Soft Computing

, Volume 21, Issue 22, pp 6605–6632 | Cite as

Novel migration operators of biogeography-based optimization and Markov analysis

  • Weian Guo
  • Lei Wang
  • Chenyong Si
  • Yongwei Zhang
  • Hongjun Tian
  • Junjie Hu
Methodologies and Application

Abstract

Biogeography-based optimization (BBO) is a nature-inspired optimization algorithm and has been developed in both theory and practice. In canonical BBO, migration operator is crucial to affect algorithm’s performance. In migration operator, a good solution has a large probability to be selected as an immigrant, while a poor solution has a large probability to be selected as an emigrant. The features in an emigrant will be completely replaced by the features in the corresponding immigrant. Hence, the migration operator in canonical BBO causes a significant deterioration of population diversity, and therefore, the algorithm’s performance worsens. In this paper, we propose three novel migration operators to enhance the exploration ability of BBO. To present a mathematical proof, Markov analysis is conducted to confirm the advantages of the proposed migration operators over existing ones. In addition, a number of benchmark tests are carried out to empirically assess the performance of the proposed migration operators, on both low-dimensional and high-dimensional numerical optimization problems. The comparison results demonstrate that the proposed migration operators are feasible and effective to enhance BBO’s performance.

Keywords

Biogeography-based optimization Nature-inspired optimization algorithm Population diversity Migration operator Markov analysis 

