A flexible programming approach based on intuitionistic fuzzy optimization and geometric programming for solving multi-objective nonlinear programming problems

• Published in: Expert systems with applications Vol. 93; pp. 245 - 256
• Main Authors: Jafarian, E., Razmi, J., Baki, M.F.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.03.2018; Elsevier BV
• Subjects: Constraint modelling; Decision making; Fuzzy sets; Geometric programming; Interactive decision making; Intuitionistic fuzzy optimization; Iterative methods; Mathematical programming; Multi-objective nonlinear programming; Multiple objective analysis; Nonlinear programming; Optimization; Problem solving; Intuitionistic fuzzy optimization; Multi-objective nonlinear programming; Interactive decision making; Geometric programming
• ISSN: 0957-4174; 1873-6793
• DOI: 10.1016/j.eswa.2017.10.030

•We propose a new method for solving nonlinear programming problems.•It integrates the concepts of intuitionistic fuzzy sets and geometric programming.•A two steps approach is employed to determine satisfying solutions to the problem.•The obtained solutions satisfy the conditions of Pareto-optimality.•The formulation of the models does not affect the posynomiality of the problem. In this paper, a novel method is proposed to support the process of solving multi-objective nonlinear programming problems subject to strict or flexible constraints. This method assumes that the practical problems are expressed in the form of geometric programming problems. Integrating the concept of intuitionistic fuzzy sets into the solving procedure, a rich structure is provided which can include the inevitable uncertainties into the model regarding different objectives and constraints. Another important feature of the proposed method is that it continuously interacts with the decision maker. Thus, the decision maker could learn about the problem, thereby a compromise solution satisfying his/hers preferences could be obtained. Further, a new two-step geometric programming approach is introduced to determine Pareto-optimal compromise solutions for the problems defined during different iterative steps. Employing the compensatory operator of “weighted geometric mean”, the first step concentrates on finding an intuitionistic fuzzy efficient compromise solution. In the cases where one or more intuitionistic fuzzy objectives are fully achieved, a second geometric programming model is developed to improve the resulting compromise solution. Otherwise, it is concluded that the resulting solution vectors simultaneously satisfy both of the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The models forming the proposed solving method are developed in a way such that, the posynomiality of the defined problem is not affected. This property is of great importance when solving nonlinear programming problems. A numerical example of multi-objective nonlinear programming problem is also used to provide a better understanding of the proposed solving method.