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An oracle penalty and modified augmented Lagrangian methods with firefly algorithm for constrained optimization problems

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  • Umesh Balande

    (VNIT)

  • Deepti Shrimankar

    (VNIT)

Abstract

Almost all engineering optimization problems in the real world are constrained in nature. Swarm intelligence is a bio-inspired technique based on studying and observing fireflies, ants, birds and fish in nature. Firefly algorithm (FA) is the most prominent swarm based metaheuristic algorithm used for solving a global optimization problem. This paper presents two new constrained optimization algorithms: (1) firefly algorithm with extended oracle penalty method (FA-EOPM) and (2) modified augmented Lagrangian with firefly algorithm (MAL-FA). These proposed algorithms are applied for solving classic thirteen benchmark constraint problems as well as a few good engineering problem designs. The efficiency, effectiveness, and performance of MAL-FA and FA-EOPM algorithms are estimated on the basis of statistical analysis such as best optimal value, worst value, mean value, p value and standard deviation value against the existing methods. The experimental results show that the proposed MAL-FA algorithm offers better outcomes for most of the cases in terms of the number of function evaluations compared to various optimization algorithms.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:2:d:10.1007_s12351-017-0346-1
    DOI: 10.1007/s12351-017-0346-1
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    References listed on IDEAS

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    1. David W. Coit & Alice E. Smith & David M. Tate, 1996. "Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems," INFORMS Journal on Computing, INFORMS, vol. 8(2), pages 173-182, May.
    2. 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.
    3. Lina Zhang & Liqiang Liu & Xin-She Yang & Yuntao Dai, 2016. "A Novel Hybrid Firefly Algorithm for Global Optimization," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-17, September.
    4. 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.
    5. Garg, Harish, 2016. "A hybrid PSO-GA algorithm for constrained optimization problems," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 292-305.
    6. Martin Schlüter & Matthias Gerdts, 2010. "The oracle penalty method," Journal of Global Optimization, Springer, vol. 47(2), pages 293-325, June.
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    Cited by:

    1. Jinzhong Zhang & Tan Zhang & Gang Zhang & Min Kong, 2023. "Parameter optimization of PID controller based on an enhanced whale optimization algorithm for AVR system," Operational Research, Springer, vol. 23(3), pages 1-26, September.

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