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Diversity enhanced and local search accelerated gravitational search algorithm for data fitting with B-splines

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Abstract

Gravitational search algorithm (GSA) has shown an effective performance for solving real-world optimization problems. However, it suffers from premature convergence because of quick losing of diversity. To enhance its performance, this paper proposes a novel GSA algorithm, called GSA–PWL (piecewise linear)–SQP (sequential quadratic programming), which employs a diversity enhancing mechanism and an accelerated local search strategy to achieve a trade-off between exploration and exploitation abilities. A comprehensive experimental study is conducted on a set of benchmark functions. Comparison results show that GSA–PWL–SQP obtains a promising performance on the majority of the test problems. Furthermore, the GSA–PWL–SQP is applied to data fitting with B-splines to solve very difficult continuous multimodal and multivariate nonlinear optimization problem. The method of data fitting based on GSA–PWL–SQP yields very accurate results even for curves with singularities and/or cusps and is very efficient in terms of data points error, AIC and BIC criteria.

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Acknowledgments

This research has been supported by National Natural Science Foundation program of China (51035007).

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Authors and Affiliations

  1. Key Laboratory of Advanced Transducers and Intelligent Control Systems, Ministry of Education China, Institute of Mechatronic Engineering, Taiyuan University of Technology, No. 79, West Yingze Street, Taiyuan, Shanxi, China

    XiaoHong Han, Long Quan, XiaoYan Xiong & Bing Wu

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  1. XiaoHong Han
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  2. Long Quan
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  3. XiaoYan Xiong
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  4. Bing Wu
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Corresponding author

Correspondence to XiaoHong Han.

Appendix A

Appendix A

See Tables 9, 10 and 11.

Table 9 Unimodal test functions and their optimum values
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Table 10 Multimodal test functions and their optimum values
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Table 11 Multimodal test functions with fix dimension and their optimum values
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Han, X., Quan, L., Xiong, X. et al. Diversity enhanced and local search accelerated gravitational search algorithm for data fitting with B-splines. Engineering with Computers 31, 215–236 (2015). https://doi.org/10.1007/s00366-013-0343-9

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