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Effect of Initial Assignment on Local Search Performance for Max Sat

Authors Daniel Berend, Yochai Twitto

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Author Details

Daniel Berend
  • Departments of Mathematics and of Computer Science, Ben-Gurion University, Beer Sheva 84105, Israel
Yochai Twitto
  • Department of Computer Science, Ben-Gurion University, Beer Sheva 84105, Israel

Funding

This research was partially supported by the Milken Families Foundation Chair in Mathematics and by the Lynne and William Frankel Center for Computer Science.

Acknowledgements

We thank Shaowei Cai for providing us access to the original authors' implementation of the CCLS solver used in Max Sat Evaluation 2016, and André Abramé for providing us access to the Abramé-Habet benchmark used (partially) in that evaluation. We also thank Gregory Gutin and Shahar Golan for their helpful comments on this paper.

Cite As Get BibTex

Daniel Berend and Yochai Twitto. Effect of Initial Assignment on Local Search Performance for Max Sat. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.SEA.2020.8

Abstract

In this paper, we explore the correlation between the quality of initial assignments provided to local search heuristics and that of the corresponding final assignments. We restrict our attention to the Max r-Sat problem and to one of the leading local search heuristics - Configuration Checking Local Search (CCLS). We use a tailored version of the Method of Conditional Expectations (MOCE) to generate initial assignments of diverse quality. 
We show that the correlation in question is significant and long-lasting. Namely, even when we delve deeper into the local search, we are still in the shadow of the initial assignment. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics. 
To demonstrate our point, we improve CCLS by combining it with MOCE. Instead of starting CCLS from random initial assignments, we start it from excellent initial assignments, provided by MOCE. Indeed, it turns out that this kind of initialization provides a significant improvement of this state-of-the-art solver. This improvement becomes more and more significant as the instance grows.

Subject Classification

ACM Subject Classification
  • Theory of computation → Theory of randomized search heuristics
  • Theory of computation → Stochastic approximation
Keywords
  • Combinatorial Optimization
  • Maximum Satisfiability
  • Local Search
  • Probabilistic Algorithms

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