Generalized Traveling Salesman Problem Reduction Algorithms

TL;DR

This paper introduces a reduction algorithm for the generalized traveling salesman problem that efficiently deletes redundant vertices and edges, significantly reducing problem size and solution time while preserving optimal solutions.

Contribution

It presents a novel reduction algorithm for GTSP that decreases problem size by 15-20% with an O(N^3) worst-case running time, improving solver efficiency.

Findings

Reduced problem size by 15-20% on average

Decreased solution time by 10-60% in experiments

Algorithm preserves optimal solutions

Abstract

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The aim of this paper is to present a problem reduction algorithm that deletes redundant vertices and edges, preserving the optimal solution. The algorithm's running time is O(N^3) in the worst case, but it is significantly faster in practice. The algorithm has reduced the problem size by 15-20% on average in our experiments and this has decreased the solution time by 10-60% for each of the considered solvers.