A O(n^8) X O(n^7) Linear Programming Model of the Traveling Salesman Problem

TL;DR

This paper introduces a new linear programming model for the Traveling Salesman Problem with significantly reduced computational times compared to previous models, using an LP with O(n^8) variables and O(n^7) constraints.

Contribution

The paper presents a novel LP formulation of TSP with a specific structure that improves computational efficiency over existing models.

Findings

Computational times are several orders of magnitude smaller.

The model has O(n^8) variables and O(n^7) constraints.

Numerical experiments validate the efficiency improvements.

Abstract

In this paper, we present a new linear programming (LP) formulation of the Traveling Salesman Problem (TSP). The proposed model has O(n^8) variables and O(n^7) constraints, where n is the number of cities. Our numerical experimentation shows that computational times for the proposed linear program are several orders of magnitude smaller than those for the existing model [3].