Constrained multiobjective distance minimization problems

Various distance minimization problems (DMPs) have been proposed to visualize the search behaviors of evolutionary multiobjective optimization (EMO) algorithms in solving many-objective problems, multiobjective multimodal problems, and dynamic multiobjective problems. Among those DMPs, only the box constraints are considered. In this paper, we propose several constraint DMPs to visualize the behaviors of EMO algorithms with constraint handling techniques. In the proposed constraint DMPs, constraints are simply specified in the two-dimensional decision space. In the same manner, high-dimensional problems and multimodal problems can also be generated. Computational experiments show different behaviors by different algorithms in various constraint DMPs.

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

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

[3]  D.A. Van Veldhuizen,et al.  On measuring multiobjective evolutionary algorithm performance , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[4]  Hisao Ishibuchi,et al.  A Double-Niched Evolutionary Algorithm and Its Behavior on Polygon-Based Problems , 2018, PPSN.

[5]  Erik D. Goodman,et al.  An improved epsilon constraint-handling method in MOEA/D for CMOPs with large infeasible regions , 2017, Soft Computing.

[6]  Carlos A. Coello Coello,et al.  A Study of the Parallelization of a Coevolutionary Multi-objective Evolutionary Algorithm , 2004, MICAI.

[7]  Gary G. Yen,et al.  Constraint Handling in Multiobjective Evolutionary Optimization , 2009, IEEE Transactions on Evolutionary Computation.

[8]  Hisao Ishibuchi,et al.  Many-objective and many-variable test problems for visual examination of multiobjective search , 2013, 2013 IEEE Congress on Evolutionary Computation.

[9]  Hisao Ishibuchi,et al.  A many-objective test problem for visually examining diversity maintenance behavior in a decision space , 2011, GECCO '11.

[10]  Sanaz Mostaghim,et al.  Dynamic Distance Minimization Problems for dynamic multi-objective optimization , 2017, 2017 IEEE Congress on Evolutionary Computation (CEC).

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

[12]  Sanaz Mostaghim,et al.  Properties of scalable distance minimization problems using the Manhattan metric , 2015, 2015 IEEE Congress on Evolutionary Computation (CEC).

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

[14]  Mario Köppen,et al.  Substitute Distance Assignments in NSGA-II for Handling Many-objective Optimization Problems , 2007, EMO.

[15]  Hisao Ishibuchi,et al.  Many-Objective Test Problems to Visually Examine the Behavior of Multiobjective Evolution in a Decision Space , 2010, PPSN.

[16]  Christoph Steup,et al.  Multi-objective distance minimization problems – applications in technical systems , 2018, Autom..

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

[18]  Kalyanmoy Deb,et al.  An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach , 2014, IEEE Transactions on Evolutionary Computation.

[19]  Xin Yao,et al.  Multiline Distance Minimization: A Visualized Many-Objective Test Problem Suite , 2018, IEEE Transactions on Evolutionary Computation.