skip to main content
10.1145/2576768.2598302acmconferencesArticle/Chapter ViewAbstractPublication PagesgeccoConference Proceedingsconference-collections
research-article

A fixed budget analysis of randomized search heuristics for the traveling salesperson problem

Published:12 July 2014Publication History

ABSTRACT

Randomized Search heuristics are frequently applied to NP-hard combinatorial optimization problems. The runtime analysis of randomized search heuristics has contributed tremendously to their theoretical understanding. Recently, randomized search heuristics have been examined regarding their achievable progress within a fixed time budget. We follow this approach and present a first fixed budget runtime analysis for a NP-hard combinatorial optimization problem. We consider the well-known Traveling Salesperson problem (TSP) and analyze the fitness increase that randomized search heuristics are able to achieve within a given fixed budget.

References

  1. A. Auger and B. Doerr. Theory of Randomized Search Heuristics: Foundations and Recent Developments. World Scientific Publishing Co., Inc., 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. B. Chandra, H. Karloff, and C. Tovey. New results on the old k-Opt algorithm for the TSP. In Proc. of SODA'94, pages 150--159, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. B. Doerr, T. Jansen, C. Witt, and C. Zarges. A method to derive fixed budget results from expected optimisation times. In Proc. of GECCO'13, pages 1581--1588. ACM, 2013. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science, 276(1--2):51--81, 2002. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. M. Englert, H. Röglin, and B. Vöcking. Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP. Algorithmica, 68(1):190--264, 2014.Google ScholarGoogle ScholarCross RefCross Ref
  6. T. Jansen. Analyzing Evolutionary Algorithms - The Computer Science Perspective. Natural Computing Series. Springer, 2013. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. T. Jansen and C. Zarges. Analysis of evolutionary algorithms: From computational complexity analysis to algorithm engineering. In Proc. of FOGA '11, pages 1--14. ACM, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. T. Jansen and C. Zarges. Fixed budget computations: a different perspective on run time analysis. In Proc. of GECCO'12, pages 1325--1332, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. W. Kern. A probabilistic analysis of the switching algorithm for the euclidean TSP. Mathematical programming: Series A, 44(1--3):213--219, 1989. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. J. Lassig and D. Sudholt. Analysis of speedups in parallel evolutionary algorithms for combinatorial optimization. In Proc. of ISAAC'11, pages 405--414. Springer, 2011. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. R. Motwani and P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. F. Neumann and I. Wegener. Randomized local search, evolutionary algorithms, and the minimum spanning tree problem. In Proc. of GECCO'04, pages 713--724, 2004.Google ScholarGoogle ScholarCross RefCross Ref
  13. F. Neumann and C. Witt. Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity. Springer, 2010. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. P. S. Oliveto, J. He, and X. Yao. Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results. International Journal of Automation and Computing, 4(3):281--293, 2007.Google ScholarGoogle ScholarCross RefCross Ref
  15. P. Sanders and D. Wagner. Algorithm engineering. Informatik-Spektrum, 36(2):187--190, 2013.Google ScholarGoogle ScholarCross RefCross Ref
  16. D. A. Spielman and S.-H. Teng. Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time. J. ACM, 51(3):385--463, May 2004. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. B. M. R. Veenstra. Smoothed analysis of the 2-Opt heuristic for the TSP: Polynomial bounds for gaussian noise. In Proc. of ISAAC'13, 2013.Google ScholarGoogle Scholar
  18. D. Zhou, D. Luo, R. Lu, and Z. Han. The use of tail inequalities on the probable computational time of randomized search heuristics. Theoretical Computer Science, 436(0):106 -- 117, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. A fixed budget analysis of randomized search heuristics for the traveling salesperson problem

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in
    • Published in

      cover image ACM Conferences
      GECCO '14: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation
      July 2014
      1478 pages
      ISBN:9781450326629
      DOI:10.1145/2576768

      Copyright © 2014 ACM

      Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 12 July 2014

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article

      Acceptance Rates

      GECCO '14 Paper Acceptance Rate180of544submissions,33%Overall Acceptance Rate1,669of4,410submissions,38%

      Upcoming Conference

      GECCO '24
      Genetic and Evolutionary Computation Conference
      July 14 - 18, 2024
      Melbourne , VIC , Australia

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader