Predicting Metaheuristic Performance on Graph Coloring Problems Using Data Mining

Abstract

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.

Application of Machine Learning to Algorithm Selection for TSP

“…Mersmann et al [8] also used instances with up to 100 vertices but only a particular search operator was studied. Algorithm selection has been used also for different other combinatorial problems like for example graph coloring [9], [10] etc. For more information we refer the reader to the following surveys [11], [12].…”

Algorithm selection for black-box continuous optimization problems: A survey on methods and challenges

“…The algorithm selection framework based on the work of Rice [125] has been applied in many domains, including combinatorial auctions [39,74,75], clustering [2,77,76,148], feature selection [157], graph coloring [138,141], mixed integer programming [65,168], planning [61], program induction [44,45], quadratic assignment [136], satisfiability [39,62,65,69,[87][88][89]166], scheduling [9,139], time series [46], the traveling salesman problem [65,70], among other domains [73,137]. Most of these works use one of two alternative implementations of a meta-model, both illustrated in Fig.…”

Relating training instances to automatic design of algorithms for bin packing via features

“…ese features can be used to visualise the sets of instances, following the well-known work of Smith-Miles et al [7]. Our analysis focuses on statistical analysis of the results, but these illustrations help indicate the distribution of the instances in terms of their features.…”