Soft Computing

, Volume 15, Issue 4, pp 645–665 | Cite as

DE/BBO: a hybrid differential evolution with biogeography-based optimization for global numerical optimization

Original Paper
First Online:

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.

Keywords

Differential evolution Biogeography-based optimization Hybridization Global numerical optimization Exploration Exploitation 
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Notes

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.

References

  1. Alatas B, Akin E, Karci A (2008) MODENAR: multi-objective differential evolution algorithm for mining numeric association rules. Appl Soft Comput 8(1):646–656CrossRefGoogle Scholar
  2. 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 1769–1776Google Scholar
  3. Bäck T (1996) Evolutionary algorithms in theory and Practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, Oxford, UKMATHGoogle Scholar
  4. Brest J, Maučec MS (2008) Population size reduction for the differential evolution algorithm. Appl Intell 29(3):228–247CrossRefGoogle Scholar
  5. 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):646–657CrossRefGoogle Scholar
  6. Caponio A, Neri F, Tirronen V (2009) Super-fit control adaptation in memetic differential evolution frameworks. Soft Comput 13(8–9):811–831CrossRefGoogle Scholar
  7. Chakraborty U (2008) Advances in differential evolution. Springer, BerlinMATHCrossRefGoogle Scholar
  8. Das S, Abraham A, Konar A (2008) Automatic clustering using an improved differential evolution algorithm. IEEE Trans Syst Man Cybern A 38(1):218–237CrossRefGoogle Scholar
  9. 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 991–998Google Scholar
  10. Demsar J (2006) Statistical comparisons of classifiers over multiple data sets. J Mach Learn Res 7:1–30MathSciNetGoogle Scholar
  11. Fan HY, Lampinen J (2003) A trigonometric mutation operation to differential evolution. J Global Opt 27(1):105–129MathSciNetMATHCrossRefGoogle Scholar
  12. Feoktistov V (2006) Differential evolution: in search of solutions. Springer, New YorkMATHGoogle Scholar
  13. Feoktistov V, Janaqi S (2004) Generalization of the strategies in differential evolution. IEEE Comput Soc, Los Alamitos, CA, USA, p 165aGoogle Scholar
  14. 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 293–298Google Scholar
  15. García S, Herrera F (2008) An extension on “statistical comparisons of classifiers over multiple data sets” for all pairwise comparisons. J Mach Learn Res 9:2677–2694Google Scholar
  16. 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 CrossRefGoogle Scholar
  17. 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 MATHCrossRefGoogle Scholar
  18. 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 709–718Google Scholar
  19. Goulden CH (1956) Methods of statistical analysis, 2nd ed. Wiley, New YorkGoogle Scholar
  20. Grosan C, Abraham A, Ishibuchi H (2009) Hybrid evolutionary algorithms. Springer, Berlin, GermanyGoogle Scholar
  21. 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 282–291Google Scholar
  22. Herrera FML (2000) Two-loop real-coded genetic algorithms with adaptive control of mutation step sizes. Appl Intell 13(3):187–204CrossRefGoogle Scholar
  23. Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for behavioural analysis. Artif Intell Rev 12:265–319MATHCrossRefGoogle Scholar
  24. 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):1234–1253CrossRefGoogle Scholar
  25. Kaelo P, Ali MM (2007) Differential evolution algorithms using hybrid mutation. Comput Optim Appl 37(2):231–246MathSciNetMATHCrossRefGoogle Scholar
  26. Langdon WB, Poli R (2007) Evolving problems to learn about particle swarm optimizers and other search algorithms. IEEE Trans Evol Comput 11(5):561–578CrossRefGoogle Scholar
  27. 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):281–295CrossRefGoogle Scholar
  28. Liu J, Lampinen J (2005) A fuzzy adaptive differential evolution algorithm. Soft Comput 9(6):448–462MATHCrossRefGoogle Scholar
  29. 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):481–497MathSciNetMATHCrossRefGoogle Scholar
  30. Lozano M, Herrera F, Krasnogor N, Molina D (2004) Real-coded memetic algorithms with crossover hill-climbing. Evol Comput 12(3):273–302CrossRefGoogle Scholar
  31. Nobakhti A, Wang H (2008) A simple self-adaptive differential evolution algorithm with application on the alstom gasifier. Appl Soft Comput 8(1):350–370CrossRefGoogle Scholar
  32. 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 967–974Google Scholar
  33. Noman N, Iba H (2008) Accelerating differential evolution using an adaptive local search. IEEE Trans Evol Comput 12(1):107–125CrossRefGoogle Scholar
  34. Onwubolu GC, Davendra D (2009) Differential evolution: a handbook for global permutation-based combinatorial optimization. Springer, BerlinMATHCrossRefGoogle Scholar
  35. Price K, Storn R, Lampinen J (2005) Differential evolution: a practical approach to global optimization. Springer, BerlinMATHGoogle Scholar
  36. Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: IEEE congress on evolutionary computation (CEC2005), IEEE, pp 1785–1791Google Scholar
  37. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417CrossRefGoogle Scholar
  38. Rahnamayan S, Tizhoosh H, Salama M (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79CrossRefGoogle Scholar
  39. Salman A, Engelbrecht AP, Omran MGH (2007) Empirical analysis of self-adaptive differential evolution. Euro J Oper Res 183(2):785–804MATHCrossRefGoogle Scholar
  40. Simon D (2008a) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  41. Simon D (2008b) The Matlab code of biogeography-based optimization. http://academic.csuohio.edu/simond/bbo/
  42. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Opt 11(4):341–359MathSciNetMATHCrossRefGoogle Scholar
  43. Storn R, Price K (2008) Home page of differential evolution. http://www.ICSI.Berkeley.edu/~storn/code.html
  44. 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
  45. Sun J, Zhang Q, Tsang EPK (2005) DE/EDA: a new evolutionary algorithm for global optimization. Inform Sci 169(3–4):249–262MathSciNetCrossRefGoogle Scholar
  46. Teng NS, Teo J, Hijazi MHA (2009) Self-adaptive population sizing for a tune-free differential evolution. Soft Comput 13(7):709–724CrossRefGoogle Scholar
  47. Teo J (2006) Exploring dynamic self-adaptive populations in differential evolution. Soft Comput 10(8):673–686CrossRefGoogle Scholar
  48. Wang YJ, Zhang JS, Zhang GY (2007) A dynamic clustering based differential evolution algorithm for global optimization. Euro J Oper Res 183(1):56–73MATHCrossRefGoogle Scholar
  49. Yao X, Liu Y (1997) Fast evolution strategies. Control Cybern 26(3):467–496MathSciNetMATHGoogle Scholar
  50. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evol Comput 3(2):82–102CrossRefGoogle Scholar
  51. 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):1128–1141CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.School of Computer ScienceChina University of GeosciencesWuhanPeople’s Republic of China
  2. 2.Department of Computer ScienceThe University of Western OntarioLondonCanada

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