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.

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. Figure optionsDownload as PowerPoint slideHighlights
► Stochastic ranking (SR) and constraint domination principle (CDP) are studied in the MOEA/D framework to solve CMOPs.
► CDP works better than SR in the MOEA/D framework on most of the CTP-series and CF-series test instances.
► Our algorithms beat IDEA and NSGA-II on five out of eight CTP-series test instances.
► Our algorithms found competitive results with the three best performers in CEC 2009 on six out of ten CF-series test instances.
► Our algorithms can find evenly distributed optimal solutions with a small population size.