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Guided Hybrid Modified Simulated Annealing Algorithm for Solving Constrained Global Optimization Problems

Author

Listed:
  • Khalid Abdulaziz Alnowibet

    (Statistics and Operations Research Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia)

  • Salem Mahdi

    (Educational Research and Development Center Sanaa, Sanaa 31220, Yemen)

  • Mahmoud El-Alem

    (Department of Mathematics & Computer Science, Faculty of Science, Alexandria University, Alexandria 21544, Egypt)

  • Mohamed Abdelawwad

    (Institute for Computer Architecture and System Programming, University of Kassel, 34127 Kassel, Germany)

  • Ali Wagdy Mohamed

    (Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
    Department of Mathematics and Actuarial Science, School of Sciences Engineering, The American University in Cairo, Cairo 11835, Egypt)

Abstract

In this paper, a hybrid gradient simulated annealing algorithm is guided to solve the constrained optimization problem. In trying to solve constrained optimization problems using deterministic, stochastic optimization methods or hybridization between them, penalty function methods are the most popular approach due to their simplicity and ease of implementation. There are many approaches to handling the existence of the constraints in the constrained problem. The simulated-annealing algorithm (SA) is one of the most successful meta-heuristic strategies. On the other hand, the gradient method is the most inexpensive method among the deterministic methods. In previous literature, the hybrid gradient simulated annealing algorithm (GLMSA) has demonstrated efficiency and effectiveness to solve unconstrained optimization problems. In this paper, therefore, the GLMSA algorithm is generalized to solve the constrained optimization problems. Hence, a new approach penalty function is proposed to handle the existence of the constraints. The proposed approach penalty function is used to guide the hybrid gradient simulated annealing algorithm (GLMSA) to obtain a new algorithm (GHMSA) that finds the constrained optimization problem. The performance of the proposed algorithm is tested on several benchmark optimization test problems and some well-known engineering design problems with varying dimensions. Comprehensive comparisons against other methods in the literature are also presented. The results indicate that the proposed method is promising and competitive. The comparison results between the GHMSA and the other four state-Meta-heuristic algorithms indicate that the proposed GHMSA algorithm is competitive with, and in some cases superior to, other existing algorithms in terms of the quality, efficiency, convergence rate, and robustness of the final result.

Suggested Citation

  • Khalid Abdulaziz Alnowibet & Salem Mahdi & Mahmoud El-Alem & Mohamed Abdelawwad & Ali Wagdy Mohamed, 2022. "Guided Hybrid Modified Simulated Annealing Algorithm for Solving Constrained Global Optimization Problems," Mathematics, MDPI, vol. 10(8), pages 1-25, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1312-:d:794128
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    References listed on IDEAS

    as
    1. Irene Samora & Mário J. Franca & Anton J. Schleiss & Helena M. Ramos, 2016. "Simulated Annealing in Optimization of Energy Production in a Water Supply Network," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(4), pages 1533-1547, March.
    2. Irene Samora & Mário Franca & Anton Schleiss & Helena Ramos, 2016. "Simulated Annealing in Optimization of Energy Production in a Water Supply Network," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(4), pages 1533-1547, March.
    3. M. M. El-Alem & S. El-Sayed & B. El-Sobky, 2004. "Local Convergence of the Interior-Point Newton Method for General Nonlinear Programming," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 487-502, March.
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    5. Ali Wagdy Mohamed, 2018. "A novel differential evolution algorithm for solving constrained engineering optimization problems," Journal of Intelligent Manufacturing, Springer, vol. 29(3), pages 659-692, March.
    6. L. Ingber, 1993. "Simulated annealing: Practice versus theory," Lester Ingber Papers 93sa, Lester Ingber.
    7. Amal Amin Mohamed & Salah Kamel & Mohamed H. Hassan & Mohamed I. Mosaad & Mansour Aljohani, 2022. "Optimal Power Flow Analysis Based on Hybrid Gradient-Based Optimizer with Moth–Flame Optimization Algorithm Considering Optimal Placement and Sizing of FACTS/Wind Power," Mathematics, MDPI, vol. 10(3), pages 1-31, January.
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    Citations

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    Cited by:

    1. Savin Treanţă, 2022. "Variational Problems and Applications," Mathematics, MDPI, vol. 11(1), pages 1-4, December.
    2. Eltiyeb Ali & Salem Mahdi, 2023. "Adaptive Hybrid Mixed Two-Point Step Size Gradient Algorithm for Solving Non-Linear Systems," Mathematics, MDPI, vol. 11(9), pages 1-35, April.
    3. Ahmad M. Alshamrani & Adel Fahad Alrasheedi & Khalid Abdulaziz Alnowibet & Salem Mahdi & Ali Wagdy Mohamed, 2022. "A Hybrid Stochastic Deterministic Algorithm for Solving Unconstrained Optimization Problems," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    4. Khalid Abdulaziz Alnowibet & Salem Mahdi & Ahmad M. Alshamrani & Karam M. Sallam & Ali Wagdy Mohamed, 2022. "A Family of Hybrid Stochastic Conjugate Gradient Algorithms for Local and Global Minimization Problems," Mathematics, MDPI, vol. 10(19), pages 1-37, October.
    5. Yunshan Sun & Qian Huang & Ting Liu & Yuetong Cheng & Yanqin Li, 2023. "Multi-Strategy Enhanced Harris Hawks Optimization for Global Optimization and Deep Learning-Based Channel Estimation Problems," Mathematics, MDPI, vol. 11(2), pages 1-28, January.
    6. Wang, Huijie & Qiu, Baoyun & Zhao, Fangling & Yan, Tianxu, 2023. "Method for increasing net power of power plant based on operation optimization of circulating cooling water system," Energy, Elsevier, vol. 282(C).

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