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Adaptive Information Granulation in Fitness Estimation for Evolutionary Optimization

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Abstract

Evolutionary algorithms ordinarily need to conduct lots of fitness evaluations, requiring big computational overhead particularly in complex optimization problems. This paper proposes an adaptive information granulation approach which inspired from on the granule computing, and then reduces the expensive original fitness evaluation by the aid of the fitness inheritance strategy based on the proposed adaptive information granulation approach. The proposed algorithm is compared with few fitness inheritance assisted evolutionary algorithm on both traditional benchmark problems with four different dimensions, the CEC 2013 functions and the CEC 2014 expensive optimization test problems with 30 dimensions. Experimental results show both high effectiveness and efficiency with better solutions than those compared algorithm within different finite budget of computation for different benchmark problems. Its advantages are further verified by a real-world light aircraft wing design problem.

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Acknowledgements

The authors acknowledge the National Natural Science Foundation of China (Grant Nos. 61403272 and 61472269).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan, China

    Jie Tian, Jianchao Zeng & Ying Tan

  2. School of Information Technology, Shandong Womens University, Jinan, China

    Jie Tian

  3. School of Computer Science and Control Engineering, North University of China, Taiyuan, China

    Jianchao Zeng

  4. Department of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan, China

    Chaoli Sun

Authors
  1. Jie Tian
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  2. Jianchao Zeng
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  3. Ying Tan
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  4. Chaoli Sun
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Corresponding author

Correspondence to Ying Tan.

Appendix

Appendix

For PSO, each particle i has one speed \({\text{V}}_{i} = [v_{i1} ,v_{i2} , \ldots ,v_{iD} ]\) and a position \({\text{X}}_{i} = [x_{i1} ,x_{i2} , \ldots ,x_{iD} ]\) during the search of the D-dimensional hyperspace. The vectors Vi and Xi are randomly initialized and updated by (16) and (17) under the guidance of the Pi, and the Pn:

$${\text{V}}_{\text{i}}^{{({\text{t + 1}})}} = \omega {\text{V}}_{i}^{(t)} + c_{1} r_{1} ({\text{P}}_{i}^{(t)} - {\text{X}}_{i}^{(t)} ) + c_{2} r_{2} ({\text{P}}_{\text{n}}^{(t)} - {\text{X}}_{i}^{(t)} )$$
(16)
$${\text{X}}_{i}^{(t + 1)} {\text{ = X}}_{i}^{(t)} {\text{ + V}}_{i}^{(t + 1)}$$
(17)

where, \({\text{X}}_{i}^{(t)}\) and \({\text{V}}_{i}^{(t)}\) are i particle`s position and speed in generation t, respectively, coefficient ω represents inertia weight, c1 and c2 as two acceleration parameters. r1 and r2 refer to two diagonal matrices, and diagonal elements are consistently generated with a random number in scope of [0, 1].

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Tian, J., Zeng, J., Tan, Y. et al. Adaptive Information Granulation in Fitness Estimation for Evolutionary Optimization. Wireless Pers Commun 103, 741–759 (2018). https://doi.org/10.1007/s11277-018-5474-2

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