European Journal of Operational Research ( IF 6.4 ) Pub Date : 2021-05-06 , DOI: 10.1016/j.ejor.2021.04.055 Di H. Nguyen , J. Cole Smith
We study a shortest-path interdiction problem in which the interdictor acts first to lengthen a subset of arcs, and an evader acts second to select a shortest path across the network. In this problem, the cost for an evader’s arc consists of a base cost if the arc is not interdicted, plus an additional cost that is incurred if the arc is interdicted. The interdictor is not aware of the base costs when the interdiction action is taken, but does know that the base cost values are uniformly distributed within given (arc-specific) intervals. The evader, on the other hand, observes the exact value of the base costs, plus the additional costs due to interdiction actions. The interdictor’s problem is thus to maximize the expected minimum cost attainable by the evader. We provide a partitioning algorithm for computing an exact optimal solution to this problem, leveraging bounds gleaned from Jensen’s inequality as proposed in an earlier study on a maximum-flow interdiction problem. We also provide several algorithmic strategies for accelerating the convergence of the algorithm and demonstrate their effectiveness on randomly generated instances.
中文翻译:
具有非对称成本不确定性的网络拦截
我们研究了一个最短路径拦截问题,其中拦截器首先采取行动来延长弧子集,然后逃避者采取行动选择跨网络的最短路径。在这个问题中,躲避者的弧线的成本包括如果弧线未被阻止的基本成本,加上弧线被阻止时产生的额外成本。拦截器在执行拦截操作时不知道基本成本,但知道基本成本值在给定(特定于弧的)间隔内均匀分布。另一方面,逃避者观察到基本成本的确切值,加上由于拦截行动而产生的额外成本。因此,阻止者的问题是最大化逃避者可获得的预期最小成本。我们提供了一种分区算法,用于计算该问题的精确最优解,利用从 Jensen 不等式收集的边界,如先前关于最大流量拦截问题的研究中提出的那样。我们还提供了几种加速算法收敛的算法策略,并证明了它们在随机生成的实例上的有效性。