标题： 一种求解树型拓扑下双层定价与枢纽选址问题的新型协同进化算法 显示英文标题

标题： A Novel Co-Evolutionary Algorithm for Solving a Bilevel Pricing and Hubs Location Problem under a Tree Topology

摘要： 本文介绍了带价格的双层树状枢纽定位问题（BTHLPwP）。 BTHLPwP 是一个多分配枢纽定位问题，在该问题中，除了确定树状枢纽骨干网络的节点和链接外，还需要设定使用该网络的价格。 我们假设在这个问题中有两种不同类型的代理做出决策。 一方面，一个代理（领导者）决定枢纽骨干网络的结构并设定使用该网络的价格。 另一方面，另一个代理（追随者）决定对该网络的最佳使用方式。 领导者的目标是最小化其利润，而追随者则旨在最小化使用该网络运输其商品所发生的成本。 我们提出了该问题的一个双层优化公式，随后进行了等价的单层重新表述。 然后，我们提出了一种新的协同进化算法（Co-EA）来解决三个为适应我们的问题而改编的著名数据集实例。 提出的Co-EA的主要新颖之处在于协同进化的种群的考虑方式。 传统上，一个种群专注于领导者的解决方案，另一个种群则关注追随者的解决方案，而在我们的方法中，每个种群都与领导者的决策变量的一个子集相关联。 因此，对于领导者做出的具体决策，可以获得追随者的最佳反应，从而产生双层可行解。 然后，我们分析了使用提出的Co-EA进行广泛计算实验所获得的结果。 显示英文摘要

摘要： This paper introduces the Bilevel Tree-of-Hubs Location Problem with Prices (BTHLPwP). The BTHLPwP is a multiple-allocation hub location problem in which, in addition to determining the nodes and links of a tree-shaped hub backbone network, the prices for using this network must also be set. We assume that two different types of agents make decisions in this problem. On the one hand, one agent (the leader) determines the structure and sets the prices for using the hub backbone network. On the other hand, the other agent (follower) decides on the optimal usage of the network. The leader seeks to maximize its profit, while the follower aims to minimize the costs incurred for using the network to ship their commodities. We present a bilevel optimization formulation for this problem, followed by an equivalent single-level reformulation. Then, we propose a novel Co-Evolutionary Algorithm (Co-EA) to solve three well-known datasets of instances adapted for our problem. The main novelty of the proposed Co-EA lies in the way the co-evolving populations are considered. While traditionally one population focuses on the leader's solutions and the other on the follower's, in our approach, each population is associated with a subset of the leader's decision variables. Consequently, the follower's optimal reaction is obtained for a specific decision made by the leader, resulting in bilevel feasible solutions. We then analyze the results obtained from extensive computational experimentation using the proposed Co-EA.