research-article

Modified Backtracking Search Optimization Algorithm Inspired by Simulated Annealing for Constrained Engineering Optimization Problems

Authors:

Xuewen Xia Academic Editor:

Silvia ConfortoAuthors Info & Claims

Computational Intelligence and Neuroscience, Volume 2018

https://doi.org/10.1155/2018/9167414

Published: 01 January 2018 Publication History

Abstract

The backtracking search optimization algorithm (BSA) is a population-based evolutionary algorithm for numerical optimization problems. BSA has a powerful global exploration capacity while its local exploitation capability is relatively poor. This affects the convergence speed of the algorithm. In this paper, we propose a modified BSA inspired by simulated annealing (BSAISA) to overcome the deficiency of BSA. In the BSAISA, the amplitude control factor (F) is modified based on the Metropolis criterion in simulated annealing. The redesigned F could be adaptively decreased as the number of iterations increases and it does not introduce extra parameters. A self-adaptive ε-constrained method is used to handle the strict constraints. We compared the performance of the proposed BSAISA with BSA and other well-known algorithms when solving thirteen constrained benchmarks and five engineering design problems. The simulation results demonstrated that BSAISA is more effective than BSA and more competitive with other well-known algorithms in terms of convergence speed.

References

[1]

P. Posik, W. Huyer, and L. Pal, “A comparison of global search algorithms for continuous black box optimization,” Evolutionary Computation, vol. 20, no. 4, pp. 509–541, 2012.

Digital Library

[2]

A. P. Piotrowski, M. J. Napiorkowski, J. J. Napiorkowski, and P. M. Rowinski, “Swarm Intelligence and Evolutionary Algorithms: Performance versus speed,” Information Sciences, vol. 384, pp. 34–85, 2017.

Digital Library

[3]

S. Das and A. Konar, “A swarm intelligence approach to the synthesis of two-dimensional IIR filters,” Engineering Applications of Artificial Intelligence, vol. 20, no. 8, pp. 1086–1096, 2007.

Digital Library

[4]

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks, pp. 1942–1948, Perth, Australia, December 1995.

[5]

M. Dorigo, V. Maniezzo, and A. Colorni, “Ant system: optimization by a colony of cooperating agents,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 26, no. 1, pp. 29–41, 1996.

Digital Library

[6]

X. S. Yang and S. Deb, “Cuckoo search via LΘvy flights,” in Proceedings of the In World Congress on Nature Biologically Inspired Computing, pp. 210–214, NaBIC, 2009.

[7]

D. Karaboga, “An idea based on honey bee swarm for numerical optimization,” Erciyes University, Engineering Faculty, Computer Engineering Department, 2005.

[8]

J. Q. Zhang and A. C. Sanderson, “JADE: adaptive differential evolution with optional external archive,” IEEE Transactions on Evolutionary Computation, vol. 13, no. 5, pp. 945–958, 2009.

Digital Library

[9]

S. M. Elsayed, R. A. Sarker, and D. L. Essam, “Adaptive Configuration of evolutionary algorithms for constrained optimization,” Applied Mathematics and Computation, vol. 222, pp. 680–711, 2013.

Digital Library

[10]

J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, University of Michigan Press, Oxford, UK, 1975.

Digital Library

[11]

R. Storn and K. Price, “Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997.

Digital Library

[12]

Z. Hu, Q. Su, X. Yang, and Z. Xiong, “Not guaranteeing convergence of differential evolution on a class of multimodal functions,” Applied Soft Computing, vol. 41, pp. 479–487, 2016.

Digital Library

[13]

Q. Su and Z. Hu, “Color image quantization algorithm based on self-adaptive differential Evolution,” Computational Intelligence and Neuroscience, vol. 2013, 8 pages, 2013.

Digital Library

[14]

Z. Hu, Q. Su, and X. Xia, “Multiobjective image color quantization algorithm based on self-adaptive hybrid differential evolution,” Computational Intelligence and Neuroscience, vol. 2016, 12 pages, 2016.

Digital Library

[15]

C. Igel, N. Hansen, and S. Roth, “Covariance matrix adaptation for multi-objective optimization,” Evolutionary Computation, vol. 15, no. 1, pp. 1–28, 2007.

Digital Library

[16]

P. Civicioglu, “Backtracking search optimization algorithm for numerical optimization problems,” Applied Mathematics and Computation, vol. 219, no. 15, pp. 8121–8144, 2013.

Digital Library

[17]

A. El-Fergany, “Optimal allocation of multi-type distributed generators using backtracking search optimization algorithm,” International Journal of Electrical Power & Energy Systems, vol. 64, pp. 1197–1205, 2015.

