Numerical study of augmented Lagrangian algorithms for constrained global optimization

Optimization

Volumn 60, Issue 10-11, 2011, Pages 1359-1378

  Rocha, Ana Maria A C ^a   Fernandes, Edite M G P ^a  

^a UNIVERSITY OF MINHO   (Portugal)

Author keywords

augmented Lagrangian; electromagnetism like mechanism; global optimization; heuristics

Indexed keywords

EID: 84858234726     PISSN: 02331934     EISSN: 10294945     Source Type: Journal    
DOI: 10.1080/02331934.2011.628671     Document Type: Article

References (29)

1. Barbosa, HJC. 1999. A coevolutionary genetic algorithm for constrained optimization, in Proceedings of the 1999 Congress on Evolutionary Computation, Vol. 3. pp. 1605-611, DOI:10.1109/CEC.1999.785466
2. Barbosa, HJC and Lemonge, ACC. 2008. "An adaptive penalty method for genetic algorithms in constrained optimization problems". In Frontiers in Evolutionary Robotics, Edited by: Iba, H. Austria: I-Tech Education. 34pp. (ISBN: 978-3-902613-19-6)
3. Bertsekas, DP. 1999. Nonlinear Programming, 2nd, Belmont: Athena Scientific.
4. Birbil, SI. Stochastic global optimization techniques, Ph.D. diss., North Carolina State University, 2002
5. Birbil, SI and Fang, S-C. 2003. An electromagnetism-like mechanism for global optimization. J. Global Optim., 25: 263-282.
6. Birgin, EG, Castillo, R and Martinez, JM. 2004. Numerical comparison of Augmented Lagrangian algorithms for nonconvex problems. Comput. Optim. Appl., 31: 31-56.
7. Birgin, EG, Floudas, CA and Martinez, JM. 2010. Global minimization using an Augmented Lagrangian method with variable lower-level constraints. Math. Program. Ser. A, 125: 139-162.
8. Coello Coello, CA. 2000. Use of a self-adaptive penalty approach for engineering optimization problems. Comput. Ind., 41: 113-127.
9. Deb, K. 1998. An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng., 186: 311-338.
10. Dolan, ED and Moré, JJ. 2002. Benchmarking optimization software with performance profiles. Math. Program., 91: 201-213.
11. Fourer, R, Gay, DM and Kernighan, BW. 1990. A modeling language for mathematical programming. Manag. Sci., 36: 519-554.
12. Hedar, AR and Fukushima, M. 2004. Heuristic pattern search and its hybridization with simulated annealing for nonlinear global optimization. Optim. Methods Softw., 19: 291-308.
13. Hedar, AR and Fukushima, M. 2006. Derivative-free filter simulated annealing method for constrained continuous global optimization. J. Global Optim., 35: 521-549.
14. Karaboga, D and Basturk, B. 2007. "Artificial Bee Colony (ABC) Optimization Algorithm for Solving Constrained Optimization Problems". In Lecture Notes Artificial Intelligence Edited by: Melin, P, Castillo, O, Aguilar, L, Kacprzyk, J and Pedrycz, W. Vol. 4529, 789-798.
15. Liang, JJ, Runarsson, TP, Mezura, E, Clerc, M, Suganthan, PN, Coello, CAC and Deb, K. Problem definitions and evaluation criteria for the CEC2006 special session on constrained real-parameter optimization, 2006. Available athttp://www.ntu.edu.sg/home/EPNSugan/index_files/CEC-06/CEC06.htm
16. Liao, TW. 2010. Two hybrid differential evolution algorithms for engineering design optimization. Appl. Soft Comput., 10: 1188-1199.
17. Liu, J-L and Lin, J-H. 2007. Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization. Eng. Optim., 39: 287-305.
18. Luo, H, Sun, X and Wu, H. 2008. Convergence properties of augmented Lagrangian methods for constrained global optimization. Optim. Methods Softw., 23: 763-778.
19. Petalas, YG, Parsopoulos, KE and Vrahatis, MN. 2007. Memetic particle swarm optimization. Ann. Oper. Res., 156: 99-127.
20. Rocha, AMAC and Fernandes, EMGP. 2008. "Feasibility and Dominance Rules in the Electromagnetism-like Algorithm for Constrained Global Optimization Problems". In Lecture Notes in Computer Science, Computational Science and its Applications Edited by: Gervasi, O, Murgante, B, Laganà, A, Taniar, D and Mun, Y. Vol. 5073, 768-783.
21. Rocha, AMAC and Fernandes, EMGP. 2008. Implementation of the electromagnetism-like algorithm with a constraint-handling technique for engineering optimization problems, IEEE Computer Society: 2008 Eighth International Conference on Hybrid Intelligent Systems. pp. 690-695, ISBN: 978-0-7695-3326-1
22. Rocha, AMAC and Fernandes, EMGP. 2009. Self-adaptive penalties in the electromagnestism-like algorithm for constrained global optimization problems, Proceedings of the 8th World Congress on Structural and Multidisciplinary Optimization, Lisbon: CD. 10pp
23. Rocha, AMAC and Fernandes, EMGP. 2009. Hybridizing the electromagnetism-like algorithm with descent search for solving engineering design problems. Int. J. Comput. Math., 86: 1932-1946.
24. Runarsson, TP and Yao, X. 2000. Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evol. Comput., 4: 284-294.
25. Sedlaczek, K and Eberhard, P. 2007. Augmented Lagrangian particle swarm optimization in mechanism design. J. Syst. Des. Dyn., 1: 410-421.
26. Vaz, AIF and Vicente, LN. 2007. A particle swarm pattern search method for bound constrained global optimization. J. Global Optim., 39: 197-219.
27. Wah, BW and Wang, T. 1999. Efficient and adaptive Lagrange-multipliers methods for nonlinear continuous global optimization. J. Global Optim., 14: 1-25.
28. T. Wang and B.W. Wah, Handling inequality constraints in continuous nonlinear global optimization, J. Integr. Des. Process Sci. 2 (1998),pp. 1-10
29. Zavala, AEM, Aguirre, AH and Diharce, ERV. Constrained optimization via particle evolutionary swarm optimization algorithm (PESO), GECCO'05, 2005,pp. 209-216