固定枢纽单一分配问题的改进算法
An Improved Algorithm for Fixed-Hub Single Allocation Problem
摘要：
本文讨论了固定枢纽的单一分配问题。在这个问题中，网络由枢纽节点和终端节点组成。集线器是固定的，完全连接的;每个终端节点连接到一个单一的集线器，路由所有的流量。目标是最小化网络中路由流量的成本。在本文中，我们提出了一个基于线性规划（LP）的舍入算法。该算法基于两个想法。首先，我们通过引入一组有效性约束来修改Ernst和Krishnamoorthy（1996，1999）中引入的LP松弛公式。然后，在获得LP松弛的分数解之后，我们利用几何舍入算法获得积分解。我们表明，通过将有效性约束，加强LP往往提供更严格的上限比以前的方法多一点的计算工作量，得到的解决方案往往有一个更小的差距与最优解。我们还制定了一个强大的版本的FHSAP，并表明它可以防止数据的不确定性，成本很小。
英文摘要：
This paper discusses the fixed-hub single allocation problem (FHSAP). In this problem, a network consists of hub nodes and terminal nodes. Hubs are fixed and fully connected; each terminal node is connected to a single hub which routes all its traffic. The goal is to minimize the cost of routing the traffic in the network. In this paper, we propose a linear programming (LP)-based rounding algorithm. The algorithm is based on two ideas. First, we modify the LP relaxation formulation introduced in Ernst and Krishnamoorthy (1996, 1999) by incorporating a set of validity constraints. Then, after obtaining a fractional solution to the LP relaxation, we make use of a geometric rounding algorithm to obtain an integral solution. We show that by incorporating the validity constraints, the strengthened LP often provides much tighter upper bounds than the previous methods with a little more computational effort, and the solution obtained often has a much smaller gap with the optimal solution. We also formulate a robust version of the FHSAP and show that it can guard against data uncertainty with little cost.
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