马杨, 戴锡笠, 牟廉明. 基于分治法和分支限界法的大规模TSP算法[J]. 内江师范学院学报, 2012, (10): 20-23.
    引用本文: 马杨, 戴锡笠, 牟廉明. 基于分治法和分支限界法的大规模TSP算法[J]. 内江师范学院学报, 2012, (10): 20-23.
    MA Yang, DAI Xi-li, MOU Lian-ming. A Large-scale TSP Algorithm Based on Divide-and-Conquer Method and Branch-bounding Method[J]. Journal of Neijiang Normal University, 2012, (10): 20-23.
    Citation: MA Yang, DAI Xi-li, MOU Lian-ming. A Large-scale TSP Algorithm Based on Divide-and-Conquer Method and Branch-bounding Method[J]. Journal of Neijiang Normal University, 2012, (10): 20-23.

    基于分治法和分支限界法的大规模TSP算法

    A Large-scale TSP Algorithm Based on Divide-and-Conquer Method and Branch-bounding Method

    • 摘要: 利用分治法能够处理大规模问题但精度较低,分支限界法能够得到精确解但时间复杂度很高 的优点,设计一种有效的基于分治法和分支限界法的大规模TSP求解方法.该算法利用聚类和凸包技术将大规模问题逐层进行有效划分,直到适合分支限界法求解的最佳规模;然后用分支限界法求出每个子问题和每层子问题间的最优解,合并而得到整个问题的解.比较实验表明:该算法在求解质量、稳定性和时间效率上有明显优势.

       

      Abstract: The determination of large scale TSP problem has long become a headache in the field of mathematics. The divide-and-conquer method, though capable of handling large-scale problems, yet is criticized for its poor accuracy; branch-bounding method, although reliable in obtaining exact solution, yet is blamed for its high time complexity. By integrating the advantages of the two, a new effective method for solving large-scale TSP is designed through combination of the two methods. The newly designed algorithm, using clustering and convex hull technology to divide the large-scale problem layer by layer effectively, can eventually work out the optimal size fitting for the determination of solution through branch-bounding method and then obtain the optimal solution of each sub-problem and each layer’s sub-problems by branch-bounding method, and by merging these results, thus to get the solution of the whole problem. A comparative experiment reveals that: the new algorithm boasts its quality , stability and time efficiency in the determination of solutions.

       

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