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Generating optimal and near-optimal solutions to facility location problems
Environment and Planning B: Urban Analytics and City Science ( IF 3.511 ) Pub Date : 2020-06-10 , DOI: 10.1177/2399808320930241
Richard L Church 1 , Carlos A Baez 1
Affiliation  

There is a decided bent toward finding an optimal solution to a given facility location problem instance, even when there may be multiple optima or competitive near-optimal solutions. Identifying alternate solutions is often ignored in model application, even when such solutions may be preferred if they were known to exist. In this paper we discuss why generating close-to-optimal alternatives should be the preferred approach in solving spatial optimization problems, especially when it involves an application. There exists a classic approach for finding all alternate optima. This approach can be easily expanded to identify all near-optimal solutions to any discrete location model. We demonstrate the use of this technique for two classic problems: the p-median problem and the maximal covering location problem. Unfortunately, we have found that it can be mired in computational issues, even when problems are relatively small. We propose a new approach that overcomes some of these computational issues in finding alternate optima and near-optimal solutions.

中文翻译:

为设施选址问题生成最优和接近最优的解决方案

即使可能存在多个最优解或有竞争性的接近最优解,也有一个决定性的倾向,即为给定的设施位置问题实例寻找最优解。识别替代解决方案在模型应用中经常被忽略,即使这些解决方案在已知存在的情况下可能是首选。在本文中,我们讨论了为什么生成接近最优的替代方案应该是解决空间优化问题的首选方法,尤其是当它涉及应用程序时。有一种经典的方法可以找到所有替代最优值。这种方法可以很容易地扩展到识别任何离散位置模型的所有接近最优的解决方案。我们演示了这种技术在两个经典问题中的使用:p 中值问题和最大覆盖位置问题。很遗憾,我们发现它可能陷入计算问题,即使问题相对较小。我们提出了一种新方法,可以在寻找替代最优解和接近最优解时克服其中的一些计算问题。
更新日期:2020-06-10
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