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A movable damped wave algorithm for solving global optimization problems

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Abstract

This paper presents a new optimization methodology called movable damped wave algorithm for solving global optimization problems. The proposed methodology mimics mathematically the behavior of waveform induced by oscillating phenomena. It starts by creating multiple initial random solutions which are updated through introducing a mathematical model based on a damped wave function. In the proposed methodology, the updating mechanisms of solutions are based on designing a mathematical relation for the movable wave with the aim to effectively achieve robust solutions. Therefore, this methodology can be more robust, statistically sound, and convergent quickly to the optimal global solution. The performance of the proposed is validated by carrying out on 23 benchmark problems and three engineering design problems. The results show vividly that the proposed is a reliable algorithm and outperforms the comparative algorithms in most cases.

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Author information

Authors and Affiliations

  1. Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom, Egypt

    Rizk M. Rizk-Allah

  2. Faculty of Computers and Information, Cairo University, Giza, Egypt

    Aboul Ella Hassanien

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  1. Rizk M. Rizk-Allah
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  2. Aboul Ella Hassanien
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Correspondence to Aboul Ella Hassanien.

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Rizk M. Rizk-Allah and Aboul Ella Hassanien: Scientific Research Group in Egypt, http://www.egyptscience.net.

Appendix

Appendix

See Tables 12, 13, 14, 15, 16, 17, 18, 19, 20 and 21.

Table 12 Unimodal test functions
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Table 13 2 Multimodal test functions
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Table 14 Multimodal test functions with fix dimension
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Table 15 \({a_{ij}}\)in \({F_{14}}\)
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Table 16 \({a_i}\,,{b_i}\) in \({F_{15}}\)
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Table 17 \({a_{ij}}\,,{c_i}\) in \({F_{19}}\)
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Table 18 \({p_{ij}}\)in \({F_{19}}\)
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Table 19 \({a_{ij}}\,,{c_i}\)in \({F_{20}}\)
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Table 20 \({p_{ij}}\)in \({F_{20}}\)
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Table 21 \({a_{ij}}\,,{c_i}\) in \({F_{21}},{F_{22}}\) and \({F_{23}}\)
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Rizk-Allah, R.M., Hassanien, A.E. A movable damped wave algorithm for solving global optimization problems. Evol. Intel. 12, 49–72 (2019). https://doi.org/10.1007/s12065-018-0187-8

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