This note introduce a novel method for improving CDCL-based SAT solvers by relaxing backtrack and integrating local search techniques, and we use this method to improve four state of the art CDCL solvers.
译文：本文介绍了一种通过放松回溯和集成局部搜索技术来提高基于CDCL的SAT求解器性能的新方法，并对现有的四种CDCL求解器进行了改进。
主要技术：
1. relaxing the backtracking 松弛回溯
2. CCAnr solver——一种随机局部搜索求解器
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.
3. 两者结合改进2018年的四个CDCL求解器
基本思想：
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，通过允许一些有前途的分支扩展到叶(对应于一个完整的赋值)而不进行回溯，即使在扩展赋值期间遇到了冲突。
所依据（猜测的）依据是：以这种方式获得的完整的分配结果是高度一致的，有可能与真正所求解的模型之间有较小的距离(只需要少量翻转即可一致)
实施步骤：
首先，找到分支扩展；
其次，交给SLS求解器去 find a model nearby。（a local search solver is called to find a model nearby）
最后， 如果在规定翻转次数或时间内找不到最终sat模型，就回到CDCl继续正常求解。
相关叙述原文：
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，通过允许一些有前途的分支扩展到叶(对应于一个完整的赋值)而不进行回溯，即使在扩展赋值期间遇到了冲突。
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的分配结果是高度一致的，并且更有可能与模型有较小的距离(令人满意的分配)。
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：如果局部搜索在短时间内无法找到模型，则从算法进入非回溯阶段的节点开始，CDCL搜索过程将正常进行。
核心技术：
1.实施放松回溯中，如何找到有希望的部分分配？如何确保不被修剪？
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CDCL的搜索过程中，每当到达一个有希望的赋值对应的节点时，该算法就进入一个非回溯阶段(带有一些条件)，该阶段使用CDCL中的单元传播和启发式算法来分配剩余的变量而不进行回溯，甚至检测到一个空子句。
At the end, this leads to a complete assignment β,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指派β,提供给本地搜索求解搜索附近的一个模型。
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：如果局部搜索在一定的时间内没有找到模型，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：非回溯阶段不改变CDCL搜索过程中使用的数据结构。
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不能找到一个解决方案，那么修改后的求解器的工作方式与原来的CDCL求解器相同，但是由于局部搜索的时间消耗，它的速度可能会降低。
2.将SLS类型的先进求解器嵌入到CDCL求解过程中的方法和技术要点
（1）学习使用求解器
（2）结合过程算法涉及到的参数
CCAnr solver.有3个参数：the average weight threshold parameter γ, and the two factor parameters ρ and q.
对由函数ReasonLS调用花费在SLS阶段所用时间限制有2个参数：每次调用本地搜索过程的时间不超过300秒、本地搜索的所用总时间在总运行时中的所占比例小于ξ。
--------------------------------
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用来控制回溯式过程和局部搜索解算器的配合。
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 ξ of the total runtime.
译文：同时,我们限制由ReasonLS每次调用本地搜索过程的时间不超过300秒,并限制本地搜索的所用总时间在总运行时中的所占比例小于ξ。
（3）阀值的平滑加权加权方案
There are three parameters in the local search solver ：the average weight threshold parameter γ, and the two factor parameters ρ and q.。
All of the three parameters are for the Threshold-based Smoothed Weighting (TSW) weighting scheme.
For all our relaxed CDCL solvers, the parameters are set as follows with only one exception (p is 0.9 for Relaxed LCMDistChronoBT p9).
p = 0.5; ξ = 0.3; γ = 50; ρ = 0.3; q = 0.7.
