| 361 | 11 | 736 |
| 下载次数 | 被引频次 | 阅读次数 |
最大可满足性问题(Max-SAT)是经典的NP难问题，目标是寻找一组变元赋值使得满足子句个数最多。近年来，随着算例规模在实际应用中的逐渐增大，传统的启发式算法已不再适用。传统模拟退火算法在求解Max-SAT问题时会出现收敛速度慢、局部搜索能力弱，以及无效的盲目扰动等弊端，为此提出一种改进的快速模拟退火算法，针对初始赋值的随机性和盲目性，采用变元权值计算初始解，结合基于概率的随机扰动和选择扰动两种方式，并在Metropolis接受准则中添加记忆功能，用于搜索当前局部最优解，引入高低温两种降温模式，较大程度地提高算法的全局搜索能力，进而加快算法的收敛速度，有效减少求解时间。最后，在公开数据集和随机生成的数据集上进行仿真实验，结果表明，所提算法在求解Max-3-SAT问题上优于传统启发式算法。
Abstract：The maximum satisfiability problem(Max-SAT) was a classical NP hard problem. The goal was to find a set of variable assignments to maximize the number of satisfied clauses. In recent years, with the gradual increase of the scale of examples in practical application, the traditional heuristic algorithm was no longer applicable. The traditional simulated annealing algorithm had some disadvantages in solving Max-SAT problem, such as slow convergence speed, weak local search ability and invalid blind disturbance. Therefore, an improved fast simulated annealing algorithm was proposed. Aiming at the randomness and blindness of the initial assignment, the variable weight was used to calculate the initial solution, combined with the two methods of random disturbance based on probability and selective disturbance, and the memory function was added to the Metropolis acceptance criterion. It was used to search the current local optimal solution. Two cooling modes of high and low temperature were introduced to greatly improve the global search ability of the algorithm, so as to speed up the convergence speed of the algorithm and effectively reduce the solution time. Finally, simulation experiments were carried out on public data sets and randomly generated data sets. The results showed that the algorithm was better than the traditional heuristic algorithm in solving Max-3-SAT problem.
[1] AIELLO A,BURATTINI E,MASSAROTTI A.The complexity of theorem proving procedures[J].Rairo Informat Théor,1977,11(1):75-82.
[2] 何琨，郑迥之.最大可满足性问题的算法研究综述[J].华中科技大学学报(自然科学版),2022,50(2):82-95.HE K,ZHENG J Z.Survey on algorithms for the maximum satisfiability problem[J].Journal of Huazhong university of science and technology (natural science edition),2022,50(2):82-95.
[3] 周俊萍，任雪亮，殷茜，等.求解MinSAT问题的加强式格局检测与子句加权算法[J].计算机学报，2018,41(4):745-759.ZHOU J P,REN X L,YIN Q,et al.Algorithm of strengthened configuration checking and clause weighting for solving the minimum satisfiability problem[J].Chinese journal of computers,2018,41(4):745-759.
[4] ZHANG H T.An experiment with satisfiability modulo SAT[J].Journal of automated reasoning,2016,56(2):143-154.
[5] HOSSAIN A,LAROUSSINIE F.QCTL model-checking with QBF solvers[J].Information and computation,2021,280:104642.
[6] 万仁霞，高艳龙.基于粗糙集约简与狮群优化算法的机器人路径规划研究[J].郑州大学学报(理学版),2022,54(2):32-38.WAN R X,GAO Y L.Robot path planning based on rough set reduction and lion swarm optimization[J].Journal of Zhengzhou university (natural science edition),2022,54(2):32-38.
[7] 王晓峰，于卓，赵健，等.大规模图例的最大团问题算法分析[J].计算机工程，2022,48(6):182-192,199.WANG X F,YU Z,ZHAO J,et al.Algorithm analysis for solving maximum clique problems of large-scale graphs[J].Computer engineering,2022,48(6):182-192,199.
