Efficient Local Search Algorithms for Known and New Neighborhoods for the Generalized Traveling Salesman Problem

TL;DR

This paper develops and classifies efficient local search algorithms tailored for the Generalized Traveling Salesman Problem, enhancing exploration speed and effectiveness compared to existing methods.

Contribution

It formalizes the adaptation of TSP neighborhoods for GTSP, introduces new neighborhoods, and provides faster exploration algorithms with empirical comparisons.

Findings

New neighborhoods and exploration algorithms outperform existing methods

Formal classification of GTSP neighborhoods

Empirical results show improved local search efficiency

Abstract

The Generalized Traveling Salesman Problem (GTSP) is a well-known combinatorial optimization problem with a host of applications. It is an extension of the Traveling Salesman Problem (TSP) where the set of cities is partitioned into so-called clusters, and the salesman has to visit every cluster exactly once. While the GTSP is a very important combinatorial optimization problem and is well studied in many aspects, the local search algorithms used in the literature are mostly basic adaptations of simple TSP heuristics. Hence, a thorough and deep research of the neighborhoods and local search algorithms specific to the GTSP is required. We formalize the procedure of adaptation of a TSP neighborhood for the GTSP and classify all other existing and some new GTSP neighborhoods. For every neighborhood, we provide efficient exploration algorithms that are often significantly faster than the ones known from the literature. Finally, we compare different local search implementations empirically.