Multi – objective optimization with the naive M ID E A

EDAs have been shown to perform well on a wide variety of single– objective optimization problems, for binary and real–valued variables. In this chapter we look into the extension of the EDA paradigm to multi–objective optimization. To this end, we focus the chapter around the introduction of a simple, but effective, EDA for multi–objective optimization: the naive MIDEA (mixture–based multi–objective iterated density–estimation evolutionary algorithm). The probabilistic model in this specific algorithm is a mixture distribution. Each component in the mixture is a univariate factorization. As will be shown in this chapter, mixture distributions allow for wide–spread exploration of a multi–objective front whereas most operators focus on a specific part of the multi–objective front. This wide–spread exploration aids the important preservation of diversity in multi–objective optimization. To further improve and maintain the diversity that is obtained by the mixture distribution, a specialized diversity preserving selection operator is used in the naive MIDEA. We verify the effectiveness of the naive MIDEA in two different problem domains and compare it with two other well–known efficient multi–objective evolutionary algorithms (MOEAs).

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

[2]  D. Corne,et al.  On Metrics for Comparing Non Dominated Sets , 2001 .

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

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

[5]  Wray L. Buntine Operations for Learning with Graphical Models , 1994, J. Artif. Intell. Res..

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

[7]  P. Bosman,et al.  A Thorough Documentation of Obtained Results on Real-Valued Continious and Combinatorial Multi-Objective Optimization Problems Using Diversity Preserving Mixture-Based Iterated Density Estimation Evolutionary Algorithms , 2002 .

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

[9]  Dirk Thierens,et al.  Permutation Optimization by Iterated Estimation of Random Keys Marginal Product Factorizations , 2002, PPSN.

[10]  Heinz Mühlenbein,et al.  A Factorized Distribution Algorithm Using Single Connected Bayesian Networks , 2000, PPSN.

[11]  Dirk Thierens,et al.  Multi-objective optimization with diversity preserving mixture-based iterated density estimation evolutionary algorithms , 2002, Int. J. Approx. Reason..

[12]  Lothar Thiele,et al.  Comparison of Multiobjective Evolutionary Algorithms: Empirical Results , 2000, Evolutionary Computation.

[13]  Dirk Thierens,et al.  The balance between proximity and diversity in multiobjective evolutionary algorithms , 2003, IEEE Trans. Evol. Comput..

[14]  R. Santana,et al.  The mixture of trees Factorized Distribution Algorithm , 2001 .

[15]  A. Dawid,et al.  Hyper Markov Laws in the Statistical Analysis of Decomposable Graphical Models , 1993 .

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

[17]  Xavier Gandibleux,et al.  An Annotated Bibliography of Multiobjective Combinatorial Optimization , 2000 .

[18]  Peter J. Fleming,et al.  An Overview of Evolutionary Algorithms in Multiobjective Optimization , 1995, Evolutionary Computation.

[19]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

[20]  Marco Laumanns,et al.  Why Quality Assessment Of Multiobjective Optimizers Is Difficult , 2002, GECCO.

[21]  Steffen L. Lauritzen,et al.  Graphical models in R , 1996 .

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

[23]  Kalyanmoy Deb,et al.  Multi-objective Genetic Algorithms: Problem Difficulties and Construction of Test Problems , 1999, Evolutionary Computation.

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

[25]  Marco Laumanns,et al.  On the Effects of Archiving, Elitism, and Density Based Selection in Evolutionary Multi-objective Optimization , 2001, EMO.

[26]  Carlos A. Coello Coello,et al.  A Comprehensive Survey of Evolutionary-Based Multiobjective Optimization Techniques , 1999, Knowledge and Information Systems.

[27]  Kalyanmoy Deb,et al.  A Fast Elitist Non-dominated Sorting Genetic Algorithm for Multi-objective Optimisation: NSGA-II , 2000, PPSN.

[28]  David E. Goldberg,et al.  Bayesian optimization algorithm, decision graphs, and Occam's razor , 2001 .

[29]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

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

[31]  A. Ochoa,et al.  A factorized distribution algorithm based on polytrees , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[32]  J. V. Rosenhead,et al.  The Advanced Theory of Statistics: Volume 2: Inference and Relationship , 1963 .

[33]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

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

[35]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

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

[37]  Dirk Thierens,et al.  Exploiting gradient information in continuous iterated density estimation evolutionary algorithms , 2001 .

[38]  Eckart Zitzler,et al.  Evolutionary algorithms for multiobjective optimization: methods and applications , 1999 .