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The problem of efficiently touring a theme park so as to minimize the amount of time spent in queues is an instance of the Traveling Salesman Problem with Time-Dependent Service Times (TSP-TS). In this paper, we present a mixed-integer linear programming formulation of the TSP-TS and describe a branch-and-cut algorithm based on this model. In addition, we develop a lower bound for the TSP-TS and describe two metaheuristic approaches for obtaining good quality solutions: a genetic algorithm and a tabu search algorithm. Using test instances motivated by actual theme park data, we conduct a computational study to compare the effectiveness of our algorithms.
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Elizabeth L. Bouzarth, Richard J. Forrester, Kevin R. Hutson, Rahul Isaac, James Midkiff, Danny Rivers, Leonard J. Testa, "A Comparison of Algorithms for Finding an Efficient Theme Park Tour", Journal of Applied Mathematics, vol. 2018, Article ID 2453185, 14 pages, 2018. https://doi.org/10.1155/2018/2453185