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On the Effect of Adding Nodes to TSP Instances: An Empirical Analysis

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Part of the book series: Intelligent Systems Reference Library ((ISRL,volume 116 ))

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.

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References

  1. Gendreau, M., Hertz, A., Laporte, G.: New insertion and postoptimization procedures for the traveling salesman problem. Oper. Res. 40(6), 1086–1094 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  2. Garey, M.R., Johnson, D.S.: Computers and intractability: a guide to the theory of NP-completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  3. Shafarevich, I.R., Remizov, A.O.: Linear Algebra and Geometry. Springer, Berlin (2013)

    Book  MATH  Google Scholar 

  4. Toth, P., Vigo, D.: An overview of vehicle routing problems. In: The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia, PA (2001)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. Arora, S.: Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems. J. ACM 45(5), 753–782 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. Papadimitrou, C.H.: Euclidean TSP is NP-complete. Theoret. Comput. Sci. 4, 237–244 (1977)

    Article  MathSciNet  Google Scholar 

  9. 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)

    MATH  Google Scholar 

  10. Jaillet, P.: Probabilistic Traveling Salesman Problems. PhD Thesis, MIT, Cambridge, MA, USA (1985)

    Google Scholar 

  11. 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)

    Google Scholar 

  12. 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)

    Article  MathSciNet  MATH  Google Scholar 

  13. 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)

    Article  MathSciNet  MATH  Google Scholar 

  14. Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. Eur. J. Oper. Res. 59, 231–247 (1992)

    Article  MATH  Google Scholar 

  15. 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

  16. 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

  17. Current, J.R., Schilling, D.A.: The covering salesman problem. Transp. Sci. 23(3), 208–213 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  18. Caric, T., Gold, H. (eds.): Vehicle Routing Problem. I-Tech Education and Publishing KG, Vienna (2008)

    Google Scholar 

  19. Derigs, U., Pullmann, M., Vogel, U.: Truck and trailer routing—problems, heuristics and computational experience. Comput. Oper. Res. 40(2), 536–546 (2013)

    Article  MATH  Google Scholar 

  20. 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)

    Article  Google Scholar 

  21. 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)

    Article  Google Scholar 

  22. Fischeti, M., Lodi, A.: Local branching. Math. Program. 98, 23–47 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  23. Berbeglia, G., Cordeau, J.-F., Laporte, G.: Dynamic pickup and delivery problems. Eur. J. Oper. Res. 202(1), 8–15 (2010)

    Article  MATH  Google Scholar 

  24. Reinelt, G.: The Traveling Salesman: Computational Solutions for TSP Applications. Lecture Notes in Computer Science. Springer, Berlin (1994)

    Google Scholar 

  25. Dantzig, G.B., Fulkerson, D.R., Johnson, S.M.: Solutions of a large-scale traveling salesman problem. Oper. Res. 2, 393–410 (1954)

    MathSciNet  Google Scholar 

  26. Laporte, G., Louveaux, F., Mercure, H.: A priori optimization of the probabilistic traveling salesman problem. Oper. Res. 42(3), 543–549 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  27. Carpaneto, G., Toth, P.: Some new branching and bounding criteria for the asymmetric travelling salesman problem. Manage. Sci. 26, 736–743 (1980)

    Google Scholar 

  28. Balas, E., Christofides, N.: A restricted lagrangean approach to the traveling salesman problem. Math. Program. 21, 19–46 (1981)

    Google Scholar 

  29. Miller, D.L., Pekny, J.F.: Exact solution of large asymmetric traveling salesman problems. Science 251, 754–761 (1991)

    Google Scholar 

  30. Schrijver, A.: Combinatorial optimization: polyhedra and efficiency, vol. 1. Springer, Berlin (2003)

    MATH  Google Scholar 

  31. 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)

    Article  MathSciNet  MATH  Google Scholar 

  32. Mitchell, J.E.: Branch-and-cut algorithms for combinatorial optimization problems. Handbook of Applied Optimization. Oxford University Press, Oxford (2000)

    Google Scholar 

  33. Jünger, M., Reinelt, G., Thienel, S.: Provably good solutions for the traveling salesman problem. Zeitschrift für Operations Research 22, 83–95 (1998)

