Comparing Greedy Constructive Heuristic Subtour Elimination Methods for the Traveling Salesman Problem
This work addresses subtour elimination in TSP heuristics, which is an incremental improvement for optimization researchers and practitioners.
The paper tackled the problem of subtour elimination in greedy constructive heuristics for the Traveling Salesman Problem by introducing a new method called Greedy Tracker and comparing it to existing ones. The results showed that Greedy Tracker is the fastest method for instances below 400 nodes, and a new heuristic called Ordered Greedy was introduced.
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.