Abstract
Our human society is experiencing complex problems nowadays, which require large amounts of computing resources, fast algorithms and efficient implementations. These real-world problems generate new instances for the classical, academic problems as well as new data collections that can be used for assessing the available solving packages. This paper focuses on the Traveling Salesman Problem, which is one of the most studied combinatorial optimization problems, with many variants and broad applications. In order to allow a smooth integration with the current Geographic Information Systems (GIS) technologies, the instances described in this work are specified by geographic coordinates, and they use the orthodromic distance. A sequence of similar instances is defined, and the characteristics of the state-of-the-art exact solver results on these instances are presented and discussed.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Gendreau, M., Hertz, A., Laporte, G.: New insertion and postoptimization procedures for the traveling salesman problem. Oper. Res. 40(6), 1086–1094 (1992)
Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco (1979)
Shafarevich, I.R., Remizov, A.O.: Linear Algebra and Geometry. Springer, Berlin (2013)
Toth, P., Vigo, D.: An overview of vehicle routing problems. In: The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia, PA (2001)
Papadimitrou, C.H., Steiglitz, K.: Some complexity results for the traveling salesman problem. In: STOC’76 Proceedings of the Eighth Annual ACM Symposium on Theory of Computing, pp. 1–9 (1976)
Arora, S.: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM 45(5), 753–782 (1998)
Karp, R.M.: Reducibility among combinatorial problems. In: Miller, R.E., Thatcher, J.W. (eds.) Complexity of Computer Computations, Advances in Computer Research, pp. 85–103. Plenum Press, (1972)
Papadimitrou, C.H.: Euclidean TSP is NP-complete. Theoret. Comput. Sci. 4, 237–244 (1977)
Applegate, D.L., Bixby, R.E., Chvatal, V., Cook, W.J.: The Traveling Salesman Problem: A Computational Study. Princeton University Press, Princeton, NJ, USA (2011)
Jaillet, P.: Probabilistic Traveling Salesman Problems. PhD Thesis, MIT, Cambridge, MA, USA (1985)
Henchiri, A., Ballalouna, M., Khansaji, W.: Probabilistic traveling salesman problem: a survey. In: Position Paper of the 2014 Federated Conference on Computer Science and Information Systems, pp. 55–60 (2014)
Jaillet, P.: A priori solution of a traveling salesman Problem in which a random subset of the customers are visited. Oper. Res. 36, 929–936 (1988)
Berman, O., Simchi-Levi, D.: Finding the optimal a priori tour and location of a traveling salesman with nonhomogenous customers. Transp. Sci. 22(2), 148–154 (1988)
Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. Eur. J. Oper. Res. 59, 231–247 (1992)
Agatz, N., Bouman, P., Scmidt, M.: Optimization approaches for the traveling salesman problem with drone. Technical Report, ERIM report series research in management (2015). http://repub.eur.nl/pub/78472
Popper, B.: UPS researching delivery drones that could compete with Amazon’s Prime Air (2013). http://www.theverge.com/2013/12/3/5169878/ups-is-researching-its-own-delivery-drones-to-compete-with-amazons
Current, J.R., Schilling, D.A.: The covering salesman problem. Transp. Sci. 23(3), 208–213 (1989)
Caric, T., Gold, H. (eds.): Vehicle Routing Problem. I-Tech Education and Publishing KG, Vienna (2008)
Derigs, U., Pullmann, M., Vogel, U.: Truck and trailer routing—problems, heuristics and computational experience. Comput. Oper. Res. 40(2), 536–546 (2013)
Murray, C.C., Chu, A.G.: The flying sidekick traveling salesman problem: optimization of drone-assisted parcel delivery. Transp. Res. Part C: Emerg. Technol. 54, 86–109 (2015)
Hernández-Pérez, H., Salazar-González, J.J.: Heuristics for the one-commodity pickup-and-delivery traveling salesman problem. Transp. Sci. 38(2), 245–255 (2004)
Fischeti, M., Lodi, A.: Local branching. Math. Program. 98, 23–47 (2003)
Berbeglia, G., Cordeau, J.-F., Laporte, G.: Dynamic pickup and delivery problems. Eur. J. Oper. Res. 202(1), 8–15 (2010)
Reinelt, G.: The Traveling Salesman: Computational Solutions for TSP Applications. Lecture Notes in Computer Science. Springer, Berlin (1994)
Dantzig, G.B., Fulkerson, D.R., Johnson, S.M.: Solutions of a large-scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)
Laporte, G., Louveaux, F., Mercure, H.: A priori optimization of the probabilistic traveling salesman problem. Oper. Res. 42(3), 543–549 (1994)
