A comparative study of variation operators used for evolutionary multi-objective optimization

Abstract In this paper, several variation operators based on Pareto efficiency, extracted from Differential Evolution, Estimation of Distribution Algorithms, Evolution Strategies and Evolutionary Programming, are compared in order to determine whether or not they increase the performance of the non-Pareto based versions. Firstly, we compare the selected variation operators in pairs, each operator with a modification of itself, in which we remove those elements related to the Pareto efficiency. Then, in a second experiment we compare among the selected operators, the variation operators used in the NSGA-II algorithm and the ones presented by the authors, PBCO and RBMO. In all the experiments the variation operators are incorporated in a well-known algorithm usually considered as a reference for making the comparisons, the NSGA-II algorithm. The experiments show that the Pareto based variation operators selected from the literature do not usually present a better behavior than their non-Pareto based versions; and none of them presents a better performance than the one reached by the variation operators defined by the authors, which were entirely built around the Pareto information of the individuals. These facts suggest that more effort should be placed in the design of variation operators devoted to multi-objective algorithms in order to achieve superior results to those obtained by means of general variation operators.

[1]  Lothar Thiele,et al.  Multiobjective Optimization Using Evolutionary Algorithms - A Comparative Case Study , 1998, PPSN.

[2]  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 .

[3]  Xiaodong Li,et al.  Incorporating directional information within a differential evolution algorithm for multi-objective optimization , 2006, GECCO.

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

[5]  Wei Hou,et al.  Evolutionary programming using a mixed mutation strategy , 2007, Inf. Sci..

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

[7]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

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

[9]  Min-Rong Chen,et al.  A novel elitist multiobjective optimization algorithm: Multiobjective extremal optimization , 2008, Eur. J. Oper. Res..

[10]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[11]  Bernhard Sendhoff,et al.  Voronoi-based estimation of distribution algorithm for multi-objective optimization , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[12]  Arthur C. Sanderson,et al.  Multiobjective Evolutionary Decision Support for Design–Supplier–Manufacturing Planning , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[13]  H. Abbass,et al.  PDE: a Pareto-frontier differential evolution approach for multi-objective optimization problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[14]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[15]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

[16]  Enrique Alba,et al.  Multi-objective optimization using metaheuristics: non-standard algorithms , 2012, Int. Trans. Oper. Res..

[17]  H. Abbass.  The self-adaptive Pareto differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

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

[19]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

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

[21]  Gary B. Lamont,et al.  Evolutionary algorithms for solving multi-objective problems, Second Edition , 2007, Genetic and evolutionary computation series.

[22]  Xin Yao,et al.  Evolutionary programming made faster , 1999, IEEE Trans. Evol. Comput..

[23]  Marco Laumanns,et al.  Performance assessment of multiobjective optimizers: an analysis and review , 2003, IEEE Trans. Evol. Comput..

[24]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[25]  Arthur C. Sanderson,et al.  Pareto-based multi-objective differential evolution , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[26]  Qingfu Zhang,et al.  Enhancing MOEA/D with guided mutation and priority update for multi-objective optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.

[27]  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.

[28]  Rich Caruana,et al.  Removing the Genetics from the Standard Genetic Algorithm , 1995, ICML.

[29]  Xu Ye,et al.  Advances in estimation of distribution algorithms , 2012 .

[30]  Xiaodong Li,et al.  Solving Rotated Multi-objective Optimization Problems Using Differential Evolution , 2004, Australian Conference on Artificial Intelligence.

[31]  H. B. Quek,et al.  Pareto-optimal set based multiobjective tuning of fuzzy automatic train operation for mass transit system , 1999 .

[32]  Patrick Siarry,et al.  A survey on optimization metaheuristics , 2013, Inf. Sci..

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

[34]  Jesús García,et al.  MB-GNG: Addressing drawbacks in multi-objective optimization estimation of distribution algorithms , 2011, Oper. Res. Lett..

[35]  Jing J. Liang,et al.  Problem Definitions for Performance Assessment of Multi-objective Optimization Algorithms , 2007 .

[36]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

[37]  Arthur C. Sanderson,et al.  Multi-objective differential evolution - algorithm, convergence analysis, and applications , 2005, 2005 IEEE Congress on Evolutionary Computation.

[38]  Dirk Thierens,et al.  Multi-objective Optimization with the Naive $$ \mathbb{M} $$ ID $$ \mathbb{E} $$ A , 2006, Towards a New Evolutionary Computation.

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

[40]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

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

[42]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[43]  I. Alberto,et al.  A crossover operator that uses Pareto optimality in its definition , 2011 .

[44]  Qingfu Zhang,et al.  A model-based evolutionary algorithm for bi-objective optimization , 2005, 2005 IEEE Congress on Evolutionary Computation.

[45]  Frederico G. Guimarães,et al.  A Differential Mutation operator for the archive population of multi-objective evolutionary algorithms , 2009, 2009 IEEE Congress on Evolutionary Computation.

[46]  P. M. Mateo,et al.  A mutation operator based on a Pareto ranking for multi-objective evolutionary algorithms , 2011, Journal of Heuristics.

[47]  D. Thierens.  Multi-Objective Optimization with Iterated Density Estimation Evolutionary Algorithms using Mixture Models , 2004 .

[48]  Concha Bielza,et al.  Multi-objective Optimization with Joint Probabilistic Modeling of Objectives and Variables , 2011, EMO.

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

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

[51]  Yang Shu Min,et al.  A novel evolution strategy for multiobjective optimization problem , 2005, Appl. Math. Comput..

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

[53]  Xuesong Wang,et al.  PDE-PEDA: A New Pareto-Based Multi-objective Optimization Algorithm , 2009, J. Univers. Comput. Sci..

[54]  Kumar Chellapilla,et al.  Combining mutation operators in evolutionary programming , 1998, IEEE Trans. Evol. Comput..

[55]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1992, Artificial Intelligence.

[56]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .