关于最小分散布线问题的np -硬度

Q4 Decision Sciences

Pesquisa Operacional Pub Date : 2023-01-01 DOI:10.1590/0101-7438.2023.043.00270974

Guilherme Dhein, Marcelo Serrano Zanetti, Olinto César Bassi de Araújo

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引用次数: 0

摘要

在最小分散路径问题中，为了减少车辆的分散，必须由具有定义轨迹的行程服务于一组顶点。旅行必须相互关联，并在车辆之间施加空间和时间同步，由目标函数中使用的原始分散度量来量化。本文证明了用MDRP求解器可以找到欧氏旅行商问题的解。描述了一种在多项式时间内将欧氏旅行商问题实例简化为最小离散路由问题实例的方法，证明了最后一种方法是np困难的。

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ON THE NP-HARDNESS OF THE MINIMUM DISPERSION ROUTING PROBLEM

In the Minimum Dispersion Routing Problem, a set of vertices must be served by tours with trajectories defined in order to reduce the dispersion of vehicles. Tours must be related to each other and impose a spatial and temporal synchronization among vehicles, quantified by an original dispersion metric used in an objective function to be minimized. In this paper, we demonstrate that Euclidean Traveling Salesman Problem solutions can be found by MDRP solvers. We describe a method to reduce Euclidean Traveling Salesman Problem instances to Minimum Dispersion Routing Problem instances in polynomial time, proving that the last one is NP-Hard.

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来源期刊

Pesquisa Operacional Decision Sciences-Management Science and Operations Research

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

8 weeks

期刊介绍： Pesquisa Operacional is published each semester by the Sociedade Brasileira de Pesquisa Operacional - SOBRAPO, performing one volume per year, and is distributed free of charge to its associates. The abbreviated title of the journal is Pesq. Oper., which should be used in bibliographies, footnotes and bibliographical references and strips.