[18]

M. Modiri-Delshad and N. A. Rahim, “Multi-objective backtracking search algorithm for economic emission dispatch problem,” Applied Soft Computing, vol. 40, pp. 479–494, 2016.

Digital Library

[19]

S. D. Madasu, M. L. S. S. Kumar, and A. K. Singh, “Comparable investigation of backtracking search algorithm in automatic generation control for two area reheat interconnected thermal power system,” Applied Soft Computing, vol. 55, pp. 197–210, 2017.

Digital Library

[20]

J. A. Ali, M. A. Hannan, A. Mohamed, and M. G. M. Abdolrasol, “Fuzzy logic speed controller optimization approach for induction motor drive using backtracking search algorithm,” Measurement, vol. 78, pp. 49–62, 2016.

[21]

M. A. Hannan, J. A. Ali, A. Mohamed, and M. N. Uddin, “A Random Forest Regression Based Space Vector PWM Inverter Controller for the Induction Motor Drive,” IEEE Transactions on Industrial Electronics, vol. 64, no. 4, pp. 2689–2699, 2017.

[22]

K. Guney, A. Durmus, and S. Basbug, “Backtracking search optimization algorithm for synthesis of concentric circular antenna arrays,” International Journal of Antennas and Propagation, vol. 2014, 11 pages, 2014.

[23]

R. Muralidharan, V. Athinarayanan, G. K. Mahanti, and A. Mahanti, “QPSO versus BSA for failure correction of linear array of mutually coupled parallel dipole antennas with fixed side lobe level and VSWR,” Advances in Electrical Engineering, vol. 2014, 7 pages, 2014.

[24]

M. Eskandari and Ö. Toygar, “Selection of optimized features and weights on face-iris fusion using distance images,” Computer Vision and Image Understanding, vol. 137, article no. 2225, pp. 63–75, 2015.

Digital Library

[25]

U. H. Atasevar, P. Civicioglu, E. Besdok, and C. Ozkan, “A new unsupervised change detection approach based on DWT image fusion and backtracking search optimization algorithm for optical remote sensing data,” in Proceedings of the ISPRS Technical Commission VII Mid-Term Symposium 2014, pp. 15–18, October 2014.

[26]

S. K. Agarwal, S. Shah, and R. Kumar, “Classification of mental tasks from EEG data using backtracking search optimization based neural classifier,” Neurocomputing, vol. 166, pp. 397–403, 2015.

Digital Library

[27]

L. Zhang and D. Zhang, “Evolutionary cost-sensitive extreme learning machine,” IEEE Transactions on Neural Networks and Learning Systems, vol. 28, no. 12, pp. 3045–3060, 2016.

[28]

F. Zou, D. Chen, S. Li, R. Lu, and M. Lin, “Community detection in complex networks: Multi-objective discrete backtracking search optimization algorithm with decomposition,” Applied Soft Computing, vol. 53, pp. 285–295, 2017.

Digital Library

[29]

C. Zhang, J. Zhou, C. Li, W. Fu, and T. Peng, “A compound structure of ELM based on feature selection and parameter optimization using hybrid backtracking search algorithm for wind speed forecasting,” Energy Conversion and Management, vol. 143, pp. 360–376, 2017.

[30]

C. Lu, L. Gao, X. Li, and P. Chen, “Energy-efficient multi-pass turning operation using multi-objective backtracking search algorithm,” Journal of Cleaner Production, vol. 137, pp. 1516–1531, 2016.

[31]

M. Akhtar, M. A. Hannan, R. A. Begum, H. Basri, and E. Scavino, “Backtracking search algorithm in CVRP models for efficient solid waste collection and route optimization,” Waste Management, vol. 61, pp. 117–128, 2017.

[32]

M. S. Ahmed, A. Mohamed, T. Khatib, H. Shareef, R. Z. Homod, and J. A. Ali, “Real time optimal schedule controller for home energy management system using new binary backtracking search algorithm,” Energy and Buildings, vol. 138, pp. 215–227, 2017.

[33]

S. O. Kolawole and H. Duan, “Backtracking search algorithm for non-aligned thrust optimization for satellite formation,” in Proceedings of the 11th IEEE International Conference on Control and Automation (IEEE ICCA '14), pp. 738–743, June 2014.

[34]

Q. Lin, L. Gao, X. Li, and C. Zhang, “A hybrid backtracking search algorithm for permutation flow-shop scheduling problem,” Computers & Industrial Engineering, vol. 85, pp. 437–446, 2015.

Digital Library

[35]

J. Lin, “Oppositional backtracking search optimization algorithm for parameter identification of hyperchaotic systems,” Nonlinear Dynamics, vol. 80, no. 1-2, pp. 209–219, 2015.

