Threshold Based Dynamic and Adaptive Penalty Functions for Constrained Multiobjective Optimization

Abstract

Penalty functions are frequently used for dealing with constraints in constrained optimization. Among different types of penalty functions, dynamic and adaptive penalty functions seem effective, since the penalty coefficients in them are adjusted based on the current generation number (or number of solutions searched) and feedback from the search. In this paper, we propose dynamic and adaptive versions of our recently proposed threshold based penalty function. They are then implemented in the multiobjective evolutionary algorithm based on decomposition (MOEA/D) framework to solve constrained multi objective optimization problems (CMOPs). This led to a new algorithm, denoted by CMOEA/D-DE-TDA. The performance of CMOEA/D-DE-TDA is tested on CTP-series test instances in terms of the HV-metric and SC-metric. The experimental results are compared with IDEA and NSGA-II, which show the effectiveness of the proposed algorithm.