The Use of a Fuzzy Multi-Objective Linear Programming Model to Achieve a Balanced Optimal Solution of the Traveling Salesman Problem with Case Study (Iraq)

Abstract

Traveling Salesman Problem (TSP) is one of the most important Integer Programming Problems (IPP) in the field of Operations Research (OR) and Artificial Intelligence (AI), this problem has been discussed under different titles and has been solved using different methods, but not limited to; Genetic Algorithms (GA), Linear Programming (LP) and Fuzzy Linear Programming (FLP). But the majority of these research has taken special case studies and virtual examples where the number of nodes is very small and doesn't exceed five nodes in often and it is known that this number does not represent a realistic solution to the problems of the real world; as well as that this research did not explain in detail how to solve (TSP) by using Fuzzy Multi-Objective Linear Programming (FMOLP) with sub-tours. From this point of view, this research has been resolved (TSP) in all cities of Iraq (18 cities) by using the approach of (max-min) where associated with (FMOLP) model, real-world problems are characterized by multi-objective, and most of the information available about real-life systems is in a uncertainty environment, thus, fuzzy methods have been designed to deal with such problems by finding optimal solutions for models that include multi-objective function or fuzzy parameters. We found the optimal solution for the search model based on the readymade program (Win QSB) respective of operational research applications.