# An augmented Lagrangian ant colony based method for constrained optimization

## Author

Listed:
• Asghar Mahdavi

()

## 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
as

File URL: http://hdl.handle.net/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. Socha, Krzysztof & Dorigo, Marco, 2008. "Ant colony optimization for continuous domains," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1155-1173, March.
4. Y. Zhou & X. Yang, 2012. "Augmented Lagrangian functions for constrained optimization problems," Journal of Global Optimization, Springer, vol. 52(1), pages 95-108, January.
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.
Full references (including those not matched with items on IDEAS)

### Keywords

Ant colony; Augmented Lagrangian function (ALF); Constrained optimization problems (COPs);

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