A New Column-Row Method for Traveling Salesman Problem: The Dhouib-Matrix-TSP1

Abstract

In this paper, a new column-row method named Dhouib-Matrix-TSP1 is designed to solve in polynomial time the Traveling Salesman Problem (TSP). At first, the distance matrix is defined, and then four steps are launched: 1) Selecting the starting position 2) Choosing Rows 3) Discarding by column 3) Transforming route to a tour. Some numerical examples are presented to illustrate the effectiveness of the proposed method. It can be concluded that the Dhouib-Matrix-TSP1 method consumes a small number of iterations (just n iterations, where n represents the number of cities) to solve the TSP, and its result is the closest to the optimum solution.