[8] LI C M,MANYà F,MOHAMEDOU N O,et al.Resolution-based lower bounds in MaxSAT[J].Constraints,2010,15(4):456-484.
[9] HERAS F,LARROSA J,OLIVERAS A.MiniMaxSat:a new weighted Max-SAT solver[C]//International Conference on Theory and Applications of Satisfiability Testing.Cham:Springer Press,2007:41-55.
[10] 王志华，王浩帆，程漫漫.基于启发式遗传算法的模糊测试样本集优化方案[J].北京航空航天大学学报，2022,48(2):217-224.WANG Z H,WANG H F,CHENG M M.Fuzzing testing sample set optimization scheme based on heuristic genetic algorithm[J].Journal of Beijing university of aeronautics and astronautics,2022,48(2):217-224.
[11] 王燕，聂长海，钮鑫涛，等.覆盖表生成的禁忌搜索算法[J].软件学报，2018,29(12):3665-3691.WANG Y,NIE C H,NIU X T,et al.Tabu search in covering array generation[J].Journal of software,2018,29(12):3665-3691.
[12] WU H G,GAO Y L,WANG W T,et al.A hybrid ant colony algorithm based on multiple strategies for the vehicle routing problem with time windows[J].Complex & intelligent systems,2021:1-18.
[13] 丛琳，沙宇恒，焦李成.采用正交免疫克隆粒子群算法求解SAT问题[J].西安电子科技大学学报，2007,34(4):616-621.CONG L,SHA Y H,JIAO L C.Orthogonal immune clone particle swarm optimization for the SAT problem[J].Journal of xidian university,2007,34(4):616-621.
[14] 张焕龙，张秀娇，贺振东，张建伟.基于布谷鸟搜索的图像匹配方法研究[J].郑州大学学报(理学版),2017,49(4):51-56.ZHANG H L,ZHANG X J,HE Z D,et al.The study on image matching method based on cuckoo search[J].Journal of Zhengzhou university (natural science edition),2017,49(4):51-56.
[15] 康立山，谢云，尤矢勇，等.非数值并行算法(第一册):模拟退火算法[M].北京：科学出版社，1994.KANG L Y,XIE Y,YOU S Y,et al;Non-numerical parallel algorithms (Volume 1):simulated annealing algorithm[M].Beijing:Science Press,1994.
[16] XU Z X,HE K,LI C M.An iterative path-breaking approach with mutation and restart strategies for the MAX-SAT problem[J].Computers & operations research,2019,104:49-58.
[17] 陈科胜，鲜思东，郭鹏.求解旅行商问题的自适应升温模拟退火算法[J].控制理论与应用，2021,38(2):245-254.CHEN K S,XIAN S D,GUO P.Adaptive temperature rising simulated annealing algorithm for traveling salesman problem[J].Control theory & applications,2021,38(2):245-254.
[18] TAVARES R S,MARTINS T C,TSUZUKI M S G.Simulated annealing with adaptive neighborhood:a case study in off-line robot path planning[J].Expert systems with applications,2011,38(4):2951-2965.
[19] LAYEB A.A new greedy randomised adaptive search procedure for solving the maximum satisfiability problem[J].International journal of operational research,2013,17(4):509.
[20] CAI L W,MAO Z Q.A regular expression grouping algorithm based on simulated annealing algorithm[C]//2018 8th International Conference on Electronics Information and Emergency Communication (ICEIEC).Piscataway:IEEE Press,2018:99-102.
基本信息:
DOI：10.13705/j.issn.1671-6841.2022158
中图分类号:TP18
引用信息:
[1]吴宇翔,王晓峰,于卓,等.一种求解Max-SAT问题的快速模拟退火算法[J],2023,55(04):46-53.DOI:10.13705/j.issn.1671-6841.2022158.
基金信息:
国家自然科学基金项目(62062001);; 宁夏自然科学基金项目(2022AAC05040)