Multiobjective Differential Evolution: A Comparative Study on Benchmark Problems

Differential Evolution is one of the most powerful stochastic real parameter optimization technique. During last fifteen years, it has been widely used in various domains of engineering and science for single and multi objectives optimization. For multiobjective optimization problems, Differential Evolution has been applied in various forms to optimize two conflicting objectives simultaneously. Here, we have studied the performance of six different techniques of Multiobjective Differential Evolution in comparison with four other state-of-the-art methods on five benchmark test problems. The results are demonstrated quantitatively in terms of convergence and divergence measures of the solutions produced by ten methods and visually by showing the Pareto optimal front. Finally, statistical significant test has been conducted to establish the superiority of the results.

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

[2]  A. Smilde,et al.  Multicriteria decision making , 1992 .

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

[4]  Josiah Adeyemo,et al.  Multi-Objective Differential Evolution Algorithm for Solving Engineering Problems , 2009 .

[5]  David Corne,et al.  The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

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

[7]  Bogdan Filipic,et al.  DEMO: Differential Evolution for Multiobjective Optimization , 2005, EMO.

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

[9]  John J. Grefenstette,et al.  Proceedings of the 1st International Conference on Genetic Algorithms , 1985 .

[10]  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).

[11]  C. Fonseca,et al.  GENETIC ALGORITHMS FOR MULTI-OBJECTIVE OPTIMIZATION: FORMULATION, DISCUSSION, AND GENERALIZATION , 1993 .

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

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

[14]  Ujjwal Maulik,et al.  Modified differential evolution based fuzzy clustering for pixel classification in remote sensing imagery , 2009, Pattern Recognit..

[15]  Weiyi Qian,et al.  Adaptive differential evolution algorithm for multiobjective optimization problems , 2008, Appl. Math. Comput..

[16]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[17]  P. Bickel,et al.  Mathematical Statistics: Basic Ideas and Selected Topics , 1977 .

[18]  Carlos A. Coello Coello,et al.  An updated survey of GA-based multiobjective optimization techniques , 2000, CSUR.

[19]  Yaonan Wang,et al.  Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure , 2010, Soft Comput..

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

[21]  N. Madavan.  Multiobjective optimization using a Pareto differential evolution approach , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[22]  Alan D. Christiansen,et al.  An empirical study of evolutionary techniques for multiobjective optimization in engineering design , 1996 .

[23]  Ujjwal Maulik,et al.  A new multi-objective technique for differential fuzzy clustering , 2011, Appl. Soft Comput..