A dual algorithm for the constrained shortest path problem

IF 1.3 4区计算机科学 Q4 COMPUTER SCIENCE, HARDWARE & ARCHITECTURE Networks Pub Date : 1980-12-01 DOI:10.1002/net.3230100403

G. Handler, I. Zang

引用次数: 484

Abstract

In this paper we develop a Lagrangian relaxation algorithm for the problem of finding a shortest path between two nodes in a network, subject to a knapsack-type constraint. For example, we may wish to find a minimum cost route subject to a total time constraint in a multimode transportation network. Furthermore, the problem, which is shown to be at least as hard as NP-complete problems, is generic to a class of problems that arise in the solution of integer linear programs and discrete state/stage deterministic dynamic programs. One approach to solving the problem is to utilize a kth shortest path algorithm, terminating with the first path that satisfies the constraint. This approach is impractical when the terminal value of k is large. Using Lagrangian relaxation we propose a method that is designed to reduce this value of k. Computational results indicate orders of magnitude savings when the approach is applied to large networks.

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约束最短路径问题的对偶算法

在本文中，我们开发了一个拉格朗日松弛算法，用于在背包型约束下寻找网络中两个节点之间的最短路径问题。例如，我们可能希望在多模式运输网络中找到受总时间约束的最低成本路线。此外，该问题至少与np完全问题一样难，它是一类在求解整数线性规划和离散状态/阶段确定性动态规划时出现的问题的一般问题。解决这个问题的一种方法是利用第k条最短路径算法，以满足约束的第一条路径结束。当k的终端值较大时，这种方法是不切实际的。利用拉格朗日松弛，我们提出了一种旨在降低k值的方法。计算结果表明，当该方法应用于大型网络时，节省了数量级。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Networks 工程技术-计算机：硬件

CiteScore

4.40

自引率

9.50%

发文量

审稿时长

12 months

期刊介绍： Network problems are pervasive in our modern technological society, as witnessed by our reliance on physical networks that provide power, communication, and transportation. As well, a number of processes can be modeled using logical networks, as in the scheduling of interdependent tasks, the dating of archaeological artifacts, or the compilation of subroutines comprising a large computer program. Networks provide a common framework for posing and studying problems that often have wider applicability than their originating context. The goal of this journal is to provide a central forum for the distribution of timely information about network problems, their design and mathematical analysis, as well as efficient algorithms for carrying out optimization on networks. The nonstandard modeling of diverse processes using networks and network concepts is also of interest. Consequently, the disciplines that are useful in studying networks are varied, including applied mathematics, operations research, computer science, discrete mathematics, and economics. Networks publishes material on the analytic modeling of problems using networks, the mathematical analysis of network problems, the design of computationally eﬃcient network algorithms, and innovative case studies of successful network applications. We do not typically publish works that fall in the realm of pure graph theory (without signiﬁcant algorithmic and modeling contributions) or papers that deal with engineering aspects of network design. Since the audience for this journal is then necessarily broad, articles that impact multiple application areas or that creatively use new or existing methodologies are especially appropriate. We seek to publish original, well-written research papers that make a substantive contribution to the knowledge base. In addition, tutorial and survey articles are welcomed. All manuscripts are carefully refereed.