连续多设施单调序中值问题的分枝价格法
A Branch-and-Price approach for the Continuous Multifacility Monotone Ordered Median Problem
摘要：
在本文中，我们解决连续多设施单调有序中位数问题。这个问题最小化一个单调有序的加权中值函数之间的距离给定的需求点在$\mathbb{R}^d$和它的最近的设施之间的$p$选择，也在一个连续的空间。我们提出了一个新的分支和价格的过程中，这个问题，和两个mathehuristics。其中一个是基于分解的过程，另一个是基于聚合的启发式。我们给出了详细的讨论的准确配方的有效性，并指定所有的解决方案的程序的实施细节。此外，我们评估他们的表现在一个广泛的计算经验，显示了优越性的分支和价格的方法在中等规模的情况下，紧凑的制定。要处理较大的实例，建议求助于也报告了相当好的结果的数学方法。
英文摘要：
In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. This problem minimizes a monotone ordered weighted median function of the distances between given demand points in $\mathbb{R}^d$ and its closest facility among the $p$ selected, also in a continuous space. We propose a new branch-and-price procedure for this problem, and two mathehuristics. One of them is a decomposition-based procedure and the other an aggregation-based heuristic. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performance in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results.
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