The orienteering problem is a well-studied and fundamental problem in transportation science. In the problem, we are given a graph with prizes on the nodes and lengths on the edges, together with a budget on the overall tour length. The goal is to find a tour that respects the length budget and maximizes the collected prizes. In this work, we introduce the orienteering interdiction game, in which a competitor (the leader) tries to minimize the total prize that the follower can collect within a feasible tour. To this end, the leader interdicts some of the nodes so that the follower cannot collect their prizes. The resulting interdiction game is formulated as a bilevel optimization problem, and a single-level reformulation is obtained based on interdiction cuts. A branch-and-cut algorithm with several enhancements, including the use of a solution pool, a cut pool and a heuristic method for the follower's problem, is proposed. In addition to this exact approach, a genetic algorithm is developed to obtain high-quality solutions in a short computing time. In a computational study based on instances from the literature for the orienteering problem, the usefulness of the proposed algorithmic components is assessed, and the branch-and-cut and genetic algorithms are compared in terms of solution time and quality.

翻译：定向越野问题是交通科学中一个经过深入研究的基础性问题。在该问题中，我们给定一个图结构，其中节点带有奖励值、边带有长度值，同时给定路径总长度的预算约束。目标是找到一条满足长度预算限制且能最大化收集奖励的路径。本文提出了定向越野拦截博弈，其中竞争者（领导者）试图最小化跟随者在可行路径内能收集的总奖励。为此，领导者通过拦截部分节点来阻止跟随者获取其奖励值。由此形成的拦截博弈被构建为双层优化问题，并基于拦截割获得其单层重构形式。本文提出了一种包含多项增强策略的分支割平面算法，包括使用解池、割池以及针对跟随者问题的启发式方法。除精确算法外，还开发了遗传算法以在较短计算时间内获得高质量解。通过对文献中定向越野问题算例的计算研究，评估了所提算法组件的有效性，并从求解时间和解质量两方面比较了分支割平面算法与遗传算法的性能。