Generic constraints handling techniques in constrained multi-criteria optimization and its application

• Published in: European journal of operational research Vol. 244; no. 2; pp. 576 - 591
• Main Authors: Liu, Linzhong, Mu, Haibo, Yang, Juhua
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 16.07.2015; Elsevier Sequoia S.A
• Subjects: Algorithms; Benchmarks; Constraint programming; Constraints handling technique (CHT); Evolutionary algorithm (EA); Mathematical problems; Multi-criteria optimization (MO); Multi-criteria optimization evolutionary algorithm (MOEA); Optimization; Optimization algorithms; Problem solving; Studies; Multi-criteria optimization (MO); Multi-criteria optimization evolutionary algorithm (MOEA); Constraints handling technique (CHT); Evolutionary algorithm (EA); Constraint programming
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2015.01.051

•A nonequivalent relaxation approach is proposed.•An equivalent relaxation approach is proposed.•A two-phases based CHT is proposed by using the equivalent relaxation approach.•A three-phases based CHT is proposed by using the nonequivalent relaxation approach. This paper investigates the constraints handling technique (CHT) in algorithms of the constrained multi-criteria optimization problem (CMOP). The CHT is an important research topic in constrained multi-criteria optimization (MO). In this paper, two simple and practicable CHTs are proposed, where one is a nonequivalent relaxation approach which is much suitable for the constrained multi-criteria discrete optimization problem (MDOP), and the other is an equivalent relaxation approach for the general CMOP. By using these CHTs, a CMOP (i.e., the primal problem) can be transformed into an unconstrained multi-criteria optimization problem (MOP) (i.e., the relaxation problem). Based on the first CHT, it is theoretically proven that the efficient set of the primal CMOP is a subset of the strictly efficient set E¯ of the relaxation problem and can be extracted from E¯ by simply checking the dominance relation between the solutions in E¯. Follows from these theoretical results, a three-phase based idea is given to effectively utilize the existing algorithms for the unconstrained MDOP to solve the constrained MDOP. In the second CHT, the primal CMOP is equivalently transformed into an unconstrained MOP by a special relaxation approach. Based on such a CHT, it is proven that the primal problem and its relaxation problem have the same efficient set and, therefore, general CMOPs can be solved by utilizing any of the existing algorithms for the unconstrained MOPs. The implementing idea, say two-phase based idea, of the second CHT is illustrated by implanting a known MOEA. Finally, the two-phase based idea is applied to some of the early MOEAs and the application performances are comprehensively tested with some benchmarks of the CMOP.