技术笔记——车辆路线问题集划分公式定价问题的复杂性

IF 0.7 4区管理学 Q3 Engineering

Military Operations Research Pub Date : 2023-05-11 DOI:10.1287/opre.2023.2481

R. Spliet

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引用次数: 0

摘要

车辆路线定价问题是一个强NP困难问题。许多寻找各种车辆路线问题最优解的算法依赖于一子程序来解决所谓的集划分公式的定价问题。只有已知的指数时间算法才能解决这些定价问题。因此，集合划分公式通常以较弱的LP界为代价放宽，因此现在可以使用伪多项式或多项式时间算法来解决由此产生的定价问题。在“车辆路线问题集划分公式定价问题的复杂性”一文中，Remy split证明了对于许多不同的车辆路线问题，定价问题是强NP困难的。这意味着，除非P = NP，否则定价问题不存在伪多项式或多项式时间算法，这证明了松弛的普遍使用。

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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Technical Note—The Complexity of the Pricing Problem of the Set Partitioning Formulation of Vehicle Routing Problems

The pricing problem of vehicle routing problems is strongly NP hard. Many algorithms for finding optimal solutions to various vehicle routing problems rely on a subroutine to solve a so-called pricing problem of a set partitioning formulation. Only exponential time algorithms are known for these pricing problems. Therefore, the set partitioning formulation is oftentimes relaxed at the expense of weaker LP bounds, so that the resulting pricing problem can now be solved using a pseudopolynomial or polynomial time algorithm. In “The Complexity of the Pricing Problem of the Set Partitioning Formulation of Vehicle Routing Problems,” it is proven by Remy Spliet that the pricing problem is strongly NP hard for many different vehicle routing problems. This means that, unless P = NP, no pseudopolynomial or polynomial time algorithm exists for the pricing problem, justifying the common use of relaxations.

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来源期刊

Military Operations Research 管理科学-运筹学与管理科学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Military Operations Research is a peer-reviewed journal of high academic quality. The Journal publishes articles that describe operations research (OR) methodologies and theories used in key military and national security applications. Of particular interest are papers that present: Case studies showing innovative OR applications Apply OR to major policy issues Introduce interesting new problems areas Highlight education issues Document the history of military and national security OR.