  Ivo Everts,et al.  Extended Compact Genetic Algorithm , 2004 .

[111]  Herbert A. Simon,et al.  The Sciences of the Artificial , 1970 .

[112]  David E. Goldberg,et al.  Military Antenna Design Using a Simple Genetic Algorithm and hBOA , 2006, Scalable Optimization via Probabilistic Modeling.

[113]  G. Harik Linkage Learning via Probabilistic Modeling in the ECGA , 1999 .

[114]  Shumeet Baluja,et al.  Using Optimal Dependency-Trees for Combinational Optimization , 1997, ICML.

[115]  Jianchao Zeng,et al.  Estimation of Distribution Algorithm based on copula theory , 2009, 2009 IEEE Congress on Evolutionary Computation.

[116]  Patrick Reed,et al.  Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems , 2011, Eur. J. Oper. Res..

[117]  Robert E. Smith,et al.  Fitness inheritance in genetic algorithms , 1995, SAC '95.

[118]  Chao-Hong Chen,et al.  Adaptive discretization for probabilistic model building genetic algorithms , 2006, GECCO '06.

[119]  Qingfu Zhang,et al.  An evolutionary algorithm with guided mutation for the maximum clique problem , 2005, IEEE Transactions on Evolutionary Computation.

[120]  David E. Goldberg,et al.  Efficient Genetic Algorithms Using Discretization Scheduling , 2005, Evolutionary Computation.

[121]  Jürgen Schmidhuber,et al.  Probabilistic Incremental Program Evolution: Stochastic Search Through Program Space , 1997, ECML.

[122]  Erick Cantú-Paz,et al.  Efficient and Accurate Parallel Genetic Algorithms , 2000, Genetic Algorithms and Evolutionary Computation.

[123]  W. Vent,et al.  Rechenberg, Ingo, Evolutionsstrategie — Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. 170 S. mit 36 Abb. Frommann‐Holzboog‐Verlag. Stuttgart 1973. Broschiert , 1975 .

[124]  Michèle Sebag,et al.  Avoiding the Bloat with Stochastic Grammar-Based Genetic Programming , 2001, Artificial Evolution.

[125]  James C. Bean,et al.  Genetic Algorithms and Random Keys for Sequencing and Optimization , 1994, INFORMS J. Comput..

[126]  Joseph R. Kasprzyk,et al.  A new epsilon-dominance hierarchical Bayesian optimization algorithm for large multiobjective monitoring network design problems , 2008 .

[127]  M. Pelikán,et al.  The Bivariate Marginal Distribution Algorithm , 1999 .

[128]  P. Bosman,et al.  Continuous iterated density estimation evolutionary algorithms within the IDEA framework , 2000 .

[129]  Yong Gao,et al.  Space Complexity of Estimation of Distribution Algorithms , 2005, Evolutionary Computation.

[130]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[131]  Xavier Llorà,et al.  Automated alphabet reduction method with evolutionary algorithms for protein structure prediction , 2007, GECCO '07.

[132]  Dirk Thierens,et al.  Advancing continuous IDEAs with mixture distributions and factorization selection metrics , 2001 .

[133]  David E. Goldberg,et al.  Linkage Identification by Non-monotonicity Detection for Overlapping Functions , 1999, Evolutionary Computation.

[134]  David E. Goldberg,et al.  The compact genetic algorithm , 1999, IEEE Trans. Evol. Comput..

[135]  D. Goldberg,et al.  Evolutionary Algorithm Using Marginal Histogram Models in Continuous Domain , 2007 .

[136]  Georges R. Harik,et al.  Finding Multimodal Solutions Using Restricted Tournament Selection , 1995, ICGA.

[137]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[138]  David E. Goldberg,et al.  Linkage Problem, Distribution Estimation, and Bayesian Networks , 2000, Evolutionary Computation.

[139]  Hussein A. Abbass,et al.  Grammar model-based program evolution , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[140]  C. Priebe Adaptive Mixtures , 2010 .

[141]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[142]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

[143]  Alexander Mendiburu,et al.  Parallel implementation of EDAs based on probabilistic graphical models , 2005, IEEE Transactions on Evolutionary Computation.

[144]  Martin V. Butz,et al.  Substructural Neighborhoods for Local Search in the Bayesian Optimization Algorithm , 2006, PPSN.

[145]  David E. Goldberg,et al.  Multiobjective hBOA, clustering, and scalability , 2005, GECCO '05.

[146]  David E. Goldberg,et al.  Efficiency Enhancement of Estimation of Distribution Algorithms , 2006, Scalable Optimization via Probabilistic Modeling.

[147]  Dirk Thierens,et al.  New IDEAs and more ICE by learning and using unconditional permutation factorizations , 2001 .

[148]  Dirk Thierens,et al.  Linkage Information Processing In Distribution Estimation Algorithms , 1999, GECCO.

[149]  David Heckerman,et al.  Learning Gaussian Networks , 1994, UAI.

[150]  Marco Laumanns,et al.  Bayesian Optimization Algorithms for Multi-objective Optimization , 2002, PPSN.

[151]  Franz Rothlauf,et al.  Evaluation-Relaxation Schemes for Genetic and Evolutionary Algorithms , 2004 .

[152]  David E. Goldberg,et al.  Efficiency enhancement of genetic algorithms via building-block-wise fitness estimation , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[153]  Marco Laumanns,et al.  Combining Convergence and Diversity in Evolutionary Multiobjective Optimization , 2002, Evolutionary Computation.

[154]  David E. Goldberg,et al.  Multiobjective Estimation of Distribution Algorithms , 2006, Scalable Optimization via Probabilistic Modeling.

[155]  Martin Pelikan,et al.  Dependency trees, permutations, and quadratic assignment problem , 2007, GECCO '07.

[156]  Lawrence Davis,et al.  Genetic Algorithms and Simulated Annealing , 1987 .

[157]  Alden H. Wright,et al.  Efficient Linkage Discovery by Limited Probing , 2003, Evolutionary Computation.

[158]  C. S. Wallace,et al.  An Information Measure for Classification , 1968, Comput. J..

[159]  Heinz Mühlenbein,et al.  A Maximum Entropy Approach to Sampling in EDA ? The Single Connected Case , 2003, CIARP.

[160]  Yew-Soon Ong,et al.  Advances in Natural Computation, First International Conference, ICNC 2005, Changsha, China, August 27-29, 2005, Proceedings, Part I , 2005, ICNC.

[161]  D. Goldberg,et al.  Don't evaluate, inherit , 2001 .

[162]  Qingfu Zhang,et al.  On stability of fixed points of limit models of univariate marginal distribution algorithm and factorized distribution algorithm , 2004, IEEE Transactions on Evolutionary Computation.

[163]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[164]  David E. Goldberg,et al.  Population sizing for entropy-based model building in discrete estimation of distribution algorithms , 2007, GECCO '07.

[165]  David E. Goldberg,et al.  Hierarchical BOA Solves Ising Spin Glasses and MAXSAT , 2003, GECCO.

[166]  David E. Goldberg,et al.  Using Previous Models to Bias Structural Learning in the Hierarchical BOA , 2008, Evolutionary Computation.

[167]  Heinz Mühlenbein,et al.  Evolutionary optimization and the estimation of search distributions with applications to graph bipartitioning , 2002, Int. J. Approx. Reason..

[168]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[169]  David E. Goldberg,et al.  Hierarchical Bayesian Optimization Algorithm , 2006, Scalable Optimization via Probabilistic Modeling.