Fuzzy Goal Programming Technique for Multi-Objective Optimisation Problem

Multi-objective optimization is a natural extension of the traditional optimization of a single-objective function. Many current problems are multi-objective in nature and their solution requires taking into account conflicting objectives. Usually, they propose a number of potentially Pareto optimal solutions. In-depth knowledge of the problem is necessary to distinguish solutions, eliminate undesirable ones, and accept the solution(s) required by a decision-making process. It is well known that the multi-objective optimization model has found many important applications in decision-making problems such as economic theory, management science and engineering design. Many papers have been published as a result of these applications to research optimality requirements, duality theories, and topological aspects of solutions to multi-objective optimization problems. In this chapter, a multi-objective optimization problem formulation based on objective programming methods solves the multi-objective problem which can tackle relatively large test systems. This strategy optimizes the desired target while treating the other objectives as constraints. We will present a road accident constraint in which the data from three networks are fuzzy values and the objective function assumes multiple objectives. We will take nonlinear constraints and auxiliary constraints. Our optimal solution of the problem is based on solving the linear programming problem with fuzzy constraints by applying a fuzzy programming technique. Our approach consists of giving a simple procedure for solving multi-objective fuzzy programming problems.