程亚南,王晓峰,刘凇佐,刘子琳

• 1:北方民族大学计算机科学与工程学院
• 2:北方民族大学图像图形智能处理国家民委重点实验室

摘要(Abstract)：

针对旅行商问题求解精度较差、容易陷入局部最优等缺点，提出一种新的求解旅行商问题的信息传播算法。根据旅行商问题的特征，将线性方程嵌入信息传播算法方程中得到旅行商问题的势函数，进而将其转换为因子图，在因子图上利用信息传播算法的迭代方程进行迭代计算。在迭代过程中选择边际信念的最小值，从而得到旅行商问题的初始解，在算法达到设定的迭代次数后，引入局部搜索算法进行求解。在若干数据集上的实验结果表明，新算法能够有效求解旅行商问题。

关键词(KeyWords)： 旅行商问题;置信传播;因子图;局部搜索

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金项目(62062001,61762019,61862051,61962002);; 宁夏自然科学基金项目(2020AAC03214,2020AAC03219,2019AAC03120,2019AAC03119);; 北方民族大学重大专项资助项目(ZDZX201901)

作者(Author): 程亚南,王晓峰,刘凇佐,刘子琳

DOI: 10.13705/j.issn.1671-6841.2021293

参考文献(References)：

• [1] GUNDUZ M,ASLAN M.DJAYA:a discrete Jaya algorithm for solving traveling salesman problem[J].Applied soft computing,2021,105:107275.
• [2] NOVELLANI S.Models and algorithms for the optimization of real-world routing and logistics problems[J].A quarterly journal of operations research,2016,14(3):331-332.
• [3] MOUSAEI A,TAGHADDOS H,TAK A N,et al.Optimized mobile crane path planning in discretized polar space[J].Journal of construction engineering and management,2021,147(5):04021036.
• [4] ZHANG Z F,MA J X,CUI X.Genetic algorithm with three-dimensional population dominance strategy for university course timetabling problem[J].International journal of grid and high performance computing,2021,13(2):56-69.
• [5] 程毕芸，鲁海燕，黄洋，等.求解TSP的自适应优秀系数粒子群优化算法[J].计算机应用，2017,37(3):750-754,781.CHENG B Y,LU H Y,HUANG Y,et al.Particle swarm optimization algorithm based on self-adaptive excellence coefficients for solving traveling salesman problem[J].Journal of computer applications,2017,37(3):750-754,781.
• [6] TIAN D P,SHI Z Z.MPSO:modified particle swarm optimization and its applications[J].Swarm and evolutionary computation,2018,41:49-68.
• [7] 陈思远，林丕源，黄沛杰.指针网络改进遗传算法求解旅行商问题[J].计算机工程与应用，2020,56(19):231-236.CHEN S Y,LIN P Y,HUANG P J.Pointer network improved genetic algorithm for solving traveling salesman problem[J].Computer engineering and applications,2020,56(19):231-236.
• [8] PARK S,SHIN J.Convergence and correctness of max-product belief propagation for linear programming[J].SIAM journal on discrete mathematics,2017,31(3):2228-2246.
• [9] 张丹丹，王晓峰，冯琬晶，等.一种求解0-1背包问题的置信传播算法[J].郑州大学学报(理学版),2021,53(1):29-34.ZHANG D D,WANG X F,FENG W J,et al.A belief propagation algorithm for 0-1 knapsack problem[J].Journal of Zhengzhou university (natural science edition),2021,53(1):29-34.
• [10] 左逢源，王晓峰，任雪娇，等.求解网络最大流问题的信念传播算法[J].计算机工程与设计，2021,42(5):1346-1352.ZUO F Y,WANG X F,REN X J,et al.Belief algorithm propagation for network maximum flow problem[J].Computer engineering and design,2021,42(5):1346-1352.
• [11] 王辛，王晓峰，许道云，等.一种求解双目标最小生成树的警示传播算法[J].中国科学：信息科学，2020,50(10):1501-1510.WANG X,WANG X F,XU D Y,et al.A warning propagation algorithm to solve the double-objective minimum spanning tree[J].Scientia sinica (informationis),2020,50(10):1501-1510.
• [12] WANG X M,CAO W L,LI J,et al.Improved min-sum algorithm based on density evolution for low-density parity check codes[J].IET communications,2017,11(10):1582-1586.
• [13] RAVANBAKHSH S,RABBANY R,GREINER R.Augmentative message passing for traveling salesman problem and graph partitioning[J].Advances in neural information processing systems,2014,27:289-297.
• [14] CHO I,PARK S,PARK S,et al.Practical message-passing framework for large-scale combinatorial optimization[C]//Proceedings of the IEEE International Conference on Big Data.Piscataway:IEEE Press,2015:24-31.
• [15] 袁汪凰，游晓明，刘升，等.求解TSP问题的自适应模拟退火蚁群算法[J].计算机应用与软件，2018,35(2):261-266.YUAN W H,YOU X M,LIU S,et al.Adaptive simulated annealing ant colony algorithm for solving TSP problem[J].Computer applications and software,2018,35(2):261-266.
• [16] 尚宝平，焦建强，裴杰，等.一种求解TSP问题的多策略改进蚁群算法[J].数学的实践与认识，2019,49(2):215-224.SHANG B P,JIAO J Q,PEI J,et al.Research on an improved multi-strategy ant colony algorithm for TSP problem[J].Mathematics in practice and theory,2019,49(2):215-224.
• [17] 吴虎胜，张凤鸣，李浩，等.求解TSP问题的离散狼群算法[J].控制与决策，2015,30(10):1861-1867.WU H S,ZHANG F M,LI H,et al.Discrete wolf pack algorithm for traveling salesman problem[J].Control and decision,2015,30(10):1861-1867.
• [18] 张瑾，毕国通，李丽丽.一种求解TSP问题的离散蝙蝠算法[J].计算机工程与科学，2018,40(11):2085-2091.ZHANG J,BI G T,LI L L.A discrete bat algorithm for the traveling salesman problem[J].Computer engineering & science,2018,40(11):2085-2091.
• [19] 林子彬，蔡延光.求解TSP的变邻域量子蝙蝠算法[J].电子世界，2020(9):50-51.LIN Z B,CAI Y G.Variable neighborhood quantum bat algorithm for TSP [J].Electronics world,2020(9):50-51.