Carpaneto, G., Toth, P.: Some new branching and bounding criteria for the asymmetric travelling salesman problem. Manage. Sci. 26, 736–743 (1980)
Balas, E., Christofides, N.: A restricted lagrangean approach to the traveling salesman problem. Math. Program. 21, 19–46 (1981)
Miller, D.L., Pekny, J.F.: Exact solution of large asymmetric traveling salesman problems. Science 251, 754–761 (1991)
Schrijver, A.: Combinatorial optimization: polyhedra and efficiency, vol. 1. Springer, Berlin (2003)
Padberg, M., Rinaldi, G.: A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev. 33(1), 60–100 (1991)
Mitchell, J.E.: Branch-and-cut algorithms for combinatorial optimization problems. Handbook of Applied Optimization. Oxford University Press, Oxford (2000)
Jünger, M., Reinelt, G., Thienel, S.: Provably good solutions for the traveling salesman problem. Zeitschrift für Operations Research 22, 83–95 (1998)
Gutin, G., Punnen, A.P. (eds.): The Traveling Salesman Problem and Its Variations. Springer, New York (2007)
OR/MS Today magazine, Institute for Operations Research and the Management Sciences: 2015 Linear Programming Software Survey. http://www.orms-today.org/surveys/LP/LP-survey.html
COIN-OR resources. http://www.coin-or.org/projects/, http://www.coin-or.org/resources.html
COIN-OR Project. http://www.coin-or.org/
Galea, F., Le Cun, B.: Bob++: a Framework for exact combinatorial optimization methods on parallel machines. In: Proceedings of the 21st European Conference on Modelling and Simulation (2007)
ABACUS system. http://www.informatik.uni-koeln.de/abacus/index.html
Applegate, D.L., Bixby, R.E., Chvatal, V., Cook, W.J.: TSP cuts which do not conform to the template paradigm. Computational Combinatorial Optimization. Springer, Berlin (2001)
Concorde TSP solver. http://www.math.uwaterloo.ca/tsp/concorde/
Lin, S.: Computer solutions of the traveling salesman problem. Bell Syst. Tech. J. 44, 2245–2269 (1965)
Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling salesman problem. Oper. Res. 21, 972–989 (1973)
Or, I.: Traveling salesman-type combinatorial problems and their relation to the logistics of regional blood banking, PhD thesis, North-Western University, Evanston, IL (1976)
Croes, G.A.: A method for solving large scale symmetric traveling salesman problems to optimality. Oper. Res. 6, 791–812 (1958)
Rosenkrantz, D.J., Stearns, R.E., Philip, I., Lewis, M.: An analysis of several heuristics for the traveling salesman problem. SIAM J. Comput. 6(3), 563–581 (1977)
Babin, G., Deneault, S., Laporte, G.: Improvements of the Or-opt Heuristic for the Traveling Salesman Problem. GERARD—Group for Research in Decision Analysis. Montreal, Quebec, Canada (2005). https://blogue.hec.ca/permanent/babin/pub/Babi05a.pdf
Golden, B.L., Stewart, Jr.W.R.: Empirical analysis of heuristics. In: Hawler, E.L., Lenstra, J.K., Rinnouy Kan, A.H.G., Shmoys, D.B. (eds.) The Traveling Salesman Problem, pp. 207–249. Wiley, New York (1985)
Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)
Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers (1997)
Hansen, P., Mladenovic, N., Perez, J.A.M.: Variable neighbourhood search: methods and applications. Ann. Oper. Res. 175, 367–407 (2010)
Ardalan, Z., Karimi, S., Poursabzi, O., Naderi, B.: A novel imperialist competitive algorithm for generalized traveling salesman problems. Appl. Soft Comput. 26, 546–555 (2015)
Dorigo, M., Stüzle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)
Crişan, G.C., Pintea, C.M., Pop, P.: On the resilience of an ant-based system in fuzzy environments. an empirical study. In: Proceedings of the 2014 IEEE International Conference on Fuzzy Systems, Beijing, China, pp. 2588–2593 (2014)
Jati, G.K., Suyanto, S.: Evolutionary discrete firefly algorithm for traveling salesman problem, ICAIS 2011. Lecture Notes in Artificial Intelligence (LNAI 6943), pp. 393–403 (2011)
Karaboga, D., Basturk, B.: On the performance of artificial bee colony (ABC) algorithm. Appl. Soft Comput. 8(1), 687–697 (2008)
Iantovics, B., Chira, C., Dumitrescu, D.: Principles of Intelligent Agents. Casa Cărţii de Ştiinţă, Cluj-Napoca (2007)
Nechita, E., Muraru C.V., Talmaciu M.: Mechanisms in social insect societies and their use in optimization. a case study for trail laying behavior. In: Proceedings of the 1st International Conference Bio-Inspired Computational Methods Used for Solving Difficult Problems—Development of Intelligent and Complex Systems BICS’2008, Târgu Mureş, AIP Conference Proceedings, Melville, New York (2009)
