Distributed Estimation of Distribution Algorithms for continuous optimization: How does the exchanged information influence their behavior?

One of the most promising areas in which probabilistic graphical models have shown an incipient activity is the field of heuristic optimization and, in particular, in Estimation of Distribution Algorithms. Due to their inherent parallelism, different research lines have been studied trying to improve Estimation of Distribution Algorithms from the point of view of execution time and/or accuracy. Among these proposals, we focus on the so-called distributed or island-based models. This approach defines several islands (algorithms instances) running independently and exchanging information with a given frequency. The information sent by the islands can be either a set of individuals or a probabilistic model. This paper presents a comparative study for a distributed univariate Estimation of Distribution Algorithm and a multivariate version, paying special attention to the comparison of two alternative methods for exchanging information, over a wide set of parameters and problems - the standard benchmark developed for the IEEE Workshop on Evolutionary Algorithms and other Metaheuristics for Continuous Optimization Problems of the ISDA 2009 Conference. Several analyses from different points of view have been conducted to analyze both the influence of the parameters and the relationships between them including a characterization of the configurations according to their behavior on the proposed benchmark.

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

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

[3]  Jose Miguel Puerta,et al.  Migration of Probability Models Instead of Individuals: An Alternative When Applying the Island Model to EDAs , 2004, PPSN.

[4]  Heinz Mühlenbein,et al.  The Equation for Response to Selection and Its Use for Prediction , 1997, Evolutionary Computation.

[5]  Enrique Alba,et al.  Influence of the Migration Policy in Parallel Distributed GAs with Structured and Panmictic Populations , 2000, Applied Intelligence.

[6]  A. A. Zhigli︠a︡vskiĭ,et al.  Theory of Global Random Search , 1991 .

[7]  Xin Yao,et al.  Unified eigen analysis on multivariate Gaussian based estimation of distribution algorithms , 2008, Inf. Sci..

[8]  Alberto Ochoa,et al.  A Parallel Island Model for Estimation of Distribution Algorithms , 2006, Towards a New Evolutionary Computation.

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

[10]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[11]  Nelis Franken,et al.  Visual exploration of algorithm parameter space , 2009, 2009 IEEE Congress on Evolutionary Computation.

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

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

[14]  Roberto Santana,et al.  Univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints , 2011, Inf. Sci..

[15]  Dana S. Richards,et al.  Punctuated Equilibria: A Parallel Genetic Algorithm , 1987, ICGA.

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

[17]  Hans-Peter Kriegel,et al.  A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise , 1996, KDD.

[18]  Pedro Larrañaga,et al.  Combinatonal Optimization by Learning and Simulation of Bayesian Networks , 2000, UAI.

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

[20]  Francisco Herrera,et al.  A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 Special Session on Real Parameter Optimization , 2009, J. Heuristics.

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

[22]  S. Baluja,et al.  Combining Multiple Optimization Runs with Optimal Dependency Trees , 1997 .

[23]  Francisco Herrera,et al.  Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power , 2010, Inf. Sci..

[24]  Petr Posík.  Estimation of Distribution Algorithms , 2006 .

[25]  Víctor Robles,et al.  Machine Learning to Analyze Migration Parameters in Parallel Genetic Algorithms , 2008, Innovations in Hybrid Intelligent Systems.

[26]  Jirí Jaros,et al.  Parallel BMDA with probability model migration , 2007, 2007 IEEE Congress on Evolutionary Computation.

[27]  Chrisila C. Pettey,et al.  A Theoretical Investigation of a Parallel Genetic Algorithm , 1989, ICGA.

[28]  Jirí Jaros,et al.  Parallel BMDA with an aggregation of probability models , 2009, 2009 IEEE Congress on Evolutionary Computation.

[29]  J. A. Lozano,et al.  Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms (Studies in Fuzziness and Soft Computing) , 2006 .

[30]  David E. Goldberg,et al.  Multiple-Deme Parallel Estimation of Distribution Algorithms: Basic Framework and Application , 2003, PPAM.

[31]  Darrell Whitley,et al.  The Island Model Genetic Algorithm: On Separability, Population Size and Convergence , 2015, CIT 2015.

[32]  Paul A. Viola,et al.  Structure Driven Image Database Retrieval , 1997, NIPS.

[33]  Pedro Larrañaga,et al.  Optimization in Continuous Domains by Learning and Simulation of Gaussian Networks , 2000 .

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

[35]  J. Douglas Barrett,et al.  Taguchi's Quality Engineering Handbook , 2007, Technometrics.

[36]  Jose Miguel Puerta,et al.  Initial approaches to the application of islands-based parallel EDAs in continuous domains , 2005, 2005 International Conference on Parallel Processing Workshops (ICPPW'05).

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

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

[39]  Enrique Alba,et al.  Parallel evolutionary algorithms can achieve super-linear performance , 2002, Inf. Process. Lett..

[40]  Ponnuthurai Nagaratnam Suganthan,et al.  Benchmark Functions for the CEC'2013 Special Session and Competition on Large-Scale Global Optimization , 2008 .

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

[42]  Enrique Alba,et al.  Improving flexibility and efficiency by adding parallelism to genetic algorithms , 2002, Stat. Comput..