α -Satisfactory goal programming method for multi-objective optimization with priorities and fuzzy parameters

Abstract

In this paper, the α-satisfactory goal programming (GP) method is proposed for multi-objective optimization (MOO) with priorities and fuzzy parameters. Fuzzy parameters are treated as fuzzy numbers, and all objectives are modeled into fuzzy goals over α-level sets. The order of α-satisfactory degrees is applied to preemptive priority requirement, where the objectives with higher priority can achieve the higher α-satisfactory degree. In order to guarantee the feasibility and seek the preferred solution, a priority variable is introduced to relax the strict order. For three fuzzy relations, GP is combined with the relaxed order constraint to formulate the different α-satisfactory optimization models. By regulating optimization parameters λ and α, the most satisfactory solution over fuzzy parameters can be obtained, and the balance between optimization and priority can be realized. The reformulated α-GP models are proved to be feasible, and their solutions are guaranteed to be M-α-Pareto optimal by the test model. In order to decrease optimization burden, the algorithm to compute the α-maximum regulating parameter is proposed, by which the bound of λ can be determined. The effectiveness of the proposed method is well demonstrated by numerical examples.