References

  1. Ahn C (2006) Advances in evolutionary algorithms: theory, design and practice. Springer, New YorkMATHGoogle Scholar
  2. Bagdonavius V, Kruopis J, Nikulin M (2011) Nonparametric tests for complete data. Wiley-ISTE, New YorkCrossRefGoogle Scholar
  3. Brest J, Zamuda A, Fister I, Maučec MS (2010) Large scale global optimization using self-adaptive differential evolution algorithm. In: IEEE congress on evolutionary computation (CEC), 2010, pp 1–8Google Scholar
  4. Castillo O, Melin P (2012) Optimization of type-2 fuzzy systems based on bio-inspired methods: a concise review. Inf Sci 205:1–19CrossRefGoogle Scholar
  5. Chatterjee A, Siarry P, Nakib A, Blanc R (2012) An improved biogeography based optimization approach for segmentation of human head CT-scan images employing fuzzy entropy. Eng Appl Artif Intell 25(8):1698–1709CrossRefGoogle Scholar
  6. Chang J, Shi P (2011) Using investment satisfaction capability index based particle swarm optimization to construct a stock portfolio. Inf Sci 181(14):2989–2999MathSciNetCrossRefGoogle Scholar
  7. Chen BJ, Shu HZ, Coatrieux G, Chen G, Xun XM, Coatrieux JL (2015) Color image analysis by quaternion-type moments. J Math Imaging Vis 51:124–144Google Scholar
  8. Cheng R, Jin Y (2015) A social learning particle swarm optimization algorithm for scalable optimization. Inf Sci 291:43–60MathSciNetCrossRefMATHGoogle Scholar
  9. Cheng R, Jin Y (2015) A competitive swarm optimizer for large scale optimization. IEEE Trans Cybern 45(2):191–204CrossRefGoogle Scholar
  10. Clerc M (1999) The swarm and the queen: toward a deterministic and adaptive particle swarm optimization, vol 3. In: Proceedings of the 1999 congress on evolutionary computation, Washington, DC, pp 1951–1957Google Scholar
  11. Clerc M, Kennedy J (2002) The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans Evolut Comput 6(1):58–73CrossRefGoogle Scholar
  12. Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, CambridgeMATHGoogle Scholar
  13. Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval schemata. Found Genet Algorithms II:187–202Google Scholar
  14. Feng Q, Liu S, Wu Q, Tang GQ, Zhang H, Chen H (2013) Modified biogeography-based optimization with local search mechanism. J Appl Math. doi:10.1155/2013/960524
  15. Fu ZJ, Sun XM, Liu Q, Zhou L, Shu JG (2015) Achieving efficient cloud search services: multi-keyword ranked search over encrypted cloud date supporting parallel computing. IEICE Trans Commun E98B(1):190–200Google Scholar
  16. Gu B, Sheng VS, Wang Z, Ho D, Osman S, Li S (2015) Incremental learning for nu-support vector regression. Neual Netw 67:140–150CrossRefGoogle Scholar
  17. Gu B, Sheng VS, Tay KY, Romano W, Li S (2015) Incremental support vector learning for ordinal regression. IEEE Trans Neural Netw Learn Syst 26(7):1403–1416MathSciNetCrossRefGoogle Scholar
  18. Guo W, Wang L, Wu Q (2014) An analysis of the migration rates of biogeography-based optimization. Inf Sci 254(1):111–140MathSciNetCrossRefGoogle Scholar
  19. Guo W, Wang L, Ge SS, Ren H, Mao Y (2015) Drift analysis of mutation operations for biogeography-based optimization. Soft Comput 19(7):1881–1892CrossRefMATHGoogle Scholar
  20. Guo W, Wang L, Qidi W (2016) Numerical comparisons of migration models for multi-objective biogeography-based optimization. Inf Sci 328:302–320CrossRefGoogle Scholar
  21. He W, Ge SS (2015) Vibration control of a flexible beam with output constraint. IEEE Trans Ind Electron 62(8):5023–5030CrossRefGoogle Scholar
  22. He W, Ge SS (2016) Cooperative control of a nonuniform gantry crane with constrained tension. Automatica 66(4):146–154MathSciNetCrossRefMATHGoogle Scholar
  23. He W, Zhang S, Ge SS (2014) Adaptive control of a flexible crane system with the boundary output constraint. IEEE Trans Ind Electron 61(8):4126–4133CrossRefGoogle Scholar
  24. He W, Chen Y, Yin Z (2016) Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Trans Cybern 46(3):620–629Google Scholar
  25. Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT Press, CambridgeGoogle Scholar
  26. Kankanala P, Srivastava S, Srivastava A, Schulz N (2012) Optimal control of voltage and power in a multi-zonal mvdc shipboard power system. IEEE Trans Power Syst 27(2):642–650CrossRefGoogle Scholar
