无约束旅行比武问题三次形式的多面体研究

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-11-01 DOI:10.1016/j.disopt.2022.100741

Marije R. Siemann, Matthias Walter

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引用次数: 1

摘要

我们考虑无约束旅行比赛问题，这是一个最小化球队旅行的运动时间表问题。自20年前引入以来，大多数研究都致力于建模和重新制定方法。本文通过建立整型船体的尺寸以及由模型不等式引起的面的尺寸，对三次整数规划公式进行了多面体研究。此外，我们引入了一类新的不等式，并证明了它们是面定义的。最后，我们评估了这些不等式对线性规划界的影响。

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A polyhedral study for the cubic formulation of the unconstrained traveling tournament problem

We consider the unconstrained traveling tournament problem, a sports timetabling problem that minimizes traveling of teams. Since its introduction about 20 years ago, most research was devoted to modeling and reformulation approaches. In this paper we carry out a polyhedral study for the cubic integer programming formulation by establishing the dimension of the integer hull as well as of faces induced by model inequalities. Moreover, we introduce a new class of inequalities and show that they are facet-defining. Finally, we evaluate the impact of these inequalities on the linear programming bounds.

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.