Performance assessment of Generalized Differential Evolution 3 with a given set of constrained multi-objective test problems

This paper presents results for the CEC 2009 Special Session on “Performance Assessment of Constrained / Bound Constrained Multi-Objective Optimization Algorithms” when Generalized Differential Evolution 3 has been used to solve a given set of test problems. The set consist of 23 problems having two, three, or five objectives. Problems have different properties in the sense of separability, modality, and geometry of the Pareto-front. The most of the problems are unconstrained, but 10 problems have one or two constraints. According to the numerical results with an inverted generational distance, Generalized Differential Evolution 3 performed well with all the problems except with one five objective problem. It was noticed that a low crossover control parameter value provides the best average results according to the metric.

[1]  Godfrey C. Onwubolu,et al.  New optimization techniques in engineering , 2004, Studies in Fuzziness and Soft Computing.

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

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

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

[5]  Jouni Lampinen,et al.  GDE3: the third evolution step of generalized differential evolution , 2005, 2005 IEEE Congress on Evolutionary Computation.

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

[7]  Jouni Lampinen,et al.  An Empirical Study of Control Parameters for The Third Version of Generalized Differential Evolution (GDE3) , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[8]  J. Lampinen.  A constraint handling approach for the differential evolution algorithm , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[9]  Mehmet Fatih Tasgetiren,et al.  Multi-objective optimization based on self-adaptive differential evolution algorithm , 2007, 2007 IEEE Congress on Evolutionary Computation.

[10]  Jouni Lampinen,et al.  Performance assessment of Generalized Differential Evolution 3 (GDE3) with a given set of problems , 2007, 2007 IEEE Congress on Evolutionary Computation.

[11]  Kalyanmoy Deb,et al.  Improved Pruning of Non-Dominated Solutions Based on Crowding Distance for Bi-Objective Optimization Problems , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[12]  J. Lampinen.  Multi-Constrained Nonlinear Optimization by the Differential Evolution Algorithm , 2002 .

[13]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. II. Application example , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[14]  Jouni Lampinen,et al.  An Extension of Generalized Differential Evolution for Multi-objective Optimization with Constraints , 2004, PPSN.

[15]  Mikkel T. Jensen,et al.  Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms , 2003, IEEE Trans. Evol. Comput..

[16]  Jouni Lampinen,et al.  DE’s Selection Rule for Multiobjective Optimization , 2001 .

[17]  Nirupam Chakraborti,et al.  Solving the Molecular Sequence Alignment Problem with Generalized Differential Evolution 3 (GDE3) , 2007, 2007 IEEE Symposium on Computational Intelligence in Multi-Criteria Decision-Making.

[18]  Janez Brest,et al.  Differential evolution for multiobjective optimization with self adaptation , 2007, 2007 IEEE Congress on Evolutionary Computation.

[19]  Kenneth V. Price,et al.  An introduction to differential evolution , 1999 .

[20]  Rainer Laur,et al.  Differential evolution with adaptive parameter setting for multi-objective optimization , 2007, 2007 IEEE Congress on Evolutionary Computation.

[21]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[22]  Kalyanmoy Deb,et al.  A Fast and Effective Method for Pruning of Non-dominated Solutions in Many-Objective Problems , 2006, PPSN.

[23]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[24]  Kalyanmoy Deb,et al.  Multi-objective test problems, linkages, and evolutionary methodologies , 2006, GECCO.

[25]  Jouni Lampinen,et al.  Constrained Real-Parameter Optimization with Generalized Differential Evolution , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[26]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.