Abstract
Differential evolution (DE) has become a very powerful tool for global continuous optimization problems. Parameter adaptations are the most commonly used techniques to improve its performance. The adoption of these techniques has assisted the success of many adaptive DE variants. However, most studies on these adaptive DEs are limited to some small-scale problems, e.g. with less than 100 decision variables, which may be quite small comparing to the requirements of real-world applications. The scalability performance of adaptive DE is still unclear. In this paper, based on the analyses of similarities and drawbacks of existing parameter adaptation schemes in DE, we propose a generalized parameter adaptation scheme. Applying the scheme to DE results in a new generalized adaptive DE (GaDE) algorithm. The scalability performance of GaDE is evaluated on 19 benchmark functions with problem scale from 50 to 1,000 decision variables. Based on the comparison with three other algorithms, GaDE is very competitive in both the performance and scalability aspects.
Similar content being viewed by others
Notes
Without loss of generality, we consider only minimization problem in this paper.
The Holm procedure test is not performed on the result of 1,000-dimensional functions because the results of G-CMA-ES are not available for such problems.
References
Auger A, Hansen N (2005) A restart CMA evolution strategy with increasing population size. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 1769–1776
Brest J, Greiner S, Boskovic B, Mernik M, Žumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657
Benchmark functions for the Special Issue of Soft Computing. http://sci2s.ugr.es/eamhco/updated-functions1-19.pdf
Components and Parameters of DE, Real-coded CHC, and G-CMA-ES. http://sci2s.ugr.es/eamhco/descriptions.pdf
Das S, Abraham A, Chakraborty UK, Konar A (2009) Differential evolution using a neighborhood-based mutation operator. IEEE Trans Evol Comput 13(3):526–553
Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Whitley LD, (ed), Foundations of genetic algorithms 2. Morgan Kaufmann, pp 187–202
Eshelman LJ (1991) The CHC adaptive search algorithm: How to have safe search when engaging in nontraditional genetic recombination. Found Genetic Algorithms 1:265–283
Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. Found Genetic Algorithms 2(1993):187–202
Experimental results of differential evolution with exponential crossover and binomial crossover. http://sci2s.ugr.es/eamhco/decross_values.xls
García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms behaviour: a case study on the CEC2005 special session on real parameter optimization. J Heuristics 15(6):617–644
Hansen N (2005) Compilation of results on the CEC benchmark function set, technical report, vol 13. Institute of Computational Science, ETH Zurich, Switerland
Hansen N, Ostermeier A (2001) Completely derandomized self-adaptation in evolution strategies. Evol Comput 9(2):159–195
Hansen N, Kern S (2004) Evaluating the CMA evolution strategy on multimodal test functions. In: Proceedings of the eighth international conference on parallel problem solving from nature (PPSN VIII), pp 282–291
Liu Y, Yao X, Zhao Q, Higuchi T (2001) Scaling up fast evolutionary programming with cooperative coevolution. In: Proceedings of the 2001 congress on evolutionary computation, pp 1101–1108
Lee CY, Yao X (2004) Evolutionary programming using mutations based on the Lévy probability distribution. IEEE Trans Evol Comput 8(1):1–13
Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33(1):61–106
Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization. Springer, Berlin. ISBN:3-540-20950-6
Peng F, Tang K, Chen G, Yao X (2009) Population-based algorithm portfolios for numerical optimization. IEEE Trans Evol Comput (in press)
Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: Proceedings of the 2005 IEEE congress on evolutionary computation, vol 2, pp 1785–1791
Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optimization 11(4):341–359
Storn R (1999) System design by constraint adaptation and differential evolution. IEEE Trans Evol Comput 3(1):22–34
Tang K, Li X, Suganthan PN, Yang Z, Weise T (2009) Benchmark Functions for the CEC2010 Special session and competition on large-scale global optimization, technical report. Nature Inspired Computation and Applications Laboratory, University of Science and Technology of China, China. http://nical.ustc.edu.cn/cec10ss.php
Vesterstrom J, Thomsen R (2004) A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. In: Proceedings of the 2004 IEEE congress on evolutionary computation, vol 2, pp 1980–1987
Whitley D, Rana S, Dzubera J, Mathias KE (1996) Evaluating evolutionary algorithms. Artif Intell 85(1–2):245–276
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82
Yang Z, Tang K, Yao X (2008) Large scale evolutionary optimization using cooperative coevolution. Inf Sci 178(15):2985–2999
Yang Z, He J, Yao X (2008) Making a difference to differential evolution. In: Michalewicz Z, Siarry P, (eds) Advances in metaheuristics for hard optimization. Springer, Berlin, pp 397–414
Yang Z, Tang K, Yao X (2008) Self-adaptive differential evolution with neighborhood search. In: Proceedings of the 2008 IEEE congress on evolutionary computation, pp 1110–1116
Yang Z, Zhang J, Tang K, Yao X, Sanderson AC (2009) An adaptive coevolutionary differential evolution algorithm for large-scale optimization. In: Proceedings of the 2009 IEEE congress on evolutionary computation, pp 102–109
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102
Zaharie D (2002) Critical values for the control parameters of differential evolution algorithms. In: Proceedings of the 8th international conference on soft computing, pp 62–67
Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958
Acknowledgments
This work was partially supported by the Fund for Foreign Scholars in University Research and Teaching Programs (Grant No. B07033), National Natural Science Foundation of China Grants (No. 60802036 and U0835002), and an EPSRC project (No. EP/D052785/1) on “SEBASE: Software Engineering By Automated SEarch”.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yang, Z., Tang, K. & Yao, X. Scalability of generalized adaptive differential evolution for large-scale continuous optimization. Soft Comput 15, 2141–2155 (2011). https://doi.org/10.1007/s00500-010-0643-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-010-0643-6