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Further Extension of the TSP Assign Neighborhood

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Abstract

We introduce a new extension of Punnen's exponential neighborhood for the traveling salesman problem (TSP). In contrast to an interesting generalization of Punnen's neighborhood by De Franceschi, Fischetti, and Toth (2005), our neighborhood is searchable in polynomial time, a feature that invites exploitation by heuristic and metaheuristic procedures for the TSP and related problems, including those of De Franceschi, Fischetti, and Toth (2005) for the vehicle routing problem.

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References

  • Ahuja, R., J. Orlin, and D. Sharma. (2003). “A Composite Neighborhood Search Algorithm for the Capacitated Minimum Spanning Tree Problem.” Oper. Res. Lett. 31, 185–194.

    Article  Google Scholar 

  • Balas, E. and N. Simonetti. (2001). “Linear Time Dynamic Programming Algorithms for New Classes of Restricted TSPs: A Computational Study.” INFORMS J. Comput. 13, 56–75. The code is currently available from www.contrib.andrew.cmu.edu/∼neils/tsp/index.html.

  • Balcazar, J.L., J. Diaz, and J. Gabarro. (1995). Structural Complexity I, EATCS Monographs on Theoretical Computer Science, 2nd ed., Berlin: Springer-Verlag.

  • Bang-Jensen, J. and G. Gutin. (2000). Digraphs: Theory, Algorithms and Apllications. London: Springer-Verlag.

    Google Scholar 

  • Burkard, R.E., V.G. Deineko, and G.J. Woeginger. (1998). “The Travelling Salesman Problem and the PQ-tree.” Math. Oper. Res. 23, 613–623.

    Google Scholar 

  • Deineko, V.G. and G.J. Woeginger. (2000). “A Study of Exponential Neighbourhoods for the Traveling Salesman Problem and the Quadratic Assignment Problem.” Math. Program. Ser. A 87, 519–542.

    Google Scholar 

  • De Franceschi, R., M. Fischetti, and P. Toth. (2005). “A New ILP-based Refinement Heuristic for Vehicle Routing Problems.” Math. Programming (to appear).

  • Ergun, O. and J.B. Orlin. (2005). “Dynamic Programming Metodologies in Very Large Scale Neighborhood Search Applied to the Traveling Salesman Problem.” Submitted. See http://web.mit.edu/jorlin/www/ working_papers.html.

  • Gamboa, D., C. Rego, and F. Glover. (2005). “Data Structures and Ejection Chains for Solving Large Scale Traveling Salesman Problems.” Europ. J. Oper. Res. 160, 154–171.

    Article  Google Scholar 

  • Gutin, G. (1984). “On an Approach to Solving the Traveling Salesman Problem.” In Proc. The USSR Conference on System Research (Moscow, USSR), (in Russian), pp. 184–185.

  • Gutin, G. (1999). “Exponential Neighborhood Local Search for the Traveling Salesman Problem.” Computers and OR 26, 313–320.

    Article  Google Scholar 

  • Gutin, G. and A. Yeo. (2003). “Upper Bounds on ATSP Neighborhood Size.” Discrete Appl. Math. 129, 533–538.

    Article  Google Scholar 

  • Gutin, G., A. Yeo, and A. Zverovitch. (2002). “Exponential Neighborhoods and Domination Analysis for the TSP.” In G. Gutin and A.P. Punnen (eds.), The Traveling Salesman Problem and its Variations. Dordrecht: Kluwer.

  • Punnen, A.P. (2001). “The Traveling Salesman Problem: New Polynomial Approximation Algorithms and Domination Analysis.” J. Inform. Optim. Sci. 22, 191–206.

    Google Scholar 

  • Rego, C. and F. Glover. (2002). “Local Search and Metaheuristics for the Traveling Salesman Problem.” In G. Gutin and A.P. Punnen (eds.), The Traveling Salesman Problem and its Variations. Dordrecht: Kluwer.

  • Sarvanov, V.I. and N.N. Doroshko. (1981). “The Approximate Solution of the Traveling Salesman Problem by a Local Algorithm with Scanning Neighborhoods of Factorial Cardinality in Cubic Time.” Software: Algorithms and Programs 31, 11–13, Minsk: Math. Institute of the Belorussian Acad. Sci. (in Russian).

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Correspondence to Gregory Gutin.

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Research of GG was partially supported by Leverhulme Trust and by the IST Programme of the European Community, under the PASCAL Network of Excellence, IST-2002–506778.

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Gutin, G., Glover, F. Further Extension of the TSP Assign Neighborhood. J Heuristics 11, 501–505 (2005). https://doi.org/10.1007/s10732-005-3487-y

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