Sporadic model building for efficiency enhancement of hierarchical BOA

This paper describes and analyzes sporadic model building, which can be used to enhance the efficiency of the hierarchical Bayesian optimization algorithm (hBOA) and other advanced estimation of distribution algorithms (EDAs) that use complex multivariate probabilistic models. With sporadic model building, the structure of the probabilistic model is updated once every few iterations (generations), whereas in the remaining iterations only model parameters (conditional and marginal probabilities) are updated. Since the time complexity of updating model parameters is much lower than the time complexity of learning the model structure, sporadic model building decreases the overall time complexity of model building. The paper shows that for boundedly difficult nearly decomposable and hierarchical optimization problems, sporadic model building leads to a significant model-building speedup that decreases the asymptotic time complexity of model building in hBOA by a factor of Θ(n 0.26) to Θ(n 0.5), where n is the problem size. On the other hand, sporadic model building also increases the number of evaluations until convergence; nonetheless, the evaluation slowdown is insignificant compared to the gains in the asymptotic complexity of model building.

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

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

[3]  Martin Pelikan,et al.  Parallel Mixed Bayesian Optimization Algorithm: A Scaleup Analysis , 2004, ArXiv.

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

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

[6]  Martin Loebl,et al.  On the Theory of Pfaffian Orientations. II. T-joins, k-cuts, and Duality of Enumeration , 1998, Electron. J. Comb..

[7]  Jan Naudts,et al.  The Effect of Spin-Flip Symmetry on the Performance of the Simple GA , 1998, PPSN.

[8]  A. Hartmann Ground-state clusters of two-, three-, and four-dimensional +/-J Ising spin glasses. , 1999, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  David E. Goldberg,et al.  Optimizing Global-Local Search Hybrids , 1999, GECCO.

[10]  V. Kulish Hierarchy and hierarchical asymptotic methods in electrodynamics , 2002 .

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

[12]  David E. Goldberg,et al.  A hierarchy machine: Learning to optimize from nature and humans , 2003, Complex..

[13]  M. Troyer,et al.  Performance limitations of flat-histogram methods. , 2003, Physical review letters.

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

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

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

[17]  Mark Stefik,et al.  Planning with Constraints (MOLGEN: Part 1) , 1981, Artif. Intell..

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

[19]  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).

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

[21]  D. Goldberg,et al.  Verification and extension of the theory of global-local hybrids , 2001 .

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

[23]  Robin Hons,et al.  Estimation of Distribution Algorithms and Minimum Relative Entropy , 2005 .

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

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

[26]  Ingo Wegener,et al.  The Ising Model on the Ring: Mutation Versus Recombination , 2004, GECCO.

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

[28]  Martin Loebl,et al.  On the Theory of Pfaffian Orientations. I. Perfect Matchings and Permanents , 1998, Electron. J. Comb..

[29]  F. Guerra Spin Glasses , 2005, cond-mat/0507581.

[30]  C. V. Hoyweghen Detecting spin-flip symmetry in optimization problems , 2001 .

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

[32]  Mark Stefik,et al.  Planning and Meta-Planning (MOLGEN: Part 2) , 1981, Artif. Intell..

[33]  Ronald A. Howard,et al.  Influence Diagrams , 2005, Decis. Anal..

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

[35]  Heinz Mühlenbein,et al.  Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization , 1993, Evolutionary Computation.

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

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

[38]  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.

[39]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

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

[41]  David E. Goldberg,et al.  Hierarchical Problem Solving and the Bayesian Optimization Algorithm , 2000, GECCO.

[42]  Martin Pelikan,et al.  Design of Multithreaded Estimation of Distribution Algorithms , 2003, GECCO.

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

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

[45]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[46]  Nir Friedman,et al.  On the Sample Complexity of Learning Bayesian Networks , 1996, UAI.

[47]  David E. Goldberg,et al.  Bayesian optimization algorithm: from single level to hierarchy , 2002 .

[48]  D. Goldberg,et al.  Escaping hierarchical traps with competent genetic algorithms , 2001 .

[49]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

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

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

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

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

[54]  K. Binder,et al.  Spin glasses: Experimental facts, theoretical concepts, and open questions , 1986 .

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

[56]  Shumeet Baluja,et al.  Using a priori knowledge to create probabilistic models for optimization , 2002, Int. J. Approx. Reason..

[57]  Kalyanmoy Deb,et al.  Sufficient conditions for deceptive and easy binary functions , 1994, Annals of Mathematics and Artificial Intelligence.

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

[59]  D. Goldberg,et al.  Domino convergence, drift, and the temporal-salience structure of problems , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

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

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

[62]  Earl D. Sacerdoti,et al.  The Nonlinear Nature of Plans , 1975, IJCAI.

[63]  David E. Goldberg,et al.  Combining competent crossover and mutation operators: a probabilistic model building approach , 2005, GECCO '05.

[64]  Jordan B. Pollack,et al.  Modeling Building-Block Interdependency , 1998, PPSN.

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

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

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

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

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

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

[71]  D. Goldberg,et al.  BOA: the Bayesian optimization algorithm , 1999 .

[72]  Roberto Santana,et al.  Estimation of Distribution Algorithms with Kikuchi Approximations , 2005, Evolutionary Computation.

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

[74]  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 .