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Runtime Analysis of Ant Colony Optimization with Best-So-Far Reinforcement

Author

Listed:
  • Walter J. Gutjahr

    (University of Vienna)

  • Giovanni Sebastiani

    (CNR
    “Sapienza” University of Rome)

Abstract

The paper provides some theoretical results on the analysis of the expected time needed by a class of Ant Colony Optimization algorithms to solve combinatorial optimization problems. A part of the study refers to some general results on the expected runtime of the considered class of algorithms. These results are then specialized to the case of pseudo-Boolean functions. In particular, three well known functions and a combination of two of them are considered: the OneMax, the Needle-in-a-Haystack, the LeadingOnes, and the OneMax-Needle-in-a-Haystack. The results obtained for these functions are also compared to those from the well-investigated (1+1)-Evolutionary Algorithm. The results shed light on a suitable parameter choice for the considered class of algorithms. Furthermore, it turns out that for two of the four studied problems, the expected runtime for the considered class, expressed in terms of the problem size, is of the same order as that for (1+1)-Evolutionary Algorithm. For the other two problems, the results are significantly in favour of the considered class of Ant Colony Optimization algorithms.

Suggested Citation

  • Walter J. Gutjahr & Giovanni Sebastiani, 2008. "Runtime Analysis of Ant Colony Optimization with Best-So-Far Reinforcement," Methodology and Computing in Applied Probability, Springer, vol. 10(3), pages 409-433, September.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:3:d:10.1007_s11009-007-9047-1
    DOI: 10.1007/s11009-007-9047-1
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    References listed on IDEAS

    as
    1. Walter J. Gutjahr, 2006. "On the Finite-Time Dynamics of Ant Colony Optimization," Methodology and Computing in Applied Probability, Springer, vol. 8(1), pages 105-133, March.
    2. Giovanni Sebastiani & Giovanni Luca Torrisi, 2005. "An Extended Ant Colony Algorithm and Its Convergence Analysis," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 249-263, June.
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    Cited by:

    1. Paola Pellegrini & Elena Moretti & Daniela Favaretto, 2008. "Exploration in stochastic algorithms: An application on MAX-MIN Ant System," Working Papers 169, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    2. Karl F. Doerner & Vittorio Maniezzo, 2018. "Metaheuristic search techniques for multi-objective and stochastic problems: a history of the inventions of Walter J. Gutjahr in the past 22 years," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(2), pages 331-356, June.

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