The multiobjective optimization problem with fuzzy goal programming

Many present-day problems are multiobjective 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 multiobjective optimization models have found a lot of important applications in decision making problems such as in economics theory, management science and engineering design. Because of these applications, many papers literatures have been published to study optimality conditions, duality theories and topological properties of solutions of multiobjective optimization problems. In the case of optimization problems, the idea of regularizing a problem by adding a strongly convex term to the objective function is an option. 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 Multiobjective Optimization Problem formulation based on a Goal Programming Methods solves the multiobjective 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.