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Using Grammars to Generate Very Large Scale Neighborhoods for the Traveling Salesman Problem and Other Sequencing Problems

  • Conference paper
Book cover Integer Programming and Combinatorial Optimization (IPCO 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3509))

Abstract

Local search heuristics are among the most popular approaches to solve hard optimization problems. Among them, Very Large Scale Neighborhood Search techniques present a good balance between the quality of local optima and the time to search a neighborhood. We develop a language to generate exponentially large neighborhoods for sequencing problems using grammars. We develop efficient generic dynamic programming solvers that determine the optimal neighbor in a neighborhood generated by a grammar for sequencing problems such as the Traveling Salesman Problem or the Linear Ordering Problem. This framework unifies a variety of previous results on exponentially large neighborhood for the Traveling Salesman Problem and generalizes them to other sequencing problems.

This research was supported in part by NSF grant DMI-0217123.

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Author information

Authors and Affiliations

  1. Operations Research Center, MIT, Cambridge, MA, USA

    Agustin Bompadre

  2. Sloan School of Management, MIT, Cambridge, MA, USA

    James B. Orlin

Authors
  1. Agustin Bompadre
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  2. James B. Orlin
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Editor information

Editors and Affiliations

  1. Institut für Informatik, Universität zu Köln,  

    Michael Jünger

  2. Fakultät für Mathematik, Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, Germany

    Volker Kaibel

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Bompadre, A., Orlin, J.B. (2005). Using Grammars to Generate Very Large Scale Neighborhoods for the Traveling Salesman Problem and Other Sequencing Problems. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_32

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  • DOI: https://doi.org/10.1007/11496915_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26199-5

  • Online ISBN: 978-3-540-32102-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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