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Gaussian process assisted coevolutionary estimation of distribution algorithm for computationally expensive problems

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Abstract

In order to reduce the computation of complex problems, a new surrogate-assisted estimation of distribution algorithm with Gaussian process was proposed. Coevolution was used in dual populations which evolved in parallel. The search space was projected into multiple subspaces and searched by sub-populations. Also, the whole space was exploited by the other population which exchanges information with the sub-populations. In order to make the evolutionary course efficient, multivariate Gaussian model and Gaussian mixture model were used in both populations separately to estimate the distribution of individuals and reproduce new generations. For the surrogate model, Gaussian process was combined with the algorithm which predicted variance of the predictions. The results on six benchmark functions show that the new algorithm performs better than other surrogate-model based algorithms and the computation complexity is only 10% of the original estimation of distribution algorithm.

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References

  1. JIN Yao-chu, OLHOFER M, SENDHOFF B. A framework for evolutionary optimization with approximate fitness functions [J]. IEEE Transactions on Evolutionary Computation, 2002, 6(5): 481–494.

    Article  Google Scholar 

  2. SCHMIDT M D, LIPSON H. Coevolution of fitness predictors [J]. IEEE Transactions on Evolutionary Computation, 2008, 12(6): 736–749.

    Article  Google Scholar 

  3. VO C, PANAIT L, LUKE S, Cooperative coevolution and univariate estimation of distribution algorithms [C]// Proceedings of the 10th ACM SIGEVO Conference on Foundations of Genetic Algorithms, Association for Computing Machinery. Orlando, Florida, USA: 2009: 141–150.

  4. POTTER M A, DEJONG K A. A cooperative coevolutionary approach to function optimization [C]// DAVIDOR Y, SCHWEFEL H, MÄNNER R. The Third Parallel Problem Solving from Nature. Springer Berlin/Heidelberg, 1994: 249–257.

    Chapter  Google Scholar 

  5. PANAIT L. Theoretical convergence guarantees for cooperative coevolutionary algorithms [J]. Evolutionary Computation, 2010, 18(4): 581–615.

    Article  Google Scholar 

  6. JANSEN T, WIEGAND R P. The cooperative coevolutionary (1+1) EA[J]. Evolutionary Computation, 2004, 12(4): 405–434.

    Article  Google Scholar 

  7. BERGH F V D, ENGELBRECHT A P. A cooperative approach to particle swarm optimization [J]. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 225–239.

    Article  Google Scholar 

  8. YANG Z Y, TANGA K, YAO X. Large scale evolutionary optimization using cooperative coevolution [J]. Information Sciences, 2008, 178(15): 2985–2999.

    Article  MathSciNet  Google Scholar 

  9. EL-BELTAGY M A, KEANE A J. Evolutionary optimization for computationally expensive problems using gaussian processes [C]// Proceedings of the International Conference on Artificial Intelligence. Las Vegas: CSREA Press, 2001: 708–714.

    Google Scholar 

  10. SU Shao-guo. Accelerating particle swarm optimization algorithms using gaussian process machine learning [C]// QI L, TIAN X Z. Proceedings of the 2009 International Conference on Computational Intelligence and Natural Computing. Wuhan: IEEE Computer Society, 2009: 174–177.

    Chapter  Google Scholar 

  11. BUCHE D, SCHRAUDOLPH N N, KOUMOUTSAKOS P. Accelerating evolutionary algorithms with gaussian process fitness function models [J]. IEEE Transactions on Systems Man and Cybernetics Part C-Applications and Reviews, 2005, 35(2): 183–194.

    Article  Google Scholar 

  12. LI Bin, ZHONG Rui-tian, WANG Xian-ji, ZHUANG Zhen-quan. Continuous optimization based-on boosting gaussian mixture model [C]// TANG Y Y, WANG S P, LORETTE G, YEUNG D S, YAN H. Proceedings of the 18th International Conference on Pattern Recognition (ICPR 2006). Hong Kong, China: IEEE Computer Society, 2006: 1192–1195.

    Google Scholar 

  13. DING N, ZHOU S, SUN Z. Histogram-based estimation of distribution algorithm: A competent method for continuous optimization [J]. Journal of computer science and technology, 2008, 23(1): 35–43.

    Article  Google Scholar 

  14. KROHLING R A, COELHO L D. Coevolutionary particle swarm optimization using gaussian distribution for solving constrained optimization problems [J]. IEEE Transactions on Systems Man and Cybernetics Part B-Cybernetics, 2006, 36(6): 1407–1416.

    Article  Google Scholar 

  15. ZHAO Liang, YANG Yu-pu, ZENG Yong. Eliciting compact t-s fuzzy models using subtractive clustering and coevolutionary particle swarm optimization [J]. Neurocomputing, 2009, 72(10/11/12): 2569–2575.

    Article  Google Scholar 

  16. XIONG Zi-hua. Soft sensor modeling based on gaussian processes [J]. Journal of Central South University of Technology, 2005, 12(4): 469–471.

    Article  Google Scholar 

  17. JIN Yao-chu. A comprehensive survey of fitness approximation in evolutionary computation [J]. Soft Computing, 2005, 9(1): 3–12.

    Article  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, Shanghai, 200237, China

    Na Luo  (罗娜), Feng Qian  (钱锋), Liang Zhao  (赵亮) & Wei-min Zhong  (钟伟民)

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  1. Na Luo  (罗娜)
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  2. Feng Qian  (钱锋)
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  3. Liang Zhao  (赵亮)
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  4. Wei-min Zhong  (钟伟民)
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Corresponding author

Correspondence to Feng Qian  (钱锋).

Additional information

Foundation item: Project(2009CB320603) supported by the National Basic Research Program of China; Project(IRT0712) supported by Program for Changjiang Scholars and Innovative Research Team in University; Project(B504) supported by the Shanghai Leading Academic Discipline Program; Project(61174118) supported by the National Natural Science Foundation of China

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Luo, N., Qian, F., Zhao, L. et al. Gaussian process assisted coevolutionary estimation of distribution algorithm for computationally expensive problems. J. Cent. South Univ. Technol. 19, 443–452 (2012). https://doi.org/10.1007/s11771-012-1023-4

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  • DOI: https://doi.org/10.1007/s11771-012-1023-4

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