    MATH  Google Scholar 

  34. Gutin, G., Punnen, A.P. (eds.): The Traveling Salesman Problem and Its Variations. Springer, New York (2007)

    MATH  Google Scholar 

  35. 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

  36. COIN-OR resources. http://www.coin-or.org/projects/, http://www.coin-or.org/resources.html

  37. COIN-OR Project. http://www.coin-or.org/

  38. 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)

    Google Scholar 

  39. ABACUS system. http://www.informatik.uni-koeln.de/abacus/index.html

  40. 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)

    Google Scholar 

  41. Concorde TSP solver. http://www.math.uwaterloo.ca/tsp/concorde/

  42. Lin, S.: Computer solutions of the traveling salesman problem. Bell Syst. Tech. J. 44, 2245–2269 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  43. Lin, S., Kernighan, B.W.: An effective heuristic algorithm for the traveling salesman problem. Oper. Res. 21, 972–989 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  44. 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)

    Google Scholar 

  45. Croes, G.A.: A method for solving large scale symmetric traveling salesman problems to optimality. Oper. Res. 6, 791–812 (1958)

    Article  MathSciNet  Google Scholar 

  46. 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)

    Article  MathSciNet  MATH  Google Scholar 

  47. 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

  48. 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)

    Google Scholar 

  49. Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  50. Glover, F., Laguna, M.: Tabu Search. Kluwer Academic Publishers (1997)

    Google Scholar 

  51. Hansen, P., Mladenovic, N., Perez, J.A.M.: Variable neighbourhood search: methods and applications. Ann. Oper. Res. 175, 367–407 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  52. 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)

    Article  Google Scholar 

  53. Dorigo, M., Stüzle, T.: Ant Colony Optimization. MIT Press, Cambridge (2004)

    MATH  Google Scholar 

  54. 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)

    Google Scholar 

  55. 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)

    Google Scholar 

  56. Karaboga, D., Basturk, B.: On the performance of artificial bee colony (ABC) algorithm. Appl. Soft Comput. 8(1), 687–697 (2008)

    Article  Google Scholar 

  57. Iantovics, B., Chira, C., Dumitrescu, D.: Principles of Intelligent Agents. Casa Cărţii de Ştiinţă, Cluj-Napoca (2007)

    Google Scholar 

  58. 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)

    Google Scholar 

  59. Pintea, C.M.: Advances in Bio-inspired Computing for Combinatorial Optimization Problems. Springer, Berlin (2014)

    Book  MATH  Google Scholar 

  60. 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)

    Google Scholar 

  61. 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)

    Chapter  Google Scholar 

  62. 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)

    Google Scholar 

  63. 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)

    Google Scholar 

  64. Yang, X.S., He, X.: Bat algorithm: literature review and applications. Int. J. Bio-Inspired Comput. 5, 141–149 (2013)

    Article  Google Scholar 

  65. 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)

    Google Scholar 

  66. Helsgaun, K.: General k-opt submoves for the Lin-Kernighan TSP heuristic. Math. Program. Comput. 1(2–3), 119–163 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  67. Helsgaun, K.: Solving the Bottleneck Traveling Salesman Problem Using the Lin-Kernigan-Helsgaun Algorithm. Technical Report, Computer Science, Roskilde University (2014)

    Google Scholar 

  68. 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)

    Article  MathSciNet  Google Scholar 

  69. 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)

    Google Scholar 

  70. Library of various sample TSP and TSP-related instances. http://comopt.ifi.uni-heidelberg.de/software/TSPLIB95/

  71. TSPLIB. http://www.math.waterloo.ca/tsp/index.htm

  72. Algorithm Selection Library ASlib. http://www.coseal.net/aslib/

  73. Benchmark instances for the Traveling Salesman Problem with Time Windows. http://lopez-ibanez.eu/tsptw-instances

  74. Geonames repository. http://www.geonames.org

  75. Crişan, G.C., Pintea, C.M., Chira, C.: Risk assessment for incoherent data. Environ. Eng. Manag. J. 11(12), 2169–2174 (2012)

    Google Scholar 

  76. 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)

    Google Scholar 

  77. 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)

    Google Scholar 

  78. Papadimitriou, C.H., Steiglitz, K.: Some examples of difficult traveling salesman problems. Oper. Res. 26(3), 434–443 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  79. 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)

    Google Scholar 

  80. NEOS server. http://www.neos-server.org/neos/

  81. World cities with 15,000 people or more. http://download.geonames.org/export/dump/

  82. 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

  83. GPSVisualizer. http://www.gpsvisualizer.com

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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.

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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

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