  27. Kennedy J, Eberhart RC, Shi Y (2001) Swarm intelligence. Morgan Kaufmann Publishers, San FranciscoGoogle Scholar
  28. Khatib W, Fleming PL (1998) The stud GA: A mini revolution? In: Eiben AE, Bäck T, Schoenauer M, Schwefel H-P (eds) Parallel problem solving from nature–PPSN V: proceedings of the 5th international conference Amsterdam, The Netherlands, September 27–30, 1998, vol 1498. Springer, Berlin, Heidelberg, pp 683–691. doi:10.1007/BFb0056910
  29. Korosec P, Tashkova K, Silc J (2010) The differential ant-stigmergy algorithm for large-scale global optimization. In: IEEE congress on evolutionary computation (CEC), 2010, pp 1–8Google Scholar
  30. Larranaga P, Karshenas H, Bielza C, Santana R (2013) A review on evolutionary algorithms in bayesian network learning and inference tasks. Inf Sci 233:109–125MathSciNetCrossRefMATHGoogle Scholar
  31. Latorre A, Muelas S, Pena J-M (2013) Large scale global optimization: experimental results with mos-based hybrid algorithms, pp 2742–2749, Cancun, MexicoGoogle Scholar
  32. Li X, Wang J, Zhou J, Yin M (2011) A perturb biogeography based optimization with mutation for global numerical optimization. Appl Math Comput 218(2):598–609MathSciNetMATHGoogle Scholar
  33. Li X, Tang K, Omidvar M, Yang Z, Qin K (2013) Benchmark functions for the cec’2013 special session and competition on large scale global optimization. In: Technical report, Evolutionary Computation and Machine Learning Group, RMIT University, Australia, 2013Google Scholar
  34. Li J, Li XL, Sun XM (2015) Segmentation-based image copy-move forgery detection scheme. IEEE Trans Inf Forensics Secur 10(3):507–518CrossRefGoogle Scholar
  35. Liu J, Tang K (2013) Scaling up covariance matrix adaptation evolution strategy using cooperative coevolution. In: LNCS, vol 8206, pp 350–357, Hefei, ChinaGoogle Scholar
  36. Li X, Yao X (2012) Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans Evolut Comput 16(2):210–224MathSciNetCrossRefGoogle Scholar
  37. Lohokare MR, Pattnaik SS, Panigrahi BK, Das S (2013) Accelerated biogeography-based optimization with neighborhood search for optimization. Appl Sofy Comput 13(5):2318–2342CrossRefGoogle Scholar
  38. Ma H (2010) An analysis of the equilibrium of migration models for biogeography-based optimization. Inf Sci 180(18):3444–3464CrossRefMATHGoogle Scholar
  39. Ma H, Simon D, Fei M, Xie Z (2013) Variations of biogeography-based optimization and Markov analysis. Inf Sci 220:492–506CrossRefGoogle Scholar
  40. Ma H, Simon D (2011) Analysis of migration models of biogeography-based optimization using markov theory. Eng Appl Artif Intell 24(6):1052–1060CrossRefGoogle Scholar
  41. Ma H, Simon D (2011) Blended biogeography-based optimization for constrained optimization. Eng Appl Artif Intell 24(3):517–525CrossRefGoogle Scholar
  42. Ma TH, Zhou JJ, Tang ML, Tian Y, AL-Dhelaan A, AL-Rodhaan M, Lee S (2015) Social network and tag sources based augmenting collaborative recommender system. IEICE Trans Inf Syst E98D(4):902–910Google Scholar
  43. Michalewicz Z (1992) Genetic algorithms + data structures = evolution programs. Springer, New YorkCrossRefMATHGoogle Scholar
  44. Molina D, Lozano M., Herrera F (2010) MA-SW-chains: memetic algorithm based on local search chains for large scale continuous global optimization. In: IEEE congress on evolutionary computation (CEC), 2010, pp 1–8Google Scholar
  45. Mühlenbein H, Schlierkamp-Voosen D (1993) Predictive models for the breeder genetic algorithm i. continuous parameter optimization. Evolut Comput 1(1):25–49CrossRefGoogle Scholar
  46. Omidvar MN, Li Xiaodong, Yao Xin (2010) Cooperative co-evolution with delta grouping for large scale non-separable function optimization. In: IEEE congress on evolutionary computation (CEC), 2010, p 1–8Google Scholar
  47. Parmee I (2001) Evolutionary and adaptive computing in engineering design. Springer, New YorkCrossRefGoogle Scholar
  48. Puris A, Bello R, Molina D, Herrera F (2012) Variable mesh optimization for continuous optimization problems. Soft Comput 16(3):511–525CrossRefGoogle Scholar
  49. Savsani V, Rao R, Vakharia D (2009) Discrete optimisation of a gear train using biogeography based optimisation technique. Int J Des Eng 2(2):205–223Google Scholar
