Impact of Estimation Method of Ideal/Nadir Points on Practically-Constrained Multi-Objective Optimization Problems for Decomposition-Based Multi-Objective Evolutionary Algorithm

To apply MOEAs to industrial problems, the estimation of the ideal and nadir points becomes crucial in order to handle the differently scaled objectives by normalization and to handle the unknown Pareto Front. In this paper, the impact of the estimation methods of the ideal and nadir points for decomposition-based multi-objective evolutionary algorithms is examined on some constrained optimization problems whose constraints are explicitly designed to have the characteristics of the practical problems. The numerical experiments show that the estimation method has great impact on the performance of MOEAs.

[1]  Bernhard Sendhoff,et al.  A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

[2]  Dipti Srinivasan,et al.  A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition , 2017, IEEE Transactions on Evolutionary Computation.

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

[4]  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..

[5]  Qingfu Zhang,et al.  Decomposition of a Multiobjective Optimization Problem Into a Number of Simple Multiobjective Subproblems , 2014, IEEE Transactions on Evolutionary Computation.

[6]  Akira Oyama,et al.  A Generic Framework for Incorporating Constraint Handling Techniques into Multi-Objective Evolutionary Algorithms , 2018, EvoApplications.

[7]  Akira Oyama,et al.  Benchmarking multiobjective evolutionary algorithms and constraint handling techniques on a real-world car structure design optimization benchmark problem , 2018, GECCO.

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

[9]  Xin Yao,et al.  Many-Objective Evolutionary Algorithms , 2015, ACM Comput. Surv..

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

[11]  Hisao Ishibuchi,et al.  Performance of Decomposition-Based Many-Objective Algorithms Strongly Depends on Pareto Front Shapes , 2017, IEEE Transactions on Evolutionary Computation.

[12]  Kalyanmoy Deb,et al.  Investigating the Normalization Procedure of NSGA-III , 2019, EMO.

[13]  Beatriz Souza Leite Pires de Lima,et al.  Balanced ranking method for constrained optimization problems using evolutionary algorithms , 2016, Inf. Sci..

[14]  Hai-Lin Liu,et al.  A Constrained Multi-Objective Evolutionary Algorithm Based on Boundary Search and Archive , 2016, Int. J. Pattern Recognit. Artif. Intell..

[15]  Shengxiang Yang,et al.  A Strength Pareto Evolutionary Algorithm Based on Reference Direction for Multiobjective and Many-Objective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[16]  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.

[17]  Qingfu Zhang,et al.  A Generator for Multiobjective Test Problems With Difficult-to-Approximate Pareto Front Boundaries , 2019, IEEE Transactions on Evolutionary Computation.

[18]  Qingfu Zhang,et al.  Evolutionary Many-Objective Optimization Based on Adversarial Decomposition , 2017, IEEE Transactions on Cybernetics.

[19]  Afonso C. C. Lemonge,et al.  A rank-based constraint handling technique for engineering design optimization problems solved by genetic algorithms , 2017 .

[20]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[21]  Xin Yao,et al.  A New Dominance Relation-Based Evolutionary Algorithm for Many-Objective Optimization , 2016, IEEE Transactions on Evolutionary Computation.

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

[23]  Kalyanmoy Deb,et al.  Toward an Estimation of Nadir Objective Vector Using a Hybrid of Evolutionary and Local Search Approaches , 2010, IEEE Transactions on Evolutionary Computation.

[24]  Akira Oyama,et al.  Proposal of benchmark problem based on real-world car structure design optimization , 2018, GECCO.

[25]  H. Ishibuchi,et al.  On the effect of normalization in MOEA/D for multi-objective and many-objective optimization , 2017 .

[26]  Oswin Krause,et al.  Unbounded Population MO-CMA-ES for the Bi-Objective BBOB Test Suite , 2016, GECCO.

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

[28]  Fang Liu,et al.  MOEA/D with Adaptive Weight Adjustment , 2014, Evolutionary Computation.

[29]  Yuren Zhou,et al.  A Vector Angle-Based Evolutionary Algorithm for Unconstrained Many-Objective Optimization , 2017, IEEE Transactions on Evolutionary Computation.