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Geyser Inspired Algorithm: A New Geological-inspired Meta-heuristic for Real-parameter and Constrained Engineering Optimization

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Abstract

Over the past years, many efforts have been accomplished to achieve fast and accurate meta-heuristic algorithms to optimize a variety of real-world problems. This study presents a new optimization method based on an unusual geological phenomenon in nature, named Geyser inspired Algorithm (GEA). The mathematical modeling of this geological phenomenon is carried out to have a better understanding of the optimization process. The efficiency and accuracy of GEA are verified using statistical examination and convergence rate comparison on numerous CEC 2005, CEC 2014, CEC 2017, and real-parameter benchmark functions. Moreover, GEA has been applied to several real-parameter engineering optimization problems to evaluate its effectiveness. In addition, to demonstrate the applicability and robustness of GEA, a comprehensive investigation is performed for a fair comparison with other standard optimization methods. The results demonstrate that GEA is noticeably prosperous in reaching the optimal solutions with a high convergence rate in comparison with other well-known nature-inspired algorithms, including ABC, BBO, PSO, and RCGA. Note that the source code of the GEA is publicly available at https://www.optim-app.com/projects/gea.

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Authors and Affiliations

  1. Department of Electronics and Electrical Engineering, Shiraz University of Technology, Shiraz, Iran

    Mojtaba Ghasemi

  2. Department of Electrical Engineering, Faculty of Engineering, Jahrom University, Jahrom, Fras, Iran

    Mohsen Zare

  3. Department of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran

    Amir Zahedi

  4. Department of Electrical and Computer Engineering, University of Cyprus, Nicosia, Cyprus

    Mohammad-Amin Akbari

  5. Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Brisbane, QLD, 4006, Australia

    Seyedali Mirjalili

  6. University Research and Innovation Center, Obuda University, 1034, Budapest, Hungary

    Seyedali Mirjalili

  7. Department of Electrical and Computer Engineering, Lebanese American University, Byblos, 13-5053, Lebanon

    Laith Abualigah

  8. Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman, 19328, Jordan

    Laith Abualigah

  9. MEU Research Unit, Middle East University, Amman, 11831, Jordan

    Laith Abualigah

  10. Applied Science Research Center, Applied Science Private University, Amman, 11931, Jordan

    Laith Abualigah

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Appendix A: Portion of Exploration and Exploitation

Appendix A: Portion of Exploration and Exploitation

The following equations should be implemented to determine the proportion of exploitation and exploration processes within evolutionary algorithms and the level of population diversity [52].

Suppose the size of the initial population is Npop and the number of decision variables is D:

$${{\varvec{X}}}_{{\varvec{j}}}=[{x}_{1,j}, {x}_{2,j}, \dots , {x}_{Npop,j}] \forall \mathrm{j}\hspace{0.17em}=\hspace{0.17em}\mathrm{1,2}, \dots ,\mathrm{ D}$$
(41)
$${K}_{j}=median({{\varvec{X}}}_{j}) \forall \mathrm{j}\hspace{0.17em}=\hspace{0.17em}\mathrm{1,2}, \dots ,\mathrm{ D}$$
(42)

Xj is a vector that contains all the jth variables of all population. Now the following two parameters can be calculated.

$${dv}_{j}={\sum }_{i=1}^{Npop}{K}_{j}-{x}_{i,j} \forall \mathrm{j}\hspace{0.17em}=\hspace{0.17em}\mathrm{1,2}, \dots ,\mathrm{ D}$$
(43)
$$DV=\frac{1}{D}{\sum }_{j=1}^{D}{dv}_{j}$$
(44)

\({x}_{i,j}\) is the jth variable of ith population. \(DV\) is the average of diversity.

$$\%Pl=\frac{DV}{DV\_max}\times 100$$
(45)
$$\mathrm{\%}Pt=\frac{\left|DV-DV\_max\right|}{DV\_max}\times 100$$
(46)

DV is the population diversity in each iteration and DV_max is the maximum diversity between all iterations. %Pