On Tightly Bounding the Dubins Traveling Salesman's Optimum

TL;DR

This paper introduces a systematic method for deriving tight lower bounds for the Dubins Traveling Salesman Problem, addressing the gap between the Euclidean TSP lower bounds and feasible solution costs.

Contribution

It presents the first systematic procedure to develop tight lower bounds for the DTSP, improving upon existing bounds based on Euclidean TSP relaxations.

Findings

New lower bounds are closer to feasible solution costs.

The method enhances understanding of DTSP complexity.

Results demonstrate significant gap reduction between bounds and solutions.

Abstract

The Dubins Traveling Salesman Problem (DTSP) has generated significant interest over the last decade due to its occurrence in several civil and military surveillance applications. Currently, there is no algorithm that can find an optimal solution to the problem. In addition, relaxing the motion constraints and solving the resulting Euclidean TSP (ETSP) provides the only lower bound available for the problem. However, in many problem instances, the lower bound computed by solving the ETSP is far below the cost of the feasible solutions obtained by some well-known algorithms for the DTSP. This article addresses this fundamental issue and presents the first systematic procedure for developing tight lower bounds for the DTSP.