[2407.02959] Competing for the most profitable tour: The orienteering interdiction game
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Mathematics > Optimization and Control

arXiv:2407.02959 (math)
[Submitted on 3 Jul 2024]

Title:Competing for the most profitable tour: The orienteering interdiction game

Authors:Eduardo Álvarez-Miranda, Markus Sinnl, Kübra Tanınmış
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Abstract: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.
Subjects: Optimization and Control (math.OC); Discrete Mathematics (cs.DM)
MSC classes: 90B06, 90C10, 90C57
Cite as: arXiv:2407.02959 [math.OC]
  (or arXiv:2407.02959v1 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2407.02959

Submission history

From: Kübra Tanınmış [view email]
[v1] Wed, 3 Jul 2024 09:52:30 UTC (138 KB)
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