Exploring the Feature Space of TSP Instances Using Quality Diversity

TL;DR

This paper introduces a quality diversity-based method to explore and visualize the feature space of TSP instances, aiding in understanding solver performance differences.

Contribution

It presents a novel QD approach for TSP instance generation that covers the entire feature space, surpassing traditional evolutionary methods.

Findings

QD approach effectively explores the full feature space.

Generated instances differentiate various TSP solvers.

Comparison shows advantages over $(ul+1)$-EA.

Abstract

Generating instances of different properties is key to algorithm selection methods that differentiate between the performance of different solvers for a given combinatorial optimization problem. A wide range of methods using evolutionary computation techniques has been introduced in recent years. With this paper, we contribute to this area of research by providing a new approach based on quality diversity (QD) that is able to explore the whole feature space. QD algorithms allow to create solutions of high quality within a given feature space by splitting it up into boxes and improving solution quality within each box. We use our QD approach for the generation of TSP instances to visualize and analyze the variety of instances differentiating various TSP solvers and compare it to instances generated by a $(\mu+1)$-EA for TSP instance generation.