约束最短路径漫游问题的整数线性规划模型

Q2 Mathematics
Rafael Castro de Andrade, Rommel Dias Saraiva
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引用次数: 17

摘要

设D = (V, A)是一个有向图,有顶点集V和圆弧集A,设每个圆弧(i, j)∈A,其中i, j∈V与一个非负代价相关联。约束最短路径漫游问题(constrained shortest path tour problem,简称CSPTP)是NP-Hard问题,它包括在两个不同的顶点s∈V和t∈V之间找到一条最短路径,使得该路径不包含重复的弧线,并且必须按此顺序访问顶点不相交子集T1,…,TN的序列。在这项工作中,我们将CSPTP表述为整数线性规划(ILP)模型,并给出了该问题的有效不等式。在文献中的基准数据集上进行的计算实验表明,我们的ILP模型始终优于现有的CSPTP精确算法,并在大多数实例中找到最优解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An integer linear programming model for the constrained shortest path tour problem

Let D = (V, A) be a directed graph with set of vertices V and set of arcs A, and let each arc (i, j) ∈ A, with i, jV, be associated with a non-negative cost. The constrained shortest path tour problem (CSPTP) is NP-Hard and consists in finding a shortest path between two distinct vertices sV and tV such that the path does not include repeated arcs and must visit a sequence of vertex disjoint subsets T1, …, TN in this order. In this work, we formulate the CSPTP as an integer linear programming (ILP) model and present valid inequalities for the problem. Computational experiments performed on benchmark data sets from the literature show that our ILP model consistently outperforms existing exact algorithms for the CSPTP and finds optimal solutions for most instances.

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来源期刊
Electronic Notes in Discrete Mathematics
Electronic Notes in Discrete Mathematics Mathematics-Discrete Mathematics and Combinatorics
CiteScore
1.30
自引率
0.00%
发文量
0
期刊介绍: Electronic Notes in Discrete Mathematics is a venue for the rapid electronic publication of the proceedings of conferences, of lecture notes, monographs and other similar material for which quick publication is appropriate. Organizers of conferences whose proceedings appear in Electronic Notes in Discrete Mathematics, and authors of other material appearing as a volume in the series are allowed to make hard copies of the relevant volume for limited distribution. For example, conference proceedings may be distributed to participants at the meeting, and lecture notes can be distributed to those taking a course based on the material in the volume.
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