Abstract
This paper presents a novel method to solve unconstrained continuous optimization problems. The proposed method is called SVP (simplex variables partitioning). The SVP method uses three main processes to solve large scale optimization problems. The first process is a variable partitioning process which helps our method to achieve high performance with large scale and high dimensional optimization problems. The second process is an exploration process which generates a trail solution around a current iterate solution by applying the Nelder-Mead method in a random selected partitions. The last process is an intensification process which applies a local search method in order to refine the the best solution so far. The SVP method starts with a random initial solution, then it is divided into partitions. In order to generate a trail solution, the simplex Nelder-Mead method is applied in each partition by exploring neighborhood regions around a current iterate solution. Finally the intensification process is used to accelerate the convergence in the final stage. The performance of the SVP method is tested by using 38 benchmark functions and is compared with 2 scatter search methods from the literature. The results show that the SVP method is promising and producing good solutions with low computational costs comparing to other competing methods.
This work was partially supported by Grant of SGS No. SP2013/70, VSB - Technical University of Ostrava, Czech Republic., and was supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070) and by the Bio-Inspired Methods: research, development and knowledge transfer project, reg. no. CZ.1.07/2.3.00/20.0073 funded by Operational Programme Education for Competitiveness, co-financed by ESF and state budget of the Czech Republic.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-region methods. MPS-SIAM series on optimization. SIAM, Philadelphia (1987)
Duarte, A., Mart, R., Glover, F., Gortazar, F.: Hybrid scatter tabu search for unconstrained global optimization. Ann. Oper. Res. 183, 95–123 (2011a)
Garcia, S., Lozano, M., Herrera, F., Molina, D., Snchez, A.: Global and local real-coded genetic algorithms based on parentcentric crossover operators. Eur. J. Oper. Res. 185, 1088–1113 (2008)
Hedar, A., Fukushima, M.: Hybrid simulated annealing and direct search method for nonlinear unconstrained global optimization. Optim. Methods Softw. 17, 891–912 (2002)
Hedar, A., Fukushima, M.: Minimizing multimodal functions by simplex coding genetic algorithm. Optim. Methods Softw. 18, 265–282 (2003)
Hedar, A., Fukushima, M.: Directed evolutionary programming: towards an improved performance of evolutionary programming. In: Proceedings of Congress on Evolutionary Computation, CEC 2006, IEEE World Congress on Computational Intelligence, Vancouver, Canada, pp. 1521–1528 (July 2006)
Hedar, A., Ali, A.F.: Tabu search with multi-level neighborhood structures for high dimensional problems. Appl. Intell. 37, 189–206 (2012)
Hvattum, L.M., Duarte, A., Glover, F., Mart, R.: Designing effective improvement methods for scatter search: an experimental study on global optimization. Soft Comput. 17, 49–62 (2013)
Hvattum, L.M., Glover, F.: Finding local optima of high dimensional functions using direct search methods. Eur. J. Oper. Res. 195, 31–45 (2009)
Kolda, T.G., Lewies, R.M., Torczon, V.J.: Optimization by direct search: new perspectives on some classical and modern methods. SIAM Rev. 45, 385–482 (2003)
Laguna, M., Mart, R.: Experimental testing of advanced scatter search designs for global optimization of multimodal functions. J. Glob. Optim. 33, 235–255 (2005)
Linhares, A., Yanasse, H.H.: Search intensity versus search diversity: a false trade off? Appl. Intell. 32, 279–291 (2010)
Nelder, J.A., Mead, R.: A simplex method for function minimization. Comput. J. 7, 308–313 (1965)
Mladenovic, N., Drazic, M., Kovac, V., Angalovic, M.: General variable neighborhood search for the continuous optimization. Eur. J. Oper. Res. 191, 753–770 (2008)
Suganthan, P.N., Hansen, N., Liang, J.J., Deb, K., Chen, Y.-P., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization. Technical report, Nanyang Technological University, Singapore (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ali, A.F., Hassanien, A.E., Snášel, V. (2014). The Nelder-Mead Simplex Method with Variables Partitioning for Solving Large Scale Optimization Problems. In: Abraham, A., Krömer, P., Snášel, V. (eds) Innovations in Bio-inspired Computing and Applications. Advances in Intelligent Systems and Computing, vol 237. Springer, Cham. https://doi.org/10.1007/978-3-319-01781-5_25
Download citation
DOI: https://doi.org/10.1007/978-3-319-01781-5_25
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-01780-8
Online ISBN: 978-3-319-01781-5
eBook Packages: EngineeringEngineering (R0)