OPTIMIZATION OF FUZZY TRAVELLING SALESMAN PROBLEM USING PARAMETRIC ANALYSIS WITH MATLAB PROGRAMMING

This paper addresses the optimization of the Travelling Salesman Problem (TSP) using parametric analysis. The TSP is an NP-hard problem where the total distance and time traveled by an agent (e.g., a salesman delivering pizzas from a center to multiple centers in a city) are minimized. In the present work, a fuzzy optimization perspective has been adopted by considering center-to-center distances as parametric variables. Using α-cuts, we converted the fuzzy TSP into a crisp optimization problem by slicing the fuzzy numbers at various levels of certainty. MATLAB programming is used to analyze how parametric modifications in the variables lead to changes in the optimal solution. At the end of a numerical illustration is given to justify the proposed method and solution algorithm.