Pintea, C.M.: Advances in Bio-inspired Computing for Combinatorial Optimization Problems. Springer, Berlin (2014)
Brigham, R.M., Kalko, K.V., Jones, G., Parsons, S., Limpens, H.J.G.A (Eds.): Bat echolocation research: tools, techniques and analysis, Austin, Texas (2002)
Yang, X.S.: A new meta-heuristic bat-inspired algorithm. In: Gonzales, J.R., Pelta, D.A., Cruz, C., Terrazas, G., Krasnogor, N. (eds.) Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), pp. 65–74. Springer, Berlin (2010)
Khan, K., Nikov, A., Sahai, A.: A fuzzy bat clustering method for ergonomic screening of office workplaces. In: Third International Conference on Software, Services and Semantic Technologies, pp. 59–66. Springer (2011)
Lin, J.H., Chou, C.W., Yang, C.H., Tsai, H.L.: A chaotic Levy flight bat algorithm for parameter estimation in nonlinear dynamic biological systems. J. Comput. Inf. Technol. 2(2), 56–63 (2012)
Yang, X.S., He, X.: Bat algorithm: literature review and applications. Int. J. Bio-Inspired Comput. 5, 141–149 (2013)
Osaba, E., Yang, X.S., Diaz, F., Lopez-Garcia, P., Carballedo, R.: An improved discrete bat algorithm for symmetric and asymmetric traveling salesman problems, engineering applications of artificial intelligence (2015, in press)
Helsgaun, K.: General k-opt submoves for the Lin-Kernighan TSP heuristic. Math. Program. Comput. 1(2–3), 119–163 (2009)
Helsgaun, K.: Solving the Bottleneck Traveling Salesman Problem Using the Lin-Kernigan-Helsgaun Algorithm. Technical Report, Computer Science, Roskilde University (2014)
Nagata, Y., Kobayashi, S.: A powerful genetic algorithm using edge assembly crossover for the traveling salesman problem. INFORMS J. Comput. 25(2), 346–363 (2013)
Kotthoff, L., Kerschke, P., Hoos, H., Trautmann, H.: Improving the state of the art in inexact TSP solving using per-instance algorithm selection. Lecture Notes in Computer Science, vol. 8994, pp. 202–217. Springer (2015)
Library of various sample TSP and TSP-related instances. http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/
Algorithm Selection Library ASlib. http://www.coseal.net/aslib/
Benchmark instances for the Traveling Salesman Problem with Time Windows. http://lopez-ibanez.eu/tsptw-instances
Geonames repository. http://www.geonames.org
Crişan, G.C., Pintea, C.M., Chira, C.: Risk assessment for incoherent data. Environ. Eng. Manag. J. 11(12), 2169–2174 (2012)
Nechita, E., Muraru, C.V., Talmaciu, M.: A Bayesian approach for the assessment of risk probability. Case Study Dig. Risk Probab. Environ. Eng. Manag. J. 11(12), 2249–2256 (2012)
Bőckenhauer, H.J., Hromkovič, J., Mőmke, T., Widmaye, P.: On the Hardness of Reoptimization, SOFSEM 2008. LNCS, vol. 4910, pp. 50–65. Springer, Heidelberg (2008)
Papadimitriou, C.H., Steiglitz, K.: Some examples of difficult traveling salesman problems. Oper. Res. 26(3), 434–443 (1978)
Ahammed, F., Moscato, P.: Evolving L-systems as an intelligent design approach to find classes of difficult-to-solve traveling salesman problem instances. In: Applications of Evolutionary Computation EvoApplications 2011: EvoCOMPLEX, EvoGAMES, EvoIASP, EvoINTELLIGENCE, EvoNUM, and EvoSTOC, Torino, Italy, April 27–29, 2011, Proceedings, Part I, pp. 1–11. Springer, Berlin (2011)
NEOS server. http://www.neos-server.org/neos/
World cities with 15,000 people or more. http://download.geonames.org/export/dump/
ISO 6709:2008, Standard representation of geographic point location by coordinates. http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=39242
GPSVisualizer. http://www.gpsvisualizer.com
Acknowledgments
G.C.C. and E.N. acknowledge the support of the project “Bacau and Lugano—Teaching Informatics for a Sustainable Society”, co-financed by a grant from Switzerland through the Swiss Contribution to the enlarged European Union.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Crişan, G.C., Nechita, E., Palade, V. (2017). On the Effect of Adding Nodes to TSP Instances: An Empirical Analysis. In: Hatzilygeroudis, I., Palade, V., Prentzas, J. (eds) Advances in Combining Intelligent Methods. Intelligent Systems Reference Library, vol 116 . Springer, Cham. https://doi.org/10.1007/978-3-319-46200-4_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-46200-4_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-46199-1
Online ISBN: 978-3-319-46200-4
eBook Packages: EngineeringEngineering (R0)