Abstract
This chapter is based on a recently published paper [9] of authors of this chapter in which a method for solving bound-constrained non-linear global optimization problems has been proposed. The algorithm obtains a sphere and then generates new trial solutions on its surface. Hence, this algorithm has been named as Spherical Search (SS) algorithm. This chapter starts with an introduction to the SS algorithm and then discusses different components and steps of the algorithm, viz., initialization of population, the concept of a spherical surface, the procedure of generation of trial solutions, selection of new population using greedy selection, stopping criteria, steps of the algorithm, and space and time complexity of the algorithm. Then, the algorithm has been applied to solve 30 bound-constrained global optimization benchmark problems of IEEE CEC 2014 suite and the results of the spherical search algorithm on these benchmark problems have been compared with the results of variants of well-known algorithms such as particle swarm optimization, genetic algorithm, covariance matrix adapted evolution strategy, and Differential Evolution on these problems to demonstrate its performance. Further, the SS algorithm has been applied to solve a model order reduction problem, an example of a real-life complex optimization problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bansal, J.C., Sharma, H.: Cognitive learning in differential evolution and its application to model order reduction problem for single-input single-output systems. Memetic Comput. pp. 1–21 (2012)
Bansal, J.C., Sharma, H., Arya, K.: Model order reduction of single input single output systems using artificial bee colony optimization algorithm. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2011), pp. 85–100. Springer (2011)
Dorigo, M., Birattari, M.: Ant colony optimization. In: Encyclopedia of Machine Learning, pp. 36–39. Springer (2010)
Fogel, L.J., Owens, A.J., Walsh, M.J.: Artificial Intelligence Through Simulated Evolution. Wiley, New York (1966)
Jastrebski, G.A., Arnold, D.V.: Improving evolution strategies through active covariance matrix adaptation. In: IEEE Congress on Evolutionary Computation, CEC 2006, pp. 2814–2821. IEEE (2006)
Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Glob. Optim. 39(3), 459–471 (2007)
Kennedy, J.: Particle swarm optimization. In: Encyclopedia of Machine Learning, pp. 760–766. Springer (2010)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection, vol. 1. MIT press (1992)
Kumar, A., Misra, R.K., Singh, D., Mishra, S., Das, S.: The spherical search algorithm for bound-constrained global optimization problems. Appl. Soft Comput. 85, 105734 (2019)
Liang, J., Qu, B., Suganthan, P.: Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore, Computational Intelligence Laboratory (2013)
Mirjalili, S., Mirjalili, S.M., Lewis, A.: Grey wolf optimizer. Adv. Eng. Softw. 69, 46–61 (2014)
Parouha, R.P., Das, K.N.: A memory based differential evolution algorithm for unconstrained optimization. Appl. Soft Comput. 38, 501–517 (2016)
Rechenberg, I.: Evolution strategy: nature’s way of optimization. In: Optimization: Methods and Applications, Possibilities and Limitations, pp. 106–126. Springer (1989)
Sharma, H., Bansal, J.C., Arya, K.: Fitness based differential evolution. Memetic Comput. 4(4), 303–316 (2012)
Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)
Tang, K.S., Man, K.F., Kwong, S., He, Q.: Genetic algorithms and their applications. Signal Process. Mag. IEEE 13(6), 22–37 (1996)
Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)
Yang, X.S.: A new metaheuristic bat-inspired algorithm. In: Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), pp. 65–74. Springer (2010)
Yao, X., Liu, Y., Lin, G.: Evolutionary programming made faster. IEEE Trans. Evol. Comput. 3(2), 82–102 (1999)
Acknowledgements
The authors would like to thank the referees for their constructive comments which significantly improved the presentation of the chapter.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Misra, R.K., Singh, D., Kumar, A. (2021). Spherical Search Algorithm: A Metaheuristic for Bound-Constrained Optimization. In: Laha, V., Maréchal, P., Mishra, S.K. (eds) Optimization, Variational Analysis and Applications. IFSOVAA 2020. Springer Proceedings in Mathematics & Statistics, vol 355. Springer, Singapore. https://doi.org/10.1007/978-981-16-1819-2_19
Download citation
DOI: https://doi.org/10.1007/978-981-16-1819-2_19
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-16-1818-5
Online ISBN: 978-981-16-1819-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)