图上双目标中位数选址问题的一致路径选择
Consistent Path Selection for Bi-objective Median Location Problems on Graphs
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中文总结 AI 辅助
本文针对图上双目标中位数选址问题，提出一致路径概念，将选址与路径决策耦合，设计算法计算含一致路径的最小完全有效解集合，并在德国伍珀塔尔市实例中验证结果。
中文摘要 AI 辅助
我们考虑图上的单设施中位数选址问题，其中每条边关联两个相互冲突的成本值。例如，假设决策者要选址一个新设施，如使用自行车配送的披萨店，两个目标函数可为总配送时间与总左转次数（后者风险极高）。路径选择取决于决策者偏好，通常客户与新设施间不存在唯一最优路径。本文将选址决策与路径决策作为耦合问题研究，即同时寻找最优设施位置与一致配送路径。我们引入一致路径概念：假设从设施到需求节点的路径选择隐含特定偏好，若解的所有路径的偏好互不矛盾，则这些路径是一致的。我们提出一种算法，可计算含一致路径选择的最小完全有效解集合，并以德国伍珀塔尔市的实例说明结果。
英文摘要
We consider single-facility median location problems on graphs where two conflicting cost values are associated with the edges. As an example, suppose that a decision maker wants to locate one new facility, e. g., a pizza delivery place, which uses bicycles for delivery. The two objective functions could then be the total traveling time and the total number of left turns, as the latter are very risky. Path choices then depend on the preferences of the decision maker, and in general, there may not exist a unique optimal path between a customer and a new facility location. In this paper, we consider the location decision and the routing decision in a coupled problem, i. e., we search for an optimal location and for consistent delivery paths simultaneously. We introduce the concept of consistent paths, where we assume that the choice of a path from the facility to a demand node implies certain preferences. All paths of a solution are consistent if the preferences of all paths do not contradict each other. We present an algorithm that computes a minimum complete set of efficient solutions with consistent path choices and illustrate the results at example instances in the city of Wuppertal in Germany.
