Predicting Metaheuristic Performance on Graph Coloring Problems Using Data Mining

Abstract

This chapter illustrates the benefits of using data mining methods to gain greater understanding of the strengths and weaknesses of a metaheuristic across the whole of instance space. Using graph coloring as a case study, we demonstrate how the relationships between the features of instances and the performance of algorithms can be learned and visualized. The instance space (in this case, the set of all graph coloring instances) is characterized as a high-dimensional feature space, with each instance summarized by a set of metrics selected as indicative of instance hardness. We show how different instance generators produce instances with various properties, and how the performance of algorithms depends on these properties. Based on a set of tested instances, we reveal the generalized boundary in instance space where an algorithm can be expected to perform well. This boundary is called the algorithm footprint in instance space. We show how data mining methods can be used to visualize the footprint and relate its boundary to properties of the instances. In this manner, we can begin to develop a good understanding of the strengths and weaknesses of a set of algorithms, and identify opportunities to develop new hybrid approaches that exploit the combined strength and improve the performance across a broad instance space.