IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v7y2005i2d10.1007_s11009-005-1485-z.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-005-1485-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-005-1485-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Bruce Hajek, 1988. "Cooling Schedules for Optimal Annealing," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 311-329, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Stoica, R.S. & Gregori, P. & Mateu, J., 2005. "Simulated annealing and object point processes: Tools for analysis of spatial patterns," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1860-1882, November.
    2. Pirlot, Marc, 1996. "General local search methods," European Journal of Operational Research, Elsevier, vol. 92(3), pages 493-511, August.
    3. Löwe, Matthias, 1997. "On the invariant measure of non-reversible simulated annealing," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 189-193, December.
    4. Miclo, Laurent, 1995. "Remarques sur l'ergodicité des algorithmes de recuit simulé sur un graphe," Stochastic Processes and their Applications, Elsevier, vol. 58(2), pages 329-360, August.
    5. Yiyo Kuo, 2014. "Design method using hybrid of line-type and circular-type routes for transit network system optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 600-613, July.
    6. Rodriguez-Tello, Eduardo & Hao, Jin-Kao & Torres-Jimenez, Jose, 2008. "An improved simulated annealing algorithm for bandwidth minimization," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1319-1335, March.
    7. Sam Hui & Eric Bradlow, 2012. "Bayesian multi-resolution spatial analysis with applications to marketing," Quantitative Marketing and Economics (QME), Springer, vol. 10(4), pages 419-452, December.
    8. Gabriel M. Portal & Marcus Ritt & Leonardo M. Borba & Luciana S. Buriol, 2016. "Simulated annealing for the machine reassignment problem," Annals of Operations Research, Springer, vol. 242(1), pages 93-114, July.
    9. Graeme J. Doole & David J. Pannell, 2008. "Optimisation of a Large, Constrained Simulation Model using Compressed Annealing," Journal of Agricultural Economics, Wiley Blackwell, vol. 59(1), pages 188-206, February.
    10. Triki, E. & Collette, Y. & Siarry, P., 2005. "A theoretical study on the behavior of simulated annealing leading to a new cooling schedule," European Journal of Operational Research, Elsevier, vol. 166(1), pages 77-92, October.
    11. Adam Tauman Kalai & Santosh Vempala, 2006. "Simulated Annealing for Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 253-266, May.
    12. Pablo Adasme & Ali Dehghan Firoozabadi, 2019. "Facility Location with Tree Topology and Radial Distance Constraints," Complexity, Hindawi, vol. 2019, pages 1-29, November.
    13. Christoph Flamm & Ivo L. Hofacker & Peter F. Stadler & Michael T. Wolfinger, 2001. "Barrier Trees of Degenerate Landscapes," Working Papers 01-09-053, Santa Fe Institute.
    14. Marc Robini & Pierre-Jean Reissman, 2013. "From simulated annealing to stochastic continuation: a new trend in combinatorial optimization," Journal of Global Optimization, Springer, vol. 56(1), pages 185-215, May.
    15. Kapetanios, George, 2006. "Cluster analysis of panel data sets using non-standard optimisation of information criteria," Journal of Economic Dynamics and Control, Elsevier, vol. 30(8), pages 1389-1408, August.
    16. Alrefaei, Mahmoud H. & Alawneh, Ameen J., 2005. "Solution quality of random search methods for discrete stochastic optimization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(2), pages 115-125.
    17. Taillard, Eric D. & Gambardella, Luca M. & Gendreau, Michel & Potvin, Jean-Yves, 2001. "Adaptive memory programming: A unified view of metaheuristics," European Journal of Operational Research, Elsevier, vol. 135(1), pages 1-16, November.
    18. Robini, Marc C. & Reissman, Pierre-Jean, 2011. "On simulated annealing with temperature-dependent energy and temperature-dependent communication," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 915-920, August.
    19. Woodruff, David L., 1998. "Proposals for chunking and tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 585-598, April.
    20. Lisic Jonathan & Sang Hejian & Zhu Zhengyuan & Zimmer Stephanie, 2018. "Optimal Stratification and Allocation for the June Agricultural Survey," Journal of Official Statistics, Sciendo, vol. 34(1), pages 121-148, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:7:y:2005:i:2:d:10.1007_s11009-005-1485-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.