Multi-Pareto-Ranking Evolutionary Algorithm

This paper proposes a new multi-objective genetic algorithm, called GAME, to solve constrained optimization problems. GAME uses an elitist archive, but it ranks the population in several Pareto fronts. Then, three types of fitness assignment methods are defined: the fitness of individuals depends on the front they belong to. The crowding distance is also used to preserve diversity. Selection is based on two steps: a Pareto front is first selected, before choosing an individual among the solutions it contains. The probability to choose a given front is computed using three parameters which are tuned using the design of experiments. The influence of the number of Pareto fronts is studied experimentally. Finally GAME's performance is assessed and compared with three other algorithms according to the conditions of the CEC 2009 competition.

[1]  J. S. Hunter,et al.  Statistics for Experimenters: Design, Innovation, and Discovery , 2006 .

[2]  Antonio J. Nebro,et al.  jMetal: A Java framework for multi-objective optimization , 2011, Adv. Eng. Softw..

[3]  Sidney Addelman,et al.  trans-Dimethanolbis(1,1,1-trifluoro-5,5-dimethylhexane-2,4-dionato)zinc(II) , 2008, Acta crystallographica. Section E, Structure reports online.

[4]  Christophe Espanet,et al.  Tuning an Evolutionary Algorithm with Taguchi Methods , 2007 .

[5]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[6]  Thomas Bartz-Beielstein,et al.  Experimental Methods for the Analysis of Optimization Algorithms , 2010 .

[7]  Marco Laumanns,et al.  SPEA2: Improving the strength pareto evolutionary algorithm , 2001 .

[8]  Qingfu Zhang,et al.  Multiobjective optimization Test Instances for the CEC 2009 Special Session and Competition , 2009 .

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

[10]  Lishan Kang,et al.  A New Evolutionary Algorithm for Solving Many-Objective Optimization Problems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[11]  Patrick D. Surry,et al.  A Multi-objective Approach to Constrained Optimisation of Gas Supply Networks: the COMOGA Method , 1995, Evolutionary Computing, AISB Workshop.

[12]  Kalyanmoy Deb,et al.  SINGLE AND MULTI-OBJECTIVE OPTIMIZATION USING EVOLUTIONARY COMPUTATION , 2004 .

[13]  Zhijian Wu,et al.  Performance assessment of DMOEA-DD with CEC 2009 MOEA competition test instances , 2009, 2009 IEEE Congress on Evolutionary Computation.

[14]  Hamidreza Eskandari,et al.  FastPGA: A Dynamic Population Sizing Approach for Solving Expensive Multiobjective Optimization Problems , 2006, EMO.

[15]  Subbarao Kambhampati,et al.  Evolutionary Computing , 1997, Lecture Notes in Computer Science.

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

[17]  Jean-Paul Chilès,et al.  Wiley Series in Probability and Statistics , 2012 .

[18]  Hai-Lin,et al.  The multiobjective evolutionary algorithm based on determined weight and sub-regional search , 2009, 2009 IEEE Congress on Evolutionary Computation.

[19]  Christophe Espanet,et al.  Tuning an evolutionary algorithm with taguchi methods and application to the dimensioning of an electrical motor , 2008, CSTST.

[20]  P. J. Green,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

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

[22]  Damien Charlet,et al.  Using an evolutionary algorithm to optimize the broadcasting methods in mobile ad hoc networks , 2011, J. Netw. Comput. Appl..

[23]  Lalit M. Patnaik,et al.  Genetic algorithms: a survey , 1994, Computer.

[24]  Chun Chen,et al.  Multiple trajectory search for unconstrained/constrained multi-objective optimization , 2009, 2009 IEEE Congress on Evolutionary Computation.