具有互联设施的连续最大覆盖定位问题
Continuous maximal covering location problems with interconnected facilities
摘要：
在本文中，我们分析了一个连续的版本的最大覆盖定位问题，其中的设施被要求通过一个图结构，其中两个设施被允许连接，如果给定的距离是不超过互连。我们提供了一个数学规划框架的问题和不同的解决策略。首先，我们提出了一个混合整数非线性规划公式，并推导出问题的性质，使我们能够项目的连续变量，避免非线性约束，从而在一个等价的纯整数规划制定。由于在整数规划制定的约束条件的数量是大的，在一般情况下，难以处理的约束条件，我们提出了两个分支和切割的方法，避免了完整的枚举的限制，从而更有效的程序。我们报告了一个广泛的电池的计算实验比较不同的方法的性能的结果。
英文摘要：
In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given distance is not exceed. We provide a mathematical programming framework for the problem and different resolution strategies. First, we propose a Mixed Integer Non Linear Programming formulation, and derive properties of the problem that allow us to project the continuous variables out avoiding the nonlinear constraints, resulting in an equivalent pure integer programming formulation. Since the number of constraints in the integer programming formulation is large and the constraints are, in general, difficult to handle, we propose two branch-&-cut approaches that avoid the complete enumeration of the constraints resulting in more efficient procedures. We report the results of an extensive battery of computational experiments comparing the performance of the different approaches.
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