GO-MOCE: Greedy Order Method of Conditional Expectations for Max Sat

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-02-01 DOI:10.1016/j.disopt.2022.100685

Daniel Berend , Shahar Golan , Yochai Twitto

{"title":"GO-MOCE: Greedy Order Method of Conditional Expectations for Max Sat","authors":"Daniel Berend , Shahar Golan , Yochai Twitto","doi":"10.1016/j.disopt.2022.100685","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm is based on the Method of Conditional Expectations (MOCE, also known as Johnson’s Algorithm) and applies a greedy variable ordering to MOCE. Thus, we name it Greedy Order MOCE (GO-MOCE). We also suggest a combination of GO-MOCE with CCLS, a state-of-the-art solver. We refer to this combined solver as GO-MOCE-CCLS.</p><p>We conduct a comprehensive comparative evaluation of GO-MOCE versus MOCE on random instances and on public competition benchmark instances. We show that GO-MOCE reduces the number of unsatisfied clauses by tens of percents, while keeping the runtime almost the same. The worst case time complexity of GO-MOCE is linear. We also show that GO-MOCE-CCLS improves on CCLS consistently by up to about 80%.</p><p>We study the asymptotic performance of GO-MOCE. To this end, we introduce three measures for evaluating the asymptotic performance of algorithms for Max Sat. We point out to further possible improvements of GO-MOCE, based on an empirical study of the main quantities managed by GO-MOCE during its execution.</p></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528622000019","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

In this paper we present and study a new algorithm for the Maximum Satisfiability (Max Sat) problem. The algorithm is based on the Method of Conditional Expectations (MOCE, also known as Johnson’s Algorithm) and applies a greedy variable ordering to MOCE. Thus, we name it Greedy Order MOCE (GO-MOCE). We also suggest a combination of GO-MOCE with CCLS, a state-of-the-art solver. We refer to this combined solver as GO-MOCE-CCLS.

We conduct a comprehensive comparative evaluation of GO-MOCE versus MOCE on random instances and on public competition benchmark instances. We show that GO-MOCE reduces the number of unsatisfied clauses by tens of percents, while keeping the runtime almost the same. The worst case time complexity of GO-MOCE is linear. We also show that GO-MOCE-CCLS improves on CCLS consistently by up to about 80%.

We study the asymptotic performance of GO-MOCE. To this end, we introduce three measures for evaluating the asymptotic performance of algorithms for Max Sat. We point out to further possible improvements of GO-MOCE, based on an empirical study of the main quantities managed by GO-MOCE during its execution.

查看原文本刊更多论文

GO-MOCE:最大Sat条件期望的贪心阶方法

本文提出并研究了一种求解最大可满足性问题的新算法。该算法基于条件期望方法(Method of Conditional Expectations, MOCE)，又称约翰逊算法(Johnson’s algorithm)，并对MOCE应用贪心变量排序。因此，我们将其命名为贪心序MOCE (GO-MOCE)。我们还建议将GO-MOCE与最先进的求解器CCLS相结合。我们将这种组合求解器称为GO-MOCE-CCLS。我们在随机实例和公共竞争基准实例上对GO-MOCE与MOCE进行了全面的比较评估。我们发现GO-MOCE在保持运行时几乎相同的情况下，将不满意的子句数量减少了数十个百分点。最坏情况下，GO-MOCE的时间复杂度为线性。我们还表明，GO-MOCE-CCLS对CCLS的持续改善高达80%左右。我们研究了GO-MOCE的渐近性能。为此，我们引入了三种衡量Max Sat算法渐近性能的指标。基于GO-MOCE在执行过程中管理的主要数量的实证研究，我们指出了GO-MOCE进一步改进的可能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.