Comparative Solutions of Exact and Approximate Methods for Traveling Salesman Problem

Abstract

There are two major optimization methods: Exact and Approximate methods. A well known exact method, Branch and Bound algorithm (B&B) and approximate methods, Elimination-based Fruit Fly Optimization Algorithm (EFOA) and Artificial Atom Algorithm (A3) are used for solving the Traveling Salesman Problem (TSP). For 56 destinations, the results of total distance, processing time, and the deviation between exact and approximate method will be compared where the distance between two destinations is a Euclidean distance and this study shows that the distance of B&B is 270 , EFOA is 270 and A3 is 288.38 which deviates 6.81%. For time processing aspect, B&B needs 12.5 days to process, EFOA needs 36.59 seconds, A3 needs 35.34 seconds. But for 29 destinations, exact method is more powerful than approximate method.