Title: Evaluating the influence of parameter setup on the performance of heuristics for the graph colouring problem

Authors: Paulo Neis; Rhyd Lewis

Addresses: Universidade Tecnológica Federal do Paraná (UTFPR), Av. Sete de Setembro 3165, 80230-901 Curitiba, PR, Brazil ' School of Mathematics, Cardiff University, Cardiff, CF24 4AG, Wales, UK

Abstract: This paper aims to analyse the influence of parameter setup over a set of five heuristic methods applied to the graph colouring problem. Each heuristic is applied to a considerable set of problem instances, using a range of different parameter values. Multidimensional analysis is applied to extract and express knowledge about the performance of heuristic methods according to problem instance feature values, highlighting the effect of different parameter setups. The dynamic behaviour of the heuristics is also evaluated at different stages of execution (runtime), providing additional knowledge about speed of convergence/stagnation. Results demonstrate that it is possible to associate regions of the instance space in which problem instances exhibit particular features with specific parameter values yielding superior performance. Information relating runtime with average rate of solution improvement also suggests that certain instance features can be used to determine for how long the heuristics need to run before they converge or stagnate.

Keywords: parameter tuning; algorithm performance; heuristics; graph colouring.

DOI: 10.1504/IJMHEUR.2020.111602

International Journal of Metaheuristics, 2020 Vol.7 No.4, pp.352 - 378

Received: 20 Jul 2019
Accepted: 19 Mar 2020
Published online: 03 Dec 2020 *

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