嵌套Logit需求函数下的停车换乘设施选址
Park-and-Ride Facility Location Selection under Nested Logit Demand Function
摘要：
停车换乘设施是使用者可以换乘公共交通工具的停车场。通勤者可以使用P&R设施或选择开车前往目的地，个人选择行为被假定遵循logit模型。P&R设施定位问题从潜在位置中识别固定数量的P&R设施的位置，使得P&R设施的用户数量最大化。这个问题以前已经正式下一个多项式logit需求函数。然而，由于MNL模型对不相关备选方案的独立性施加了很强的条件，因此无法准确地描述现实世界中的P&R设施定位问题。考虑到个体选择行为的嵌套结构，本文将MNL模型推广为嵌套Logit模型，并发展了两种求解NL需求函数下大规模P&R设施定位问题的计算方法--邻域搜索法和随机舍入法.邻域搜索法首先找到一个可行解，然后沿着多面体的一条边将该可行解改进为下一个可行解，该多面体的顶点是可行解。邻域搜索法被随机化以创建自适应随机化舍入过程。通过1,000个中等规模的算例验证了该计算方法能够快速求解NL需求函数下的非线性最优化问题，得到最优解。具体而言，这些方法被验证为求解MNL模型以比文献中描述的混合整数线性规划公式快10，000倍的精确最优性。我们进行了额外的计算实验，以评估我们的计算方法在各种大规模实例上的性能。我们的计算分析也阐明了MNL和NL模型之间的差异。
英文摘要：
Park-and-ride facilities are car parks where users can transfer to public transportation. Commuters can use P&R facilities or choose to travel by car to their destinations, and individual choice behavior is assumed to follow a logit model. The P&R facility location problem identifies locations for a fixed number of P&R facilities from among potential locations such that the number of users of the P&R facilities is maximized. This problem has previously been formalized under a multinomial logit demand function. However, as it imposes the strong condition of the independence of irrelevant alternatives, the MNL model is unable to represent the real-world P&R facility location problem exactly. Respecting the nested structure of individual choice behavior, we generalize the MNL model to a nested logit model and develop two computational methods -- neighborhood search and randomized rounding -- to solve large-scale P&R facility location problems under the NL demand function. The neighborhood search method first finds one feasible solution and then improves the feasible solution to the next one along an edge of the polyhedron whose vertices are the feasible solutions. The neighborhood search method is randomized to create an adaptive randomized rounding procedure. Computational experiments verified that the computational methods were able to solve the nonlinear optimization problem under the NL demand function on 1,000 medium-scale instances to exact optimality rapidly. Specifically, the methods were verified to solve the MNL model to exact optimality 10,000 times faster than the mixed integer linear programming formulation described in the literature. We performed additional computational experiments to assess the performance of our computational methods on a variety of large-scale instances. Our computational analysis also elucidates the difference between the MNL and NL models.
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