[36]

Q. L. Xu, N. Guo, and L. Xu, “Opposition-based backtracking search algorithm for numerical optimization problems,” in Proceedings of the In International Conference on Intelligent Science and Big Data Engineering, pp. 223–234, 2015.

[37]

X. Yuan, B. Ji, Y. Yuan, R. M. Ikram, X. Zhang, and Y. Huang, “An efficient chaos embedded hybrid approach for hydro-thermal unit commitment problem,” Energy Conversion and Management, vol. 91, pp. 225–237, 2015.

[38]

X. Yuan, X. Wu, H. Tian, Y. Yuan, and R. M. Adnan, “Parameter identification of nonlinear muskingum model with backtracking search algorithm,” Water Resources Management, vol. 30, no. 8, pp. 2767–2783, 2016.

[39]

S. Vitayasak and P. Pongcharoen, “Backtracking search algorithm for designing a robust machine layout,” WIT Transactions on Engineering Sciences, vol. 95, pp. 411–420, 2014.

[40]

S. Vitayasak, P. Pongcharoen, and C. Hicks, “A tool for solving stochastic dynamic facility layout problems with stochastic demand using either a Genetic Algorithm or modified Backtracking Search Algorithm,” International Journal of Production Economics, vol. 190, pp. 146–157, 2017.

[41]

M. Li, H. Zhao, and X. Weng, “Backtracking search optimization algorithm with comprehensive learning strategy,” Journal of Systems Engineering and Electronics, vol. 37, no. 4, pp. 958–963, 2015.

[42]

W. Zhao, L. Wang, Y. Yin, B. Wang, and Y. Wei, “An improved backtracking search algorithm for constrained optimization problems,” in Proceedings of the International Conference on Knowledge Science, Engineering and Management, pp. 222–233, Springer International Publishing, 2014.

[43]

L. Wang, Y. Zhong, Y. Yin, W. Zhao, B. Wang, and Y. Xu, “A hybrid backtracking search optimization algorithm with differential evolution,” Mathematical Problems in Engineering, vol. 2015, p. 16, 2015.

[44]

S. Das, D. Mandal, R. Kar, and S. P. Ghoshal, “Interference suppression of linear antenna arrays with combined Backtracking Search Algorithm and Differential Evolution,” in Proceedings of the 3rd International Conference on Communication and Signal Processing (ICCSP '14), pp. 162–166, April 2014.

[45]

S. Das, D. Mandal, R. Kar, and S. P. Ghoshal, “A new hybridized backscattering search optimization algorithm with differential evolution for sidelobe suppression of uniformly excited concentric circular antenna arrays,” International Journal of RF and Microwave Computer-Aided Engineering, vol. 25, no. 3, pp. 262–268, 2015.

[46]

S. Mallick, R. Kar, D. Mandal, and S. P. Ghoshal, “CMOS analogue amplifier circuits optimisation using hybrid backtracking search algorithm with differential evolution,” Journal of Experimental and Theoretical Artificial Intelligence, pp. 1–31, 2015.

[47]

D. Chen, F. Zou, R. Lu, and P. Wang, “Learning backtracking search optimisation algorithm and its application,” Information Sciences, vol. 376, pp. 71–94, 2017.

Digital Library

[48]

A. F. Ali, “A memetic backtracking search optimization algorithm for economic dispatch problem,” Egyptian Computer Science Journal, vol. 39, no. 2, pp. 56–71, 2015.

[49]

Y. Wu, Q. Tang, L. Zhang, and X. He, “Solving stochastic two-sided assembly line balancing problem via hybrid backtracking search optimization algorithm,” Journal of Wuhan University of Science and Technology (Natural Science Edition), vol. 39, no. 2, pp. 121–127, 2016.

[50]

Z. Su, H. Wang, and P. Yao, “A hybrid backtracking search optimization algorithm for nonlinear optimal control problems with complex dynamic constraints,” Neurocomputing, vol. 186, pp. 182–194, 2016.

Digital Library

[51]

S. Wang, X. Da, M. Li, and T. Han, “Adaptive backtracking search optimization algorithm with pattern search for numerical optimization,” Journal of Systems Engineering and Electronics, vol. 27, no. 2, pp. 395–406, 2016.

[52]

H. Duan and Q. Luo, “Adaptive backtracking search algorithm for induction magnetometer optimization,” IEEE Transactions on Magnetics, vol. 50, no. 12, pp. 1–6, 2014.

