Abstract
Differential evolution (DE) is a fast and robust evolutionary algorithm for global optimization. It has been widely used in many areas. Biogeography-based optimization (BBO) is a new biogeography inspired algorithm. It mainly uses the biogeography-based migration operator to share the information among solutions. In this paper, we propose a hybrid DE with BBO, namely DE/BBO, for the global numerical optimization problem. DE/BBO combines the exploration of DE with the exploitation of BBO effectively, and hence it can generate the promising candidate solutions. To verify the performance of our proposed DE/BBO, 23 benchmark functions with a wide range of dimensions and diverse complexities are employed. Experimental results indicate that our approach is effective and efficient. Compared with other state-of-the-art DE approaches, DE/BBO performs better, or at least comparably, in terms of the quality of the final solutions and the convergence rate. In addition, the influence of the population size, dimensionality, different mutation schemes, and the self-adaptive control parameters of DE are also studied.
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Notes
The paired t-test determines whether two paired sets differ from each other in a significant way under the assumptions that the paired differences are independent and identically normally distributed (Goulden 1956).
The source code of DE/EDA is available online at: http://cswww.essex.ac.uk/staff/qzhang/IntrotoResearch/HybridEDA.htm.
References
Alatas B, Akin E, Karci A (2008) MODENAR: multi-objective differential evolution algorithm for mining numeric association rules. Appl Soft Comput 8(1):646–656
Auger A, Hansen N (2004) A restart CMA evolution strategy with increasing population size. In: Proceedings of the 2005 IEEE congress on evolutionary computation, pp 1769–1776
Bäck T (1996) Evolutionary algorithms in theory and Practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, Oxford, UK
Brest J, Maučec MS (2008) Population size reduction for the differential evolution algorithm. Appl Intell 29(3):228–247
Brest J, Greiner S, Bošković 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
Caponio A, Neri F, Tirronen V (2009) Super-fit control adaptation in memetic differential evolution frameworks. Soft Comput 13(8–9):811–831
Chakraborty U (2008) Advances in differential evolution. Springer, Berlin
Das S, Abraham A, Konar A (2008) Automatic clustering using an improved differential evolution algorithm. IEEE Trans Syst Man Cybern A 38(1):218–237
Das S, Konar A, Chakraborty UK (2005) Two improved differential evolution schemes for faster global search. In: Beyer HG, O’Reilly UM (eds) Genetic and evolutionary computation conference, GECCO 2005, Proceedings, ACM, Washington DC, USA, June 25–29, 2005, pp 991–998
Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30
Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Global Opt 27(1):105–129
Feoktistov V (2006) Differential evolution: in search of solutions. Springer, New York
Feoktistov V, Janaqi S (2004) Generalization of the strategies in differential evolution. IEEE Comput Soc, Los Alamitos, CA, USA, p 165a
Gäperle R, Müler S, Koumoutsakos P (2002) A parameter study for differential evolution. In: Proceedings of WSEAS International conference on advances in intelligent systems, fuzzy systems, evolutionary computation, pp 293–298
García S, Herrera F (2008) An extension on “statistical comparisons of classifiers over multiple data sets” for all pairwise comparisons. J Mach Learn Res 9:2677–2694
García S, Fernandez A, Luengo J, Herrera F (2009a) A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability. Soft Comput 13(10):959–977. doi:10.1007/s00500-008-0392-y
García S, Molina D, Lozano M, Herrera F (2009b) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15:617–644. doi:10.1007/s10732-008-9080-4
Gong W, Cai Z, Ling CX (2006) ODE: afast and robust differential evolution based on orthogonal design. In: AI 2006: advances in artificial intelligence, 19th Australian joint conference on artificial intelligence, Hobart, Australia, December 4–8, 2006, Proceedings, vol 4304. Springer, Berlin, German, pp 709–718
Goulden CH (1956) Methods of statistical analysis, 2nd ed. Wiley, New York
Grosan C, Abraham A, Ishibuchi H (2009) Hybrid evolutionary algorithms. Springer, Berlin, Germany
