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Finding Worst-Case Instances of, and Lower Bounds for, Online Algorithms Using Genetic Algorithms

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AI 2002: Advances in Artificial Intelligence (AI 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2557))

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Abstract

This paper presents a novel application of Genetic Algorithms, as an empirical method in the analysis of algorithms. Online Algorithms are designed for the case in which the problem input does not arrive in its totality, as in Offline Algorithms, but arrives piece by piece, during the course of the computation. Generating worst-case instances for these algorithms, both for use as test cases and as lower-bound proofs, is often non-trivial. We study the use of Genetic Algorithms as a novel method for finding worst-case instances of online problems, including versions of the Taxicab Problem. These worst-case instances give us lower bounds on the non-competitiveness of the approximation algorithms used. In particular, our experimental results demonstrate that 6.93 is a lower bound on the competitive ratio of the hedging and optimal offline algorithms on the Hard Planar Taxicab Problem. This experimental result has theoretical implications for the study of the problem, i.e., further research to prove an upper bound of 7 may be warranted.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Columbia University, 10027, New York, NY

    Andrew P. Kosoresow & Matthew P. Johnson

Authors
  1. Andrew P. Kosoresow
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  2. Matthew P. Johnson
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Editor information

Editors and Affiliations

  1. Australian Defence Force Academy, University of New South Wales, ACT 2600, Canberra, Australia

    Bob McKay

  2. Computer Science Laboratory, Australian National University, RSISE Building, ACT 0200, Canberra, Australia

    John Slaney

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© 2002 Springer-Verlag Berlin Heidelberg

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Kosoresow, A.P., Johnson, M.P. (2002). Finding Worst-Case Instances of, and Lower Bounds for, Online Algorithms Using Genetic Algorithms. In: McKay, B., Slaney, J. (eds) AI 2002: Advances in Artificial Intelligence. AI 2002. Lecture Notes in Computer Science(), vol 2557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36187-1_30

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  • DOI: https://doi.org/10.1007/3-540-36187-1_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00197-3

  • Online ISBN: 978-3-540-36187-9

  • eBook Packages: Springer Book Archive

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