随机效用与路径约束下的竞争性设施选址
Competitive Facility Location under Random Utilities and Routing Constraints
AI总结：
针对带路径约束的随机效用竞争性设施选址难题，提出基于三类有效割的两种精确算法及局部搜索元启发式算法，实验验证其在解质量与计算效率上均优于基线方法。
摘要：
本文研究竞争市场环境下的设施选址问题，其中客户需求由随机效用选择模型预测。与以往主要关注选址数量基数约束等简单约束的研究不同，我们引入了路径约束：要求所选选址必须能形成一条访问所有选定地点的游览路线，且该路线的总长度不超过指定上限。这类路径约束在多种现实场景中具有关键应用价值。\n由于采用随机效用，该问题的目标函数为非线性，再加上复杂的路径约束，使得问题的计算难度很高。为解决这一问题，我们探究了三类有效割：用于处理非线性目标函数的外逼近割与子模割，以及用于处理复杂路径约束的子回路消除割。基于这些割，我们提出了两种精确求解方法：嵌套割平面法和嵌套分支割算法，通过两层嵌套循环将这些有效割迭代添加到主问题中。我们还证明了嵌套割平面法在有限次迭代后总能收敛到最优解。此外，我们开发了一种适用于大规模算例的基于局部搜索的元启发式算法，并分析了其相较于精确方法的优缺点。我们在不同规模的问题算例上开展了大量实验，结果表明，与其他基线方法相比，我们的方法在解的质量和计算时间方面均表现更优。
英文摘要：
In this paper, we study a facility location problem within a competitive market context, where customer demand is predicted by a random utility choice model. Unlike prior research, which primarily focuses on simple constraints such as a cardinality constraint on the number of selected locations, we introduce routing constraints that necessitate the selection of locations in a manner that guarantees the existence of a tour visiting all chosen locations while adhering to a specified tour length upper bound. Such routing constraints find crucial applications in various real-world scenarios. The problem at hand features a non-linear objective function, resulting from the utilization of random utilities, together with complex routing constraints, making it computationally challenging. To tackle this problem, we explore three types of valid cuts, namely, outer-approximation and submodular cuts to handle the nonlinear objective function, as well as sub-tour elimination cuts to address the complex routing constraints. These lead to the development of two exact solution methods: a nested cutting plane and nested branch-and-cut algorithms, where these valid cuts are iteratively added to a master problem through two nested loops. We also prove that our nested cutting plane method always converges to optimality after a finite number of iterations. Furthermore, we develop a local search-based metaheuristic tailored for solving large-scale instances and show its pros and cons compared to exact methods. Extensive experiments are conducted on problem instances of varying sizes, demonstrating that our approach excels in terms of solution quality and computation time when compared to other baseline approaches.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
