Using the method of conditional expectations to supply an improved starting point for CCLS

Daniel Berend, Shahar Golan, Yochai Twitto

Research output: Contribution to journalArticlepeer-review


This paper proposes to combine the method of conditional expectations (MOCE, also known as Johnson’s Algorithm) with the state-of-the-art heuristic configuration checking local search (CCLS), to solve maximum satisfiability (Max Sat) instances. First, MOCE is used to find an outstanding assignment, and then CCLS explores the solution space, starting at this assignment. This combined heuristic, which we call MOCE–CCLS, is shown to provide a significant improvement over each of its parts: MOCE and CCLS. An additional contribution of this paper is the results of a comprehensive comparative evaluation of MOCE–CCLS versus CCLS on various benchmarks. On random benchmarks, the combined heuristic reduces the number of unsatisfied clauses by up to tens of percents. On Max Sat 2016 and 2021 public competition benchmarks, which include crafted and industrial instances also, MOCE–CCLS outperforms CCLS as well. To provide an empirical basis to the above result, this work further explores the correlation between the quality of initial assignments provided to CCLS and that of the corresponding final assignments. Empirical results show that the correlation is significant and long-lasting. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics.

Original languageEnglish
Pages (from-to)3711-3734
Number of pages24
JournalJournal of Combinatorial Optimization
Issue number5
StatePublished - 1 Dec 2022


  • Combinatorial optimization
  • Local search
  • Maximum satisfiability
  • Method of conditional expectations

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics


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