Multi-objective Optimization with Joint Probabilistic Modeling of Objectives and Variables

The objective values information can be incorporated into the evolutionary algorithms based on probabilistic modeling in order to capture the relationships between objectives and variables. This paper investigates the effects of joining the objective and variable information on the performance of an estimation of distribution algorithm for multiobjective optimization. A joint Gaussian Bayesian network of objectives and variables is learnt and then sampled using the information about currently best obtained objective values as evidence. The experimental results obtained on a set of multi-objective functions and in comparison to two other competitive algorithms are presented and discussed.

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

[2]  Thomas G. Dietterich.  Adaptive computation and machine learning , 1998 .

[3]  Wray L. Buntine.  Theory Refinement on Bayesian Networks , 1991, UAI.

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

[5]  R. Lyndon While,et al.  A Scalable Multi-objective Test Problem Toolkit , 2005, EMO.

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

[7]  Hisao Ishibuchi,et al.  Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems , 2008, GECCO '08.

[8]  Yong Wang,et al.  A regularity model-based multiobjective estimation of distribution algorithm with reducing redundant cluster operator , 2012, Appl. Soft Comput..

[9]  Pedro Larrañaga,et al.  Evolutionary computation based on Bayesian classifiers , 2004 .

[10]  K. Strimmer,et al.  Statistical Applications in Genetics and Molecular Biology A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics , 2011 .

[11]  Ivo F. Sbalzariniy,et al.  Multiobjective optimization using evolutionary algorithms , 2000 .

[12]  Carlos A. Coello Coello,et al.  Objective reduction using a feature selection technique , 2008, GECCO '08.

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

[14]  Arturo Hernández Aguirre,et al.  MICAI 2009: Advances in Artificial Intelligence, 8th Mexican International Conference on Artificial Intelligence, Guanajuato, Mexico, November 9-13, 2009. Proceedings , 2009, MICAI.

[15]  Concha Bielza,et al.  Mateda-2.0: A MATLAB package for the implementation and analysis of estimation of distribution algorithms , 2010 .

[16]  R. Lyndon While,et al.  A review of multiobjective test problems and a scalable test problem toolkit , 2006, IEEE Transactions on Evolutionary Computation.

[17]  DebK.,et al.  A fast and elitist multiobjective genetic algorithm , 2002 .

[18]  Eckart Zitzler,et al.  Objective Reduction in Evolutionary Multiobjective Optimization: Theory and Applications , 2009, Evolutionary Computation.

[19]  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 .

[20]  Bernhard Sendhoff,et al.  On Test Functions for Evolutionary Multi-objective Optimization , 2004, PPSN.

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

[22]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

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

[24]  Eckart Zitzler,et al.  Dimensionality Reduction in Multiobjective Optimization: The Minimum Objective Subset Problem , 2006, OR.

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

[26]  Karl-Heinz Waldmann,et al.  Operations Research Proceedings 2006 , 2007 .

[27]  Concha Bielza,et al.  Multi-dimensional classification with Bayesian networks , 2011, Int. J. Approx. Reason..

[28]  Dirk Thierens,et al.  Multi-objective mixture-based iterated density estimation evolutionary algorithms , 2001 .

[29]  Carlos A. Coello Coello,et al.  GIAA TECHNINAL REPORT GIAA2010E001 On Current Model-Building Methods for Multi-Objective Estimation of Distribution Algorithms: Shortcommings and Directions for Improvement , 2010 .

[30]  Lakhmi C. Jain,et al.  Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[31]  Marco Laumanns,et al.  Scalable multi-objective optimization test problems , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[33]  Kalyanmoy Deb,et al.  Multi-objective optimization using evolutionary algorithms , 2001, Wiley-Interscience series in systems and optimization.

[34]  Carlos A. Coello Coello,et al.  An updated survey of evolutionary multiobjective optimization techniques: state of the art and future trends , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[35]  S. Lauritzen.  Propagation of Probabilities, Means, and Variances in Mixed Graphical Association Models , 1992 .

[36]  Carlos A. Coello Coello,et al.  Ranking Methods for Many-Objective Optimization , 2009, MICAI.

[37]  Hans-Paul Schwefel,et al.  Parallel Problem Solving from Nature — PPSN IV , 1996, Lecture Notes in Computer Science.

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

[39]  Pedro Larrañaga,et al.  Evolutionary Bayesian Classifier-Based Optimization in Continuous Domains , 2006, SEAL.

[40]  Marco Laumanns,et al.  Scalable Test Problems for Evolutionary Multiobjective Optimization , 2005, Evolutionary Multiobjective Optimization.

[41]  Mark W. Schmidt,et al.  Learning Graphical Model Structure Using L1-Regularization Paths , 2007, AAAI.

[42]  L. Jain,et al.  Evolutionary multiobjective optimization : theoretical advances and applications , 2005 .

[43]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[44]  Concha Bielza,et al.  Mateda-2.0: Estimation of Distribution Algorithms in MATLAB , 2010 .