[53]

X. J. Wang, S. Y. Liu, and W. K. Tian, “Improved backtracking search optimization algorithm with new effective mutation scale factor and greedy crossover strategy,” Journal of Computer Applications, vol. 34, no. 9, pp. 2543–2546, 2014.

[54]

W. K. Tian, S. Y. Liu, and X. J. Wang, “Study and improvement of backtracking search optimization algorithm based on differential evolution,” Application Research of Computers, vol. 32, no. 6, pp. 1653–1662, 2015.

[55]

A. Askarzadeh and L. dos Santos Coelho, “A backtracking search algorithm combined with Burger's chaotic map for parameter estimation of PEMFC electrochemical model,” International Journal of Hydrogen Energy, vol. 39, pp. 11165–11174, 2014.

[56]

X. Chen, S. Y. Liu, and Y. Wang, “Emergency resources scheduling based on improved backtracking search optimization algorithm,” Computer Applications and Software, vol. 32, no. 12, pp. 235–238, 2015.

[57]

S. Nama, A. K. Saha, and S. Ghosh, “Improved backtracking search algorithm for pseudo dynamic active earth pressure on retaining wall supporting c-Φ backfill,” Applied Soft Computing, vol. 52, pp. 885–897, 2017.

Digital Library

[58]

G. Karafotias, M. Hoogendoorn, and A. E. Eiben, “Parameter Control in Evolutionary Algorithms: Trends and Challenges,” IEEE Transactions on Evolutionary Computation, vol. 19, no. 2, pp. 167–187, 2015.

Digital Library

[59]

N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, “Equation of state calculations by fast computing machines,” The Journal of Chemical Physics, vol. 21, no. 6, pp. 1087–1092, 1953.

[60]

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, no. 4598, pp. 671–680, 1983.

[61]

D. Karaboga and B. Akay, “A comparative study of artificial Bee colony algorithm,” Applied Mathematics and Computation, vol. 214, no. 1, pp. 108–132, 2009.

Digital Library

[62]

C. Zhang, Q. Lin, L. Gao, and X. Li, “Backtracking Search Algorithm with three constraint handling methods for constrained optimization problems,” Expert Systems with Applications, vol. 42, no. 21, pp. 7831–7845, 2015.

Digital Library

[63]

T. P. Runarsson and X. Yao, “Stochastic ranking for constrained evolutionary optimization,” IEEE Transactions on Evolutionary Computation, vol. 4, no. 3, pp. 284–294, 2000.

Digital Library

[64]

A. S. B. Ullah, R. Sarker, D. Cornforth, and C. Lokan, “AMA: A new approach for solving constrained real-valued optimization problems,” Soft Computing, vol. 13, no. 8-9, pp. 741–762, 2009.

Digital Library

[65]

A. R. Hedar and M. Fukushima, “Derivative-free filter simulated annealing method for constrained continuous global optimization,” Journal of Global Optimization, vol. 35, no. 4, pp. 521–549, 2006.

Digital Library

[66]

R. L. Becerra and C. A. Coello, “Cultured differential evolution for constrained optimization,” Computer Methods Applied Mechanics and Engineering, vol. 195, no. 33–36, pp. 4303–4322, 2006.

[67]

D. Karaboga and B. Akay, “A modified Artificial Bee Colony (ABC) algorithm for constrained optimization problems,” Applied Soft Computing, vol. 11, no. 3, pp. 3021–3031, 2011.

Digital Library

[68]

C.-H. Lin, “A rough penalty genetic algorithm for constrained optimization,” Information Sciences, vol. 241, pp. 119–137, 2013.

Digital Library

[69]

M. Zhang, W. Luo, and X. Wang, “Differential evolution with dynamic stochastic selection for constrained optimization,” Information Sciences, vol. 178, no. 15, pp. 3043–3074, 2008.

Digital Library

[70]

Y. Wang, Z. X. Cai, Y. R. Zhou, and Z. Fan, “Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique,” Structural and Multidisciplinary Optimization, vol. 37, no. 4, pp. 395–413, 2009.

[71]

H. Liu, Z. Cai, and Y. Wang, “Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization,” Applied Soft Computing, vol. 10, no. 2, pp. 629–640, 2010.

Digital Library

[72]

L. Wang and L.-P. Li, “An effective differential evolution with level comparison for constrained engineering design,” Structural and Multidisciplinary Optimization, vol. 41, no. 6, pp. 947–963, 2010.

[73]

C. A. C. Coello and E. M. Montes, “Constraint-handling in genetic algorithms through the use of dominance-based tournament selection,” Advanced Engineering Informatics, vol. 16, no. 3, pp. 193–203, 2002.

