Solving the clustered traveling salesman problem with d-relaxed priority rule

TL;DR

This paper addresses the Clustered Traveling Salesman Problem with prioritized clusters by introducing a d-relaxed priority rule, proposing improved exact and heuristic solution methods, and demonstrating their effectiveness through experiments.

Contribution

It develops an improved mathematical formulation and a meta-heuristic approach for the d-relaxed priority constrained CTSP, enhancing solution efficiency.

Findings

The methods effectively solve the problem with improved routes.

Meta-heuristic outperforms baseline algorithms.

Experimental results validate the approaches' efficiency.

Abstract

The Clustered Traveling Salesman Problem with a Prespecified Order on the Clusters, a variant of the well-known traveling salesman problem is studied in literature. In this problem, delivery locations are divided into clusters with different urgency levels and more urgent locations must be visited before less urgent ones. However, this could lead to an inefficient route in terms of traveling cost. This priority-oriented constraint can be relaxed by a rule called d-relaxed priority that provides a trade-off between transportation cost and emergency level. Our research proposes two approaches to solve the problem with d-relaxed priority rule. We improve the mathematical formulation proposed in the literature to construct an exact solution method. A meta-heuristic method based on the framework of Iterated Local Search with problem-tailored operators is also introduced to find approximate solutions. Experimental results show the effectiveness of our methods.