Comparing Greedy Constructive Heuristic Subtour Elimination Methods for the Traveling Salesman Problem

TL;DR

This paper compares existing and new subtour elimination methods for the Traveling Salesman Problem, introducing the Greedy Tracker and Ordered Greedy heuristics, with empirical results showing the Greedy Tracker's speed advantage on smaller instances.

Contribution

It defines new subclasses of fragment constructive heuristics, introduces the Greedy Tracker and Ordered Greedy methods, and extends subtour elimination techniques to asymmetric instances.

Findings

Greedy Tracker is the fastest subtour elimination method for instances below 400 nodes.

New node-greedy heuristic called Ordered Greedy is introduced.

Methodologies are extended to asymmetric TSP instances.

Abstract

This paper further defines the class of fragment constructive heuristics used to compute feasible solutions for the Traveling Salesman Problem into arc-greedy and node-greedy subclasses. Since these subclasses of heuristics can create subtours, two known methodologies for subtour elimination on symmetric instances are reviewed and are expanded to cover asymmetric problem instances. This paper introduces a third novel methodology, the Greedy Tracker, and compares it to both known methodologies. Computational results are generated across multiple symmetric and asymmetric instances. The results demonstrate the Greedy Tracker is the fastest method for preventing subtours for instances below 400 nodes. A distinction between fragment constructive heuristics and the subtour elimination methodology used to ensure the feasibility of resulting solutions enables the introduction of a new node-greedy fragment heuristic called Ordered Greedy.