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A modified gravitational search algorithm based on sequential quadratic programming and chaotic map for ELD optimization

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Abstract

Gravitational search algorithm (GSA) is a stochastic search algorithm based on the law of gravity and mass interactions. For the purpose of enhancing the performance of standard GSA, this paper proposes a robust hybrid gravitational search algorithm (RHGSA). This algorithm makes the best of ergodicity of PieceWise Linear chaotic map to explore the global search while utilizing the sequential quadratic programming to accelerate the local search. To verify the performance of RHGSA, different types of benchmark functions including five unimodal functions and ten functions provided by CEC 2005 special session are tested in the experiments. Comparisons with other new variants of POS and GSA show that RHGSA obtains a promising performance on the majority of the test problems. Furthermore, a practical application problem, the economic load dispatch problem of power systems (ELD), is solved to further evaluate RHGSA. Compared with the previous evolutionary algorithms applied to ELD problem, RHGSA can get better results.

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Acknowledgments

This paper is supported by the National Natural Science Foundation of China (Grant No. 51035007).

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Authors and Affiliations

  1. Key Laboratory of Advanced Transducers and Intelligent Control Systems, Ministry of Education China, Taiyuan University of Technology, No. 79, West Yingze Street, Taiyuan , 030024, China

    XiaoHong Han, Long Quan & Xiaoyan Xiong

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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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Corresponding author

Correspondence to XiaoHong Han.

Appendix A

Appendix A

See Tables 7 and 8

Table 7 The unimodal test functions used in the experiments, where \(Dim\) is the dimension, and \(f_{min}\) is the global optimum
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Table 8 The five CEC 2005 benchmark functions used in the experiments, where \(Dim\) is the dimension, and \(f_{min}\) is the global optimum
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Han, X., Quan, L. & Xiong, X. A modified gravitational search algorithm based on sequential quadratic programming and chaotic map for ELD optimization. Knowl Inf Syst 42, 689–708 (2015). https://doi.org/10.1007/s10115-013-0701-3

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