[74]

E. Mezura-Montes, C. A. C. Coello, and J. Vela'zquez-Reyes, “Increasing successful offspring and diversity in differential evolution for engineering design,” in Proceedings of the Seventh International Conference on Adaptive Computing in Design and Manufacture (ACDM '06), pp. 131–139, 2006.

[75]

Q. He and L. Wang, “An effective co-evolutionary particle swarm optimization for constrained engineering design problems,” Engineering Applications of Artificial Intelligence, vol. 20, no. 1, pp. 89–99, 2007.

Digital Library

[76]

Q. He and L. Wang, “A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization,” Applied Mathematics and Computation, vol. 186, no. 2, pp. 1407–1422, 2007.

[77]

B. Akay and D. Karaboga, “Artificial bee colony algorithm for large-scale problems and engineering design optimization,” Journal of Intelligent Manufacturing, vol. 23, no. 4, pp. 1001–1014, 2012.

[78]

A. Sadollah, A. Bahreininejad, H. Eskandar, and M. Hamdi, “Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems,” Applied Soft Computing, vol. 13, no. 5, pp. 2592–2612, 2013.

Digital Library

[79]

E. Cuevas and M. Cienfuegos, “A new algorithm inspired in the behavior of the social-spider for constrained optimization,” Expert Systems with Applications, vol. 41, no. 2, pp. 412–425, 2014.

Digital Library

[80]

J. Derrac, S. García, D. Molina, and F. Herrera, “A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms,” Swarm and Evolutionary Computation, vol. 1, no. 1, pp. 3–18, 2011.

[81]

Y. Miao, Q. Su, Z. Hu, and X. Xia, “Modified differential evolution algorithm with onlooker bee operator for mixed discrete-continuous optimization,” SpringerPlus, vol. 5, no. 1, article no. 1914, 2016.

[82]

E. L. Yu and P. N. Suganthan, “Ensemble of niching algorithms,” Information Sciences, vol. 180, no. 15, pp. 2815–2833, 2010.

Digital Library

[83]

M. Li, D. Lin, and J. Kou, “A hybrid niching PSO enhanced with recombination-replacement crowding strategy for multimodal function optimization,” Applied Soft Computing, vol. 12, no. 3, pp. 975–987, 2012.

Digital Library

Cited By

Layeb A(2022)Tangent search algorithm for solving optimization problemsNeural Computing and Applications10.1007/s00521-022-06908-z34:11(8853-8884)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1007/s00521-022-06908-z
Zaman HGharehchopogh F(2022)An improved particle swarm optimization with backtracking search optimization algorithm for solving continuous optimization problemsEngineering with Computers10.1007/s00366-021-01431-638:Suppl 4(2797-2831)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s00366-021-01431-6

Index Terms

Modified Backtracking Search Optimization Algorithm Inspired by Simulated Annealing for Constrained Engineering Optimization Problems

Index terms have been assigned to the content through auto-classification.

Recommendations

Backtracking Search Optimization Algorithm for numerical optimization problems

This paper introduces the Backtracking Search Optimization Algorithm (BSA), a new evolutionary algorithm (EA) for solving real-valued numerical optimization problems. EAs are popular stochastic search algorithms that are widely used to solve non-linear, ...
A novel modified BSA inspired by species evolution rule and simulated annealing principle for constrained engineering optimization problems
Abstract
The backtracking search optimization algorithm (BSA) is one of the recently proposed evolutionary algorithms (EAs) for solving numerical optimization problems. In this study, a nature-inspired modified BSA (called SSBSA) is proposed and ...
Multiobjective Optimization and Hybrid Evolutionary Algorithm to Solve Constrained Optimization Problems

This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In ...

Comments

Information & Contributors

Information

Published In

cover image Computational Intelligence and Neuroscience

Computational Intelligence and Neuroscience Volume 2018, Issue

2018

1665 pages

ISSN:1687-5265

EISSN:1687-5273

Issue’s Table of Contents

Copyright © 2018 Hailong Wang et al.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Publisher

Hindawi Limited

London, United Kingdom

Publication History

Published: 01 January 2018

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

2
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 14 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Layeb A(2022)Tangent search algorithm for solving optimization problemsNeural Computing and Applications10.1007/s00521-022-06908-z34:11(8853-8884)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1007/s00521-022-06908-z
Zaman HGharehchopogh F(2022)An improved particle swarm optimization with backtracking search optimization algorithm for solving continuous optimization problemsEngineering with Computers10.1007/s00366-021-01431-638:Suppl 4(2797-2831)Online publication date: 1-Oct-2022
https://dl.acm.org/doi/10.1007/s00366-021-01431-6

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Media

Figures

Other

Tables

View Issue’s Table of Contents