A fast metaheuristic for the travelling salesperson problem with hotel selection
The travelling salesperson problem with hotel selection (TSPHS) is a recently proposed variant of the travelling salesperson problem. Currently, the approach that finds the best solutions is a memetic algorithm. However, this approach is unsuitable for applications that require very short computation times. In this paper, a new set-partitioning formulation is presented along with a simple but powerful metaheuristic for the TSPHS. The algorithm is able to obtain very competitive results while remaining at least one order of magnitude faster than the best-performing method so far. The parameters of the metaheuristic were carefully tuned by means of an extensive statistical experiment.
KeywordsTSP Hotel Selection Metaheuristics Combinatorial Optimisation
Mathematics Subject Classification90B06 90C27 90C59
The first, second and fourth author gratefully thank the Fonds voor Wetenschappelijke Onderzoek—Vlaanderen (FWO) as well as the COMEX Project (Combinatorial optimization: metaheuristics and exact methods) for financial support.
- Applegate D, Bixby R, Chvátal V, Cook W (2007) The traveling salesman problem: a computational study. Princeton University Press, PrincetonGoogle Scholar
- Applegate D, Bixby R, Chvátal V, Cook W (2006) Concorde TSP solver. http://www.tsp.gatech.edu/concorde
- Berretta R, Cotta C, Moscato P (2011) Memetic algorithms. In: Cochran JJ, Cox LA, Keskinocak P, Kharoufeh JP, Smith JC (eds) Wiley encyclopedia of operations research and management science. Wiley, LondonGoogle Scholar
- Hansen P, Mladenović N, Brimberg J, Moreno-Pérez JA (2008) Variable neighbourhood search: methods and applications. 4OR 6(4):319–360Google Scholar
- Hansen P, Mladenović N, Brimberg J, Moreno-Pérez JA (2010) Variable neighborhood search. In: Gendreau M, Potvin J-Y (eds) Handbook of metaheuristics. Springer, Berlin, pp 61–86Google Scholar
- Letchford AN, Lodi A (2007) The traveling salesman problem: a book review. 4OR 5(4):315–317Google Scholar
- Lourenço HR, Martin OC, Stützle T (2010) Iterated local search: framework and applications. In: Gendreau M, Potvin J-Y (eds) Handbook of metaheuristics. Springer, Berlin, pp 363–397Google Scholar
- Or I (1976) Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking. Ph.D. thesis, Northwestern UniversityGoogle Scholar
- Toth P, Vigo D (eds) (2002) The vehicle routing problem, volume 9 of discrete mathematics and applications. Society for Industrial and Applied Mathematics, PhiladelphiaGoogle Scholar