  50. Shen J, Tan HW, Wang J, Wang JW, Lee S (2015) A novel routing protocol providing good transmission reliability in underwater sensor networks. J Internet Technol 16(1):171–178Google Scholar
  51. Shin Y-B, Kita E (2014) Search performance improvement of particle swarm optimization by second best particle information. Appl Math Comput 246:346–354Google Scholar
  52. Simon D (2008) Biogeography-based optimization. IEEE Trans Evol Comput 12(6):702–713CrossRefGoogle Scholar
  53. Simon D, Ergezer M, Dawei D, Rarick R (2011) Markov models for biogeography-based optimization. IEEE Trans Syst Man Cybern Part B Cybern 41(1):299–306CrossRefMATHGoogle Scholar
  54. Simon D, Rarick R, Ergezer M, Du D (2011) Analytical and numerical comparisons of biogeography-based optimization and genetic algorithms. Inf Sci 181(7):1224–1248CrossRefMATHGoogle Scholar
  55. Simon D (2013) Evolutionary optimization algorithms: biologically-inspired and population-based approaches to computer intelligence. Wiley, New YorkMATHGoogle Scholar
  56. 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. In: Technical report, Nature Inspired Computation and Applications LaboratoryGoogle Scholar
  57. Wang Yu, Li Bin (2010) Two-stage based ensemble optimization for large-scale global optimization. In: IEEE congress on evolutionary computation (CEC), 2010, pp 1–8Google Scholar
  58. Wang H, Wu Z, Rahnamayan S, Jiang D (2010) Sequential de enhanced by neighborhood search for large scale global optimization. In: IEEE congress on evolutionary computation (CEC), 2010, pp 1–7Google Scholar
  59. Weber M, Neri F, Tirronen V (2011) Shuffle or update parallel differential evolution for large-scale optimization. Soft Comput 15(11, SI):2089–2107CrossRefGoogle Scholar
  60. Wei F, Wang Y, Huo Y (2013) Smoothing and auxiliary functions based cooperative coevolution for global optimization, pp 2736–2741, Cancun, MexicoGoogle Scholar
  61. Wu G, Qiu D, Yu Y, Pedrycz W, Ma M, Li H (2014) Superior solution guided particle swarm optimization combined with local search techniques. Expert Syst Appl 41(16):7536–7548CrossRefGoogle Scholar
  62. Xia ZH, Wang XH, Sun XM, Wang Q (2016) A secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans Parallel Distrib Syst 27(2):340–352CrossRefGoogle Scholar
  63. Xie SD, Wang YX (2014) Construction of tree network with limited delivery latency in homogeneous wireless sensor networks. Wirel Pers Commun 78:231–246CrossRefGoogle Scholar
  64. Xiong G, Li Y, Chen J, Shi D, Duan X (2014) Polyphyletic migration operator and orthogonal learning aided biogeography-based optimization for dynamic economic dispatch with valve-point effects. Energy Convers Manag 80:457–468CrossRefGoogle Scholar
  65. Yao X, Liu Y, Lin G (1999) Evolutionary programming made faster. IEEE Trans Evolut Comput 3(2):82–102CrossRefGoogle Scholar
  66. Yu X, Zhang X (2014) Enhanced comprehensive learning particle swarm optimization. Appl Math Comput 242:265–276MathSciNetMATHGoogle Scholar
  67. Zhang P, Wei P, Yu HY (2012) Biogeography-based optimisation search algorithm for block matching motion estimation. IET Image Process 6(7):1014–1023MathSciNetCrossRefGoogle Scholar
  68. Zhang H-G, Liu Y-A, Tang B-H, Liu K-M (2014) An exploratory research of elitist probability schema and its applications in evolutionary algorithms. Appl Intell 40(4):695–709CrossRefGoogle Scholar
  69. Zhang P, Liu H, Ding Y (2014) Dynamic bee colony algorithm based on multi-species co-evolution. Appl Intell 40(3):427–440CrossRefGoogle Scholar
  70. Zheng Y, Jeon B, Xu DH, Wu J QM, Zhang H (2015) Image segmentation by generalized hierarchical fuzzy C-means algorithm. J Intell Fuzzy Syst 28:961–973Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Sino-German College of Applied SciencesTongji UniversityShanghaiChina
  2. 2.Department of Electronics and InformationTongji UniversityShanghaiChina
  3. 3.Shanghai-Humburg CollegeUniversity of Shanghai for Science and TechnologyShanghaiChina
  4. 4.College of Electronics and InformationJiangsu University of Science and TechnologyZhenjiangChina
  5. 5.Department of Electrical Engineering, Center for Electric Power and EnergyTechnical University of DenmarkCopenhagenDenmark

Personalised recommendations