A Parallel Ensemble of Metaheuristic Solvers for the Traveling Salesman Problem

TL;DR

This paper introduces a parallel ensemble approach combining multiple metaheuristic solvers, including hybrids, to improve TSP solutions, especially for large instances with over 10,000 cities, outperforming current state-of-the-art methods.

Contribution

It presents a novel ensemble framework that combines various metaheuristic solvers and hybrids, demonstrating superior performance on large-scale TSP instances.

Findings

Ensemble approach outperforms individual solvers on large TSP problems.

Hybrid of MGA and EAX is effective for hard, large-scale instances.

Performance varies with problem type, but ensemble mitigates this variability.

Abstract

The travelling salesman problem (TSP) is one of the well-studied NP-hard problems in the literature. The state-of-the art inexact TSP solvers are the Lin-Kernighan-Helsgaun (LKH) heuristic and Edge Assembly crossover (EAX). A recent study suggests that EAX with restart mechanisms perform well on a wide range of TSP instances. However, this study is limited to 2,000 city problems. We study for problems ranging from 2,000 to 85,900. We see that the performance of the solver varies with the type of the problem. However, combining these solvers in an ensemble setup, we are able to outperform the individual solver's performance. We see the ensemble setup as an efficient way to make use of the abundance of compute resources. In addition to EAX and LKH, we use several versions of the hybrid of EAX and Mixing Genetic Algorithm (MGA). A hybrid of MGA and EAX is known to solve some hard problems. We see that the ensemble of the hybrid version outperforms the state-of-the-art solvers on problems larger than 10,000 cities.