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Solution of a Large-Scale Traveling-Salesman Problem

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50 Years of Integer Programming 1958-2008

Abstract

The RAND Corporation in the early 1950s contained “what may have been the most remarkable group of mathematicians working on optimization ever assembled” [6]: Arrow, Bellman, Dantzig, Flood, Ford, Fulkerson, Gale, Johnson, Nash, Orchard-Hays, Robinson, Shapley, Simon, Wagner, and other household names. Groups like this need their challenges. One of them appears to have been the traveling salesman problem (TSP) and particularly its instance of finding a shortest route through Washington, DC, and the 48 states [4, 7].

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References

  1. G.B. Dantzig, Application of the simplex method to a transportation problem, Activity Analysis of Production and Allocation (T.C. Koopmans, ed.), Cowles Commission Monograph No. 13. JohnWiley & Sons, Inc., New York, N. Y.; Chapman & Hall, Ltd., London, 1951, pp. 359–373.

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  2. G.B. Dantzig, D.R. Fulkerson, and S.M. Johnson, Solution of a large scale traveling salesman problem, Technical Report P-510, RAND Corporation, Santa Monica, California, USA, 1954.

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  3. G.B. Dantzig, D.R. Fulkerson, and S.M. Johnson, On a linear-programming, combinatorial approach to the traveling-salesman problem, Operations Research 7 (1959) 58–66.

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  4. M.M. Flood, Merrill Flood (with Albert Tucker), Interview of Merrill Flood in San Francisco on 14 May 1984, The Princeton Mathematics Community in the 1930s, Transcript Number 11 (PMC11), Princeton University, 1984.

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  5. R.E. Gomory, Outline of an algorithm for integer solutions to linear programs, Bulletin of the American Mathematical Society 64 (1958) 275–278.

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  6. M. Gröotschel and G.L. Nemhauser, George Dantzig’s contributions to integer programming, Discrete Optimization 5 (2008) 168–173.

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  7. J. Robinson, On the Hamiltonian game (a traveling salesman problem), RAND ResearchMemorandum RM-303, RAND Corporation, Santa Monica, California, USA, 1949. The following article originally appeared as:

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Author information

Authors and Affiliations

  1. Canada Research Chair in Combinatorial Optimization, Department of Computer Science and Software Engineering, Concordia University, Please Provide City, Canada

    Vašek Chvátal

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, USA

    William Cook

Authors
  1. Vašek Chvátal
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  2. William Cook
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  3. George B. Dantzig
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  4. Delbert R. Fulkerson
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  5. Selmer M. Johnson
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Corresponding author

Correspondence to Vašek Chvátal .

Editor information

Editors and Affiliations

  1. Inst. Informatik, Universität Köln, Pohligstr. 1, Köln, 50969, Germany

    Michael Jünger

  2. Fac. Sciences de Base (FSB), Ecole Polytechnique Fédérale de Lausanne, Lausanne, 1015, Switzerland

    Thomas M. Liebling

  3. Ensimag, Institut Polytechnique de Grenoble, avenue Félix Viallet 46, Grenoble CX 1, 38031, France

    Denis Naddef

  4. School of Industrial &, Georgia Institute of Technology, Ferst Drive NW., 765, Atlanta, 30332-0205, USA

    George L. Nemhauser

  5. IBM Corporation, Route 100 294, Somers, 10589, USA

    William R. Pulleyblank

  6. Inst. Informatik, Universität Heidelberg, Im Neuenheimer Feld 326, Heidelberg, 69120, Germany

    Gerhard Reinelt

  7. ed Informatica, CNR - Ist. Analisi dei Sistemi, Viale Manzoni 30, Roma, 00185, Italy

    Giovanni Rinaldi

  8. Center for Operations Reserach &, Université Catholique de Louvain, voie du Roman Pays 34, Leuven, 1348, Belgium

    Laurence A. Wolsey

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Chvátal, V., Cook, W., Dantzig, G.B., Fulkerson, D.R., Johnson, S.M. (2010). Solution of a Large-Scale Traveling-Salesman Problem. In: Jünger, M., et al. 50 Years of Integer Programming 1958-2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68279-0_1

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