A Deterministic Annealing Approach to the Multiple Traveling Salesmen and Related Problems

TL;DR

This paper introduces a flexible heuristic framework based on deterministic annealing and maximum-entropy principles for solving the multiple traveling salesmen problem and its variants, including complex versions like CETSP.

Contribution

It extends the maximum-entropy and deterministic annealing approach to a general, adaptable heuristic framework for TSP variants, independent of edge definitions.

Findings

Effective in approximating solutions for m-TSP and variants

Independent of specific edge connections, suitable for complex variants

Demonstrated success on multiple TSP variants including CETSP

Abstract

This paper presents a novel and efficient heuristic framework for approximating the solutions to the multiple traveling salesmen problem (m-TSP) and other variants on the TSP. The approach adopted in this paper is an extension of the Maximum-Entropy-Principle (MEP) and the Deterministic Annealing (DA) algorithm. The framework is presented as a general tool that can be suitably adapted to a number of variants on the basic TSP. Additionally, unlike most other heuristics for the TSP, the framework presented in this paper is independent of the edges defined between any two pairs of nodes. This makes the algorithm particularly suited for variants such as the close-enough traveling salesman problem (CETSP) which are challenging due to added computational complexity. The examples presented in this paper illustrate the effectiveness of this new framework for use in TSP and many variants thereof.