Abstract
AbstractWe consider a generalization of the selective traveling salesman problem (STSP) in which the benefit of visiting a location changes over time. This new problem, called the selective travelling salesman problem with time-dependent profits (STSP-TDP), is defined on a graph with time-dependent profits associated with the vertices, and consists of determining a circuit of maximal total profit. In the STSP-TDP the tour length must not exceed a maximum value, and its starting and ending times must both lie within a prespecified planning horizon. This problem arises in planning tourist itineraries, mailbox collection, military surveillance, and water sampling, where the traveler accumulates different profits upon visiting the locations throughout the day. We focus on analyzing several variants of the problem depending on the shape of the time-dependent profit function. If this function is not monotonic, it may be worth visiting a site more than once. We propose formulations for the single-visit case and for when multiple visits are allowed, in which case the problem reduces to an STSP, which is adapted to be solved as a longest path problem. These formulations are then solved for piecewise-linear profit functions using a general-purpose solver, and tested on several artificially created instances and on four TSPLib instances involving up to 535 vertices. A detailed analysis of the problem and the solution is performed.
Publisher
Springer Science and Business Media LLC
Subject
Discrete Mathematics and Combinatorics,Statistics and Probability,Management Science and Operations Research,Information Systems and Management,Modeling and Simulation
Reference25 articles.
1. Afsar H, Labadie N (2013) Team orienteering problem with decreasing profits. Electronic Notes in Discrete Mathematics 41:285–293
2. Archetti C, Speranza MG, Vigo D (2014) Vehicle routing problems with profits. In: Toth P, Vigo D (eds) Vehicle routing: problems, methods, and applications, monographs on discrete mathematics and applications, vol 18. MOS-SIAM Series on Optimization, Philadelphia, pp 87–116
3. Bruck BP, Iori M (2017) Non-elementary formulations for single vehicle routing problems with pickups and deliveries. Operat Res 65(6):1597–614
4. Bruglieri M (2020) The parking warden tour problem. Networks 76:539–554
5. da Silva AA, Morabito R, Pureza V (2018) Optimization approaches to support the planning and analysis of travel itineraries. Expert Syst Appl 112:321–330
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