Combine and conquer: an evolutionary hyper-heuristic approach for solving constraint satisfaction problems

Selection hyper-heuristics are a technology for optimization in which a high-level mechanism controls low-level heuristics, so as to be capable of solving a wide range of problem instances efficiently. Hyper-heuristics are used to generate a solution process rather than producing an immediate solution to a given problem. This process is a re-usable mechanism that can be applied both to seen and unseen problem instances. In this paper, we propose a selection hyper-heuristic process with the intention to rise the level of generality and solve consistently well a wide range of constraint satisfaction problems. The hyper-heuristic technique is based on a messy genetic algorithm that generates high-level heuristics formed by rules (condition →\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document} heuristic). The high-level heuristics produced are seen to be good at solving instances from certain parts of the parameterized space of problems, producing results using effort comparable to the best single heuristic per instance. This is beneficial, as the choice of best heuristic varies from instance to instance, so the high-level heuristics are definitely preferable to selecting any one low-level heuristic for all instances. The results confirm the robustness of the proposed approach and how high-level heuristics trained for some specific classes of instances can also be applied to unseen classes without significant lost of efficiency. This paper contributes to the understanding of heuristics and the way they can be used in a collaborative way to benefit from their combined strengths.