Exploring the landscape of the space of heuristics for local search in SAT

Burnett, Andrew W.; Parkes, Andrew J.

Abstract

Local search is a powerful technique on many combinatorial optimisation problems. However, the effectiveness of local search methods will often depend strongly on the details of the heuristics used within them. There are many potential heuristics, and so finding good ones is in itself a challenging search problem. A natural method to search for effective heuristics is to represent the heuristic as a small program and then apply evolutionary methods, such as genetic programming. However, the search within the space of heuristics is not well understood, and in particular little is known of the associated search landscapes. In this paper, we consider the domain of propositional satisfiability (SAT), and a generic class of local search methods called ‘WalkSAT’. We give a language for generating the heuristics; using this we generated over three million heuristics, in a systematic manner, and evaluated their associated fitness values. We then use this data set as the basis for an initial analysis of the landscape of the space of heuristics. We give evidence that the heuristic landscape exhibits clustering. We also consider local search on the space of heuristics and show that it can perform quite well, and could complement genetic programming methods on that space.

Citation

Burnett, A. W., & Parkes, A. J. (2017). Exploring the landscape of the space of heuristics for local search in SAT.

• Conference Name: IEEE Congress on Evolutionary Computation 2017
• End Date: Jun 8, 2017
• Acceptance Date: Mar 7, 2017
• Publication Date: Jun 5, 2017
• Deposit Date: Jun 28, 2017
• Peer Reviewed: Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/864290
• Related Public URLs: http://cec2017.org/
• Additional Information: 978-1-5090-4601-0 ©2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.