文献学习——Relaxed Backtracking with Rephasing

Relaxed Backtracking with Rephasing

提出了一种通过放松回溯来改进CDCL求解器的方法。

文献来源：

sr2019_proceedings.pdf

sr2020_proceedings.pdf

 

Xindi Zhang1,2 and Shaowei Cai1,2*
1State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
2School of Computer Science and Technology, University of Chinese Academy of Sciences, China
dezhangxd@163.com, shaoweicai.cs@gmail.com

 

文献作者的主要创新点：（个人体会）

    1.在部分赋值条件下从CDCL求解状态转换到SLS求解状态，用较少的时间做尝试，如果随机求解器CCArn求解不出来则恢复到CDCL求解状态，在原来暂停处继续求解。

    2.原来应用于CDCL求解器的相位保持技术，现在以概率的方式运用到SLS求解器中；

   3.记录SLS求解过程中变元翻转的相关信息，反过来运用到CDCL分支决策中。

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2019年

I. INTRODUCTION

We propose a method to improve CDCL solvers by relaxing the backtracking. 译文：我们提出了一种通过放松回溯来改进CDCL求解器的方法。   The idea is to relax the backtrack process,by allowing some promising branches to be extended to the leaf (corresponding to a complete assignment) without backtracking, even if conflicts are met during extending the assignment. 译文：其思想是放松回溯过程，允许一些有前途的分支扩展到叶节点(对应于一个完整的分配)而不回溯，即使在扩展分配过程中遇到冲突。   The resulting complete assignments obtained in this way are highly consistent and are more likely to have small distances to a model (satisfying assignment).译文：以这种方式获得的完整任务具有高度的一致性，并且更有可能与模型有较小的距离(令人满意的任务)。   Then, a local search solver is called to find a model nearby.译文：然后，调用一个局部搜索求解器来寻找附近的模型。 If the local search cannot find a model within a short time limit, the CDCL search process continues as normal from the node where the algorithm enters the non-backtracking phase.译文：如果本地搜索在短时间内无法找到模型，CDCL搜索过程将从算法进入非回溯阶段的节点正常继续。

 

II. A RELAXED CDCL APPROACH

Our method is to relax the backtracking by protecting promising partial assignments from being pruned. 译文：我们的方法是通过保护有前途的部分分配不被修剪来放松回溯。     Specifically, during the search of CDCL, whenever reaching a node corresponding to a promising assignment, the algorithm enters a non-backtracking phase (with some condition), which uses unit propagation and heuristics in CDCL to assign the remaining variables without backtracking, even an empty clause is detected. 译文：具体来说，在搜索CDCL的过程中，只要到达一个与有希望的赋值对应的节点，算法就会进入一个非回溯阶段(带有一些条件)，这将使用CDCL中的单元传播和启发式来分配剩余的变量，而不回溯，甚至检测到一个空子句。 At the end, this leads to a complete assignment beta, which is fed to a local search solver to search for a model nearby.译文：最后这将导致一个完整的赋值集beta，它被提供给一个局部搜索求解器来搜索附近的模型。 If the local search fails to find a model within a certain time budget, then the algorithm goes back to the normal CDCL search from the node where it was interrupted (we call this a breakpoint).译文：如果本地搜索未能在一定的时间预算内找到模型，那么算法将从中断的节点(我们称之为断点)返回到正常的CDCL搜索。   The non-backtracking phase does not change the data structures used for CDCL search process.译文：非回溯阶段不会改变用于CDCL搜索过程的数据结构。   So, if all calls of local search fail to find a solution, the modified solver works in the same way just as the original CDCL solver, but it may have a lower speed due to the time consumption of local search.译文：因此，如果所有的局部搜索调用都没有找到解决方案，那么修改后的求解器与原来的CDCL求解器工作方式相同，但是由于局部搜索的时间消耗，其速度可能会慢一些。

 

III. THE LOCAL SEARCH ALGORITHM

	As for the local search solver used in our four solvers, we use the CCAnr [1] solver. There are three parameters in the local search solver : the average weight threshold parameter gama, and the two factor parameters p and q. All of the three parameters are for the Threshold-based Smoothed Weighting (TSW) weighting scheme.

 

IV. MAIN PARAMETERS

	There is one parameter p for controlling the cooperation of the backtracking style procedure and the local search solver.译文：有一个参数p用于控制回溯式程序与局部搜索求解器的协作。 Meanwhile, we limit the time of Local search procedure no more than 300 seconds every time ReasonLS call it, and limit the sum of all Local search time no more than a propotion epsilong of the total runtime.译文：我们限制本地搜索过程的时间不超过每次reason调用它时的300秒，并且限制所有本地搜索时间的总和不超过总运行时的平均值比例epsilong。 For all our relaxed CDCL solvers, the parameters are set as follows with only one exception (p is 0.9 for Relaxed LCMDistChronoBT-p9).

