A study of two penalty-parameterless constraint handling techniques in the framework of MOEA/D

Penalty functions are frequently employed for handling constraints in constrained optimization problems (COPs). In penalty function methods, penalty coefficients balance objective and penalty functions. However, finding appropriate penalty coefficients to strike the right balance is often very hard. They are problems dependent. Stochastic ranking (SR) and constraint-domination principle (CDP) are two promising penalty functions based constraint handling techniques that avoid penalty coefficients. In this paper, the extended/modified versions of SR and CDP are implemented for the first time in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework. This led to two new algorithms, CMOEA/D-DE-SR and CMOEA/D-DE-CDP. The performance of these new algorithms is tested on CTP-series and CF-series test instances in terms of the HV-metric, IGD-metric, and SC-metric. The experimental results are compared with NSGA-II, IDEA, and the three best performers of CEC 2009 MOEA competition, which showed better and competitive performance of the proposed algorithms on most test instances of the two test suits. The sensitivity of the performance of proposed algorithms to parameters is also investigated. The experimental results reveal that CDP works better than SR in the MOEA/D framework.

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

[2]  Tapabrata Ray,et al.  Infeasibility Driven Evolutionary Algorithm for Constrained Optimization , 2009 .

[3]  T. L. Saaty,et al.  The computational algorithm for the parametric objective function , 1955 .

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

[5]  Hisao Ishibuchi,et al.  A multi-objective genetic local search algorithm and its application to flowshop scheduling , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[6]  Qingfu Zhang,et al.  MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition , 2007, IEEE Transactions on Evolutionary Computation.

[7]  Andrzej Jaszkiewicz,et al.  On the performance of multiple-objective genetic local search on the 0/1 knapsack problem - a comparative experiment , 2002, IEEE Trans. Evol. Comput..

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

[9]  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).

[10]  Gary B. Lamont,et al.  Multiobjective evolutionary algorithms: classifications, analyses, and new innovations , 1999 .

[11]  Mitsuo Gen,et al.  Specification of Genetic Search Directions in Cellular Multi-objective Genetic Algorithms , 2001, EMO.

[12]  Bernhard Sendhoff,et al.  A critical survey of performance indices for multi-objective optimisation , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[13]  Kalyanmoy Deb,et al.  Constrained Test Problems for Multi-objective Evolutionary Optimization , 2001, EMO.

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

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

[16]  Yuping Wang,et al.  Multiobjective programming using uniform design and genetic algorithm , 2000, IEEE Trans. Syst. Man Cybern. Part C.

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

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

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

[20]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[21]  Qingfu Zhang,et al.  Multiobjective Optimization Problems With Complicated Pareto Sets, MOEA/D and NSGA-II , 2009, IEEE Transactions on Evolutionary Computation.

[22]  A. Messac,et al.  The normalized normal constraint method for generating the Pareto frontier , 2003 .

[23]  Marco Laumanns,et al.  SPEA2: Improving the Strength Pareto Evolutionary Algorithm For Multiobjective Optimization , 2002 .

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

[25]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[26]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

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

[28]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[29]  Qingfu Zhang,et al.  The performance of a new version of MOEA/D on CEC09 unconstrained MOP test instances , 2009, 2009 IEEE Congress on Evolutionary Computation.

[30]  E. Hughes.  Multiple single objective Pareto sampling , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[31]  Lotfi A. Zadeh,et al.  Optimality and non-scalar-valued performance criteria , 1963 .

[32]  Ralph E. Steuer.  Multiple criteria optimization , 1986 .