Instance Space Analysis for the Quadratic Assignment Problem

TL;DR

This paper enhances understanding of the Quadratic Assignment Problem by analyzing instance features, identifying limitations in existing libraries, and proposing new instance classes to better evaluate algorithm performance.

Contribution

It introduces new features for characterizing QAP instances, applies Instance Space Analysis to compare algorithms, and proposes new instance classes to improve problem space representation.

Findings

Existing instance libraries are limited and obscure true algorithm performance.

New features effectively quantify QAP instance characteristics.

Proposed instance classes expand the problem space for better evaluation.

Abstract

For any optimisation problem where diverse algorithmic approaches are available, the task of predicting algorithm performance and selecting the algorithm most likely to perform well on a given instance holds great practical interest. However, if our test instances do not adequately represent the potential problem space, we may be misled about the strengths and weaknesses of an algorithm. In this paper we consider algorithm prediction and selection for the Quadratic Assignment Problem (QAP). We identify and eliminate superficial differences between QAP instances which do not affect problem difficulty and propose several new features for quantifying the characteristics of a particular instance. We then apply Instance Space Analysis to compare the performance of evolutionary and ant colony-based algorithms. Using this analysis, we identify limitations of the existing instance libraries and generators which obscure the true performance profile of these algorithms. Finally, we propose new instance classes which expand the instance space and support new insights into the properties of the problem and algorithms.