 

VI. SAT COMPETITION 2019 SPECIFIES

	Our four solvers are submitted to “main Track”. It is compiled by g++ with the ’O3’ optimization option.  They need to be compiled in the root folder by running “./starexec build”. The running command is: “./starexec run default $1” in folder “./bin”. The parameter $1 is the absolute path of input file. For a given input file ”~/sc/a.cnf”, the call command is ”./starexec run default ~/sc/a.cnf ”.

 

REFERENCES

[1] S. Cai, C. Luo, and K. Su, “CCAnr: A configuration checking based local search solver for non-random satisfiability,” in Proceedings of18th International Conference on Theory and Applications of Satisfiability Testing, SAT 2015, Austin, TX, USA, September 24-27, 2015, 2015, pp.
1–8.

[2] M. Luo, C. Li, F. Xiao, F. Many`a, and Z. L¨u, “An effective learnt clause minimization approach for CDCL SAT solvers,” in Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence,IJCAI 2017, Melbourne, Australia, August 19-25, 2017, 2017, pp. 703–711.

[3] A. Nadel and V. Ryvchin, Chronological Backtracking, 06 2018, pp. 111–121.

[4] Y. Xu, G. Wu, Q. Chen, and S. Chen, “Maple LCM Scavel and Maple LCM Scavel 200,” in Proceeding of SAT Competition 2018 - Solver and Benchmark Descriptions, Department of Computer Science Series of Publications B, University of Helsinki, 2018, p. 27.

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2020年

 

Abstract

	Abstract—A novel relaxing CDCL method and a new probability based phase saving technology are described. Based on this method, we develop three solvers called Relaxed LCMDCBDL, Relaxed LCMDCBDL noTimeParam and Relaxed LCMDCBDL newTech, which are based on MapleLCMDistChronoBT-DL.

I. INTRODUCTION

	We improve the relaxing CDCL method [3] using the information in CCAnr [2] this year. By using some full assignments (also named phases) with certain probability before each inprocessing, the performance of solvers on satisfiable instances are improved.译文：通过在每次处理前使用一定概率的完全赋值(也称为阶段)，提高了求解器在可满足实例上的性能。

II. METHODS

	A. Relaxed CDCL Approach
	The idea is to relax the backtracking process for protecting promising partial assignment, where a promising assignment is defined according to its consistency (no conflict) and length. 译文：其思想是放松回溯过程，以保护有希望的部分分配，其中有希望的分配是根据其一致性(无冲突)和长度定义的。 When the CDCL process reaches a node with some conditions, the algorithm enters a non-backtracking phase until it gets a full assignment beta.译文：当CDCL进程到达具有某些条件的节点时，算法进入一个非回溯阶段，直到它获得一个完整的赋值。 Then Local search process is then called to seek for a model near beta. If the local search fails to find a model within certain limits, then the algorithm goes back to the normal CDCL search from the node where it was interrupted. 译文：如果本地搜索在一定范围内无法找到模型，那么算法从被中断的节点返回到正常的CDCL搜索。
	译文：c表示两个本地搜索过程之间的处理时间。
	B. Probability Based Phase Saving
	Phase saving is a well-known technique which saves the assignment of variables when traceback and uses the assignment when variables are selected as decision variables。 阶段保存是一种众所周知的技术,它可以在选择变量时节省变量的赋值,当变量被选为决策变量时使用赋值。 Like the rephase technique in CaDiCaL [1], we use vectors to save different phases, the difference is that we use probability to select which phase to use after each restart. The probability of each phase is shown in “Table. I” 译文：我们使用向量来保存不同的相位，不同的是我们使用概率来选择在每次重启后使用哪个相位。每个阶段的概率如表1所示。

 

III. IMPLEMENTATION AND MAIN PARAMETERS

REFERENCES

[1] A. Biere. Cadical at the sat race 2019. SAT RACE 2019, page 8.

[2] S. Cai, C. Luo, and K. Su. CCAnr: A configuration checking based local search solver for non-random satisfiability. In International Conference on Theory and Applications of Satisfiability Testing, pages 1–8, 2015.

[3] S. Cai and X. Zhang. Four relaxed cdcl solvers. SAT RACE 2019, page 35.

[4] S. Kochemazov, O. Zaikin, V. Kondratiev, and A. Semenov. Maplelcmdistchronobt-dl, duplicate learnts heuristic-aided solvers at the sat race 2019. SAT RACE 2019, page 24.