Lin-Kernighan Heuristic Adaptations for the Generalized Traveling Salesman Problem

TL;DR

This paper adapts the Lin-Kernighan heuristic, a successful TSP solver, for the Generalized Traveling Salesman Problem, demonstrating its effectiveness and outperforming other heuristics in solution quality and speed.

Contribution

The paper introduces several adaptations of the Lin-Kernighan heuristic specifically for the GTSP, establishing it as a state-of-the-art local search method.

Findings

Adapted Lin-Kernighan variants outperform other GTSP heuristics.

The adaptations achieve a good balance between solution quality and computational time.

The approach maintains the success of the original heuristic in the generalized problem context.

Abstract

The Lin-Kernighan heuristic is known to be one of the most successful heuristics for the Traveling Salesman Problem (TSP). It has also proven its efficiency in application to some other problems. In this paper we discuss possible adaptations of TSP heuristics for the Generalized Traveling Salesman Problem (GTSP) and focus on the case of the Lin-Kernighan algorithm. At first, we provide an easy-to-understand description of the original Lin-Kernighan heuristic. Then we propose several adaptations, both trivial and complicated. Finally, we conduct a fair competition between all the variations of the Lin-Kernighan adaptation and some other GTSP heuristics. It appears that our adaptation of the Lin-Kernighan algorithm for the GTSP reproduces the success of the original heuristic. Different variations of our adaptation outperform all other heuristics in a wide range of trade-offs between solution quality and running time, making Lin-Kernighan the state-of-the-art GTSP local search.