Constrained optimisation by solving equivalent dynamic loosely-constrained multiobjective optimisation problem

Abstract

A constrained optimisation problem (COP) is solved by solving an equivalent dynamic loosely-constrained multiobjective optimisation problem in this paper. Two strategies are considered. 1) An additional objective (constrained-violation objective) is introduced to obtain a two-objective optimisation problem. This provides a framework for adopting multi-objective techniques to solve the COP, 2) A dynamic constraint boundary is introduced to obtain an equivalent dynamic loosely-constrained multiobjective optimisation problem since a broad boundary is gradually slightly reduced to the original constraint boundary. This suggests that an dynamic constrained multiobjective evolutionary algorithm (DCMOEA) can performs as effective as that of a multiobjective evolutionary algorithm (MOEA) in solving an unconstrained multiobjective optimisation problem. The idea is implemented into three major types of MOEAs, i.e., Pareto ranking based method, decomposition based method, preference-inspired co-evolutionary method. These three instantiations are tested on two sets of benchmark problems. Experimental results show that they are better than or competitive to two state-of-the-art constraint optimisers, especially for the problems with high dimensions.