Fuzzy Goal Programming to Optimization the Multi-Objective Problem

Abstract

Many present-day problems are multi-objective in nature and their solution requires consideration of conflicting objectives. Usually, they have a number of potentially Pareto-optimal solutions. An extensive knowledge of the problem is required in discriminating between solutions, eliminating the unwanted ones and accepting the required solution(s) by a decision making process. It is well known that multi-objective optimization model had found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, a lot of literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multi-objective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function can actually be treated back at least. The regularization technique proved to be an invaluable tool in the solution of ill-posed problems, and an enormous amount of work has been devoted to its study. In this paper, a Multi-objective Optimization Problems formulation based on a Goal Programming Methods solves the multi-objective problem which can tackle relatively large test systems. This method is based on optimization of the most preferred objective and considering the other objectives as constraints.