MOEA/D with Two Types of Weight Vectors for Handling Constraints

Decomposition-based constrained multiobjective evolutionary algorithms decompose a constrained multiobjective problem into a set of constrained single-objective subproblems. For each subproblem, the aggregation function and the overall constraint violation need to be minimized simultaneously, which however may conflict with each other during the evolutionary process. To solve this issue, this paper proposes a novel decomposition-based constrained multiobjective evolutionary algorithm with two types of weight vectors, respectively emphasizing convergence and diversity. The solutions associated to the convergence weight vectors are updated only considering the aggregation function in order to search the whole search space freely, while the ones associated to the diversity weight vectors are renewed by considering both the aggregation function and the overall constraint violation, which encourages to search around the feasible region found so far. Once the replacement of solutions does not happen for the diversity weight vectors in a period, the corresponding diversity weight vectors will be transferred to convergence one. Thereafter, all solutions will finally search around the feasible region, which helps to find more feasible or superior solutions. The proposed constraint handling technique can have a good balance to search the feasible and infeasible regions and show the promising performance, which is validated when tackling several constrained multi-objective problems.

[1]  Hisao Ishibuchi,et al.  Dual-grid model of MOEA/D for evolutionary constrained multiobjective optimization , 2018, GECCO.

[2]  Yong Wang,et al.  A comparative study of constraint-handling techniques in evolutionary constrained multiobjective optimization , 2016, 2016 IEEE Congress on Evolutionary Computation (CEC).

[3]  Zhaoquan Cai,et al.  An improved epsilon constraint handling method embedded in MOEA/D for constrained multi-objective optimization problems , 2016, 2016 IEEE Symposium Series on Computational Intelligence (SSCI).

[4]  Li.  Two-Archive Evolutionary Algorithm for Constrained Multi-Objective Optimization , 2018 .

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

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

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

[8]  Yong Wang,et al.  A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization , 2006, IEEE Transactions on Evolutionary Computation.

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

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

[11]  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.

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

[13]  Tetsuyuki Takahama,et al.  Constrained Optimization by the alpha Constrained Particle Swarm Optimizer , 2005, J. Adv. Comput. Intell. Intell. Informatics.

[14]  Alan D. Christiansen,et al.  MOSES: A MULTIOBJECTIVE OPTIMIZATION TOOL FOR ENGINEERING DESIGN , 1999 .

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

[16]  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..

[17]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

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

[19]  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.

[20]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[21]  Xin Yao,et al.  Two-Archive Evolutionary Algorithm for Constrained Multiobjective Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[22]  Erik D. Goodman,et al.  MOEA/D with Angle-based Constrained Dominance Principle for Constrained Multi-objective Optimization Problems , 2018, Appl. Soft Comput..