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An augmented Lagrangian ant colony based method for constrained optimization

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  • Asghar Mahdavi
  • Mohammad Shiri

Abstract

One of the most efficient penalty based methods to solve constrained optimization problems is the augmented Lagrangian algorithm. This paper presents a constrained optimization algorithm to solve continuous constrained global optimization problems. The proposed algorithm integrates the benefit of the continuous ant colony ( $$\hbox {ACO}_\mathrm{R}$$ ACO R ) capability for discovering the global optimum with the effective behavior of the Lagrangian multiplier method to handle constraints. This method is tested on 13 well-known benchmark functions and compared with four other state-of-the-art algorithms. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Asghar Mahdavi & Mohammad Shiri, 2015. "An augmented Lagrangian ant colony based method for constrained optimization," Computational Optimization and Applications, Springer, vol. 60(1), pages 263-276, January.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:1:p:263-276
    DOI: 10.1007/s10589-014-9664-x
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    References listed on IDEAS

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    1. Samuel Amstutz, 2011. "Augmented Lagrangian for cone constrained topology optimization," Computational Optimization and Applications, Springer, vol. 49(1), pages 101-122, May.
    2. Ernesto Birgin & J. Martínez, 2012. "Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization," Computational Optimization and Applications, Springer, vol. 51(3), pages 941-965, April.
    3. Y. Zhou & X. Yang, 2012. "Augmented Lagrangian functions for constrained optimization problems," Journal of Global Optimization, Springer, vol. 52(1), pages 95-108, January.
    4. Socha, Krzysztof & Dorigo, Marco, 2008. "Ant colony optimization for continuous domains," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1155-1173, March.
    5. Kalyanmoy Deb & Soumil Srivastava, 2012. "A genetic algorithm based augmented Lagrangian method for constrained optimization," Computational Optimization and Applications, Springer, vol. 53(3), pages 869-902, December.
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    Cited by:

    1. Umesh Balande & Deepti Shrimankar, 2020. "An oracle penalty and modified augmented Lagrangian methods with firefly algorithm for constrained optimization problems," Operational Research, Springer, vol. 20(2), pages 985-1010, June.

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