Hansen N, Kern S (2004) Evaluating the CMA evolution strategy on multimodal test functions. In: Proceedings of the parallel problem solving for nature—PPSN VIII, vol LNCS 3242, pp 282–291
Herrera FML (2000) Two-loop real-coded genetic algorithms with adaptive control of mutation step sizes. Appl Intell 13(3):187–204
Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for behavioural analysis. Artif Intell Rev 12:265–319
Jiao L, Li Y, Gong M, Zhang X (2008) Quantum-inspired immune clonal algorithm for global optimization. IEEE Trans Syst Man Cybern B 38(5):1234–1253
Kaelo P, Ali MM (2007) Differential evolution algorithms using hybrid mutation. Comput Optim Appl 37(2):231–246
Langdon WB, Poli R (2007) Evolving problems to learn about particle swarm optimizers and other search algorithms. IEEE Trans Evol Comput 11(5):561–578
Liang JJ, Qin AK, Suganthan PN, Baskar S (2006) Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans Evol Comput 10(3):281–295
Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9(6):448–462
Lozano M, García-Martínez C (2010) Hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification: overview and progress report. Comput Oper Res 37(3):481–497
Lozano M, Herrera F, Krasnogor N, Molina D (2004) Real-coded memetic algorithms with crossover hill-climbing. Evol Comput 12(3):273–302
Nobakhti A, Wang H (2008) A simple self-adaptive differential evolution algorithm with application on the alstom gasifier. Appl Soft Comput 8(1):350–370
Noman N, Iba H (2005) Enhancing differential evolution performance with local search for high dimensional function optimization. In: Beyer HG, O’Reilly UM (eds) Genetic and evolutionary computation conference, GECCO 2005, Proceedings. ACM, Washington DC, USA, pp 967–974
Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12(1):107–125
Onwubolu GC, Davendra D (2009) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, Berlin
Price K, Storn R, Lampinen J (2005) Differential evolution: a practical approach to global optimization. Springer, Berlin
Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: IEEE congress on evolutionary computation (CEC2005), IEEE, 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
Rahnamayan S, Tizhoosh H, Salama M (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79
Salman A, Engelbrecht AP, Omran MGH (2007) Empirical analysis of self-adaptive differential evolution. Euro J Oper Res 183(2):785–804
Simon D (2008a) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713
Simon D (2008b) The Matlab code of biogeography-based optimization. http://academic.csuohio.edu/simond/bbo/
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Opt 11(4):341–359
Storn R, Price K (2008) Home page of differential evolution. http://www.ICSI.Berkeley.edu/~storn/code.html
Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC2005 special session on real-parameter optimization. URL http://www.ntu.edu.sg/home/EPNSugan
Sun J, Zhang Q, Tsang EPK (2005) DE/EDA: a new evolutionary algorithm for global optimization. Inform Sci 169(3–4):249–262
Teng NS, Teo J, Hijazi MHA (2009) Self-adaptive population sizing for a tune-free differential evolution. Soft Comput 13(7):709–724
Teo J (2006) Exploring dynamic self-adaptive populations in differential evolution. Soft Comput 10(8):673–686
Wang YJ, Zhang JS, Zhang GY (2007) A dynamic clustering based differential evolution algorithm for global optimization. Euro J Oper Res 183(1):56–73
Yao X, Liu Y (1997) Fast evolution strategies. Control Cybern 26(3):467–496
Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102
Zhong W, Liu J, Xue M, Jiao L (2004) A multiagent genetic algorithm for global numerical optimization. IEEE Trans Syst Man Cybern B 34(2):1128–1141
Acknowledgments
The authors would like to thank Prof. Brest for providing the SADE code. They are also grateful to the area editor and the anonymous reviewers for their valuable comments and suggestions on this paper. This work was supported in part by the Fund for Outstanding Doctoral Dissertation of China University of Geosciences, China Scholarship Council under Grant No. 2008641008, and the National High Technology Research and Development Program of China under Grant No. 2009AA12Z117.
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Gong, W., Cai, Z. & Ling, C.X. DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization. Soft Comput 15, 645–665 (2010). https://doi.org/10.1007/s00500-010-0591-1
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DOI: https://doi.org/10.1007/s00500-010-0591-1