Feature-Based Diversity Optimization for Problem Instance Classification

TL;DR

This paper introduces a framework using evolutionary algorithms to generate diverse problem instances for the TSP, enabling better classification of instance difficulty for heuristic search methods like 2-OPT.

Contribution

It presents a novel feature-based diversity optimization approach to classify TSP instances by difficulty for specific heuristics.

Findings

Certain feature combinations effectively classify TSP instance difficulty.

Diverse instance sets reveal insights into heuristic performance.

The framework generalizes to other problem types.

Abstract

Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.