A Novel Feature-Based Approach to Characterize Algorithm Performance for the Traveling Salesman Problem

TL;DR

This paper investigates the features of TSP instances that influence the effectiveness of 2-opt local search algorithms, providing insights into what makes certain instances easier or harder to approximate.

Contribution

It introduces a feature-based statistical approach to analyze and predict the difficulty of TSP instances for 2-opt algorithms, enhancing understanding of their success.

Findings

Identified key features affecting 2-opt performance

Established correlation between features and approximation ratio

Provided a framework for predicting instance difficulty

Abstract

Meta-heuristics are frequently used to tackle NP-hard combinatorial optimization problems. With this paper we contribute to the understanding of the success of 2-opt based local search algorithms for solving the traveling salesman problem (TSP). Although 2-opt is widely used in practice, it is hard to understand its success from a theoretical perspective. We take a statistical approach and examine the features of TSP instances that make the problem either hard or easy to solve. As a measure of problem difficulty for 2-opt we use the approximation ratio that it achieves on a given instance. Our investigations point out important features that make TSP instances hard or easy to be approximated by 2-opt.