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An Extended Ant Colony Algorithm and Its Convergence Analysis

Author

Listed:
  • Giovanni Sebastiani

    (Consiglio Nazionale delle Ricerche)

  • Giovanni Luca Torrisi

    (Consiglio Nazionale delle Ricerche)

Abstract

In this work, we propose a stochastic algorithm for solving $$ \mathcal{N}{\wp } - hard $$ combinatorial optimization problems. The procedure is formulated within the Ant Colony Optimization (ACO) framework, and extends the so-called Graph-based Ant System with time-dependent evaporation factor, (GBAS/tdev) studied in Gutjahr (2002). In particular, we consider an ACO search procedure which also takes into account the objective function value. We provide a rigorous theoretical study on the convergence of the proposed algorithm. Further, for a toy example, we compare by simulation the rate of convergence of the proposed algorithm with those from the Random Search (RS) and from the corresponding procedure in Gutjahr (2002).

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:7:y:2005:i:2:d:10.1007_s11009-005-1485-z
    DOI: 10.1007/s11009-005-1485-z
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    References listed on IDEAS

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    1. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
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    Cited by:

    1. 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.

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