Threshold Based Penalty Functions for Constrained Multiobjective Optimization

This paper compares the performance of our recently proposed threshold based penalty function against its dynamic and adaptive variants. These penalty functions are incorporated in the update and replacement scheme of the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework to solve constrained multiobjective optimization problems (CMOPs). As a result, the capability of MOEA/D is extended to handle constraints, and a new algorithm, denoted by CMOEA/D-DE-TDA is proposed. The performance of CMOEA/D-DE-TDA is tested, in terms of the values of IGDmetric and SC-metric, on the well known CF-series test instances. The experimental results are also compared with the three best performers of CEC 2009 MOEA competition. Empirical results show the pitfalls of the proposed penalty functions. Keywords—Constrained multiobjective optimization; decomposition; MOEA/D; dynamic and adaptive penalty functions; threshold.