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ACO for Continuous and Mixed-Variable Optimization

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Book cover Ant Colony Optimization and Swarm Intelligence (ANTS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3172))

Abstract

This paper presents how the Ant Colony Optimization (ACO) metaheuristic can be extended to continuous search domains and applied to both continuous and mixed discrete-continuous optimization problems. The paper describes the general underlying idea, enumerates some possible design choices, presents a first implementation, and provides some preliminary results obtained on well-known benchmark problems. The proposed method is compared to other ant, as well as non-ant methods for continuous optimization.

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References

  1. Audet, C., Dennis, J.J.E.: Pattern Search Algorithms for Mixed Variable Programming. SIAM Journal on Optimization 11(3), 573–594 (2001)

    Article  MathSciNet  Google Scholar 

  2. Bilchev, G., Parmee, I.C.: The Ant Colony Metaphor for Searching Continuous Design Spaces. In: Fogarty, T.C. (ed.) AISB-WS 1995. LNCS, vol. 993, pp. 25–39. Springer, Heidelberg (1995)

    Google Scholar 

  3. Bosman, P.A.N., Thierens, D.: Continuous Iterated Density Estimation Evolutionary Algorithms within the IDEA Framework. In: Pelikan, M., Mühlenbein, H., Rodriguez, A.O. (eds.) Proceedings of OBUPM Workshop at GECCO-2000, pp. 197–200. Morgan-Kaufmann Publishers, San Francisco (2000)

    Google Scholar 

  4. Box, G.E.P., Muller, M.E.: A note on the generation of random normal deviates. Annals of Mathematical Statistics 29(2), 610–611 (1958)

    Article  MATH  Google Scholar 

  5. Chelouah, R., Siarry, P.: Enhanced Continuous Tabu Search. In: Voss, S., Martello, S., Osman, I.H., Roucairol, C. (eds.) Meta-Heuristics Advances and Trends in Local Search Paradigms for Optimization, vol. 4, pp. 49–61. Kluwer Academic Publishers, Boston (1999)

    Google Scholar 

  6. Chelouah, R., Siarry, P.: A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions. Journal of Heuristics 6, 191–213 (2000)

    Article  MATH  Google Scholar 

  7. Dorigo, M., Di Caro, G.: The Ant Colony Optimization meta-heuristic. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, McGraw- Hill, New York (1999)

    Google Scholar 

  8. Dréo, J., Siarry, P.: Continuous Interacting Ant Colony Algorithm Based on Dense Heterarchy. Future Generation Computer Systems (to appear)

    Google Scholar 

  9. Dréo, J., Siarry, P.: A New Ant Colony Algorithm Using the Heterarchical Concept Aimed at Optimization of Multiminima Continuous Functions. In: Dorigo, M., Di Caro, G.A., Sampels, M. (eds.) Ant Algorithms 2002. LNCS, vol. 2463, pp. 216–221. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  10. Guntsch, M., Middendorf, M.: A population based approach for ACO. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoIASP 2002, EvoWorkshops 2002, EvoSTIM 2002, EvoCOP 2002, and EvoPlan 2002. LNCS, vol. 2279, pp. 71–80. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Kincaid, R.K., Griffith, S., Sykes, R., Sobieszczanski-Sobieski, J.: A Bell-Curve Genetic Algorithm for Mixed Continuous and Discrete Optimization Problems. In: Proceedings of 43rd AIAA Structures, Structural Dynamics, and Materials Conference, AIAA, Denver, CO, USA (2002)

    Google Scholar 

  12. Mathur, M., Karale, S.B., Priye, S., Jyaraman, V.K., Kulkarni, B.D.: Ant Colony Approach to Continuous Function Optimization. Ind. Eng. Chem. Res. 39, 3814–3822 (2000)

    Article  Google Scholar 

  13. Monmarché, N., Venturini, G., Slimane, M.: On how Pachycondyla apicalis ants suggest a new search algorithm. Future Generation Computer Systems 16, 937–946 (2000)

    Article  Google Scholar 

  14. Očenášek, J., Schwarz, J.: Estimation Distribution Algorithm for Mixed Continuous-Discreet Optimization Problems. In: Proceedings of the 2nd Euro- Inernational Symposium on Computational Inteligence, pp. 227–232. IOS Press, Amsterdam (2002)

    Google Scholar 

  15. Siarry, P., Berthiau, G., Durbin, F., Haussy, J.: Enhanced Simulated Annealing for Globally Minimizing Functions of Many Continuous Variables. ACM Transactions on Mathematical Software 23(2), 209–228 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  16. Stützle, T., Hoos, H.H.: MAX-MIN Ant System. Future Generation Computer Systems 16(8), 889–914 (2000)

    Article  Google Scholar 

  17. Wodrich, M., Bilchev, G.: Cooperative distributed search: the ant’s way. Control & Cybernetics 3, 413–446 (1997)

    MathSciNet  Google Scholar 

  18. Yuan, B., Gallagher, M.: Playing in Continuous Spaces: Some Analysis and Extension of Population-Based Incremental Learning. In: Sarker, R., et al. (eds.) Proceedings of Congress of Evolutionary Computation (CEC), pp. 443–450 (2003)

    Google Scholar 

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Socha, K. (2004). ACO for Continuous and Mixed-Variable Optimization. In: Dorigo, M., Birattari, M., Blum, C., Gambardella, L.M., Mondada, F., Stützle, T. (eds) Ant Colony Optimization and Swarm Intelligence. ANTS 2004. Lecture Notes in Computer Science, vol 3172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28646-2_3

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  • DOI: https://doi.org/10.1007/978-3-540-28646-2_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22672-7

  • Online ISBN: 978-3-540-28646-2

  • eBook Packages: Springer Book Archive

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