A Memetic Algorithm for the Generalized Traveling Salesman Problem

TL;DR

This paper introduces a new memetic algorithm for the generalized traveling salesman problem that outperforms existing heuristics in solution quality and speed, applicable to both symmetric and asymmetric cases.

Contribution

A novel memetic algorithm with an effective local search for GTSP, capable of handling both symmetric and asymmetric instances, improving over previous methods.

Findings

Outperforms existing heuristics in solution quality

Faster convergence compared to prior algorithms

Effective for both symmetric and asymmetric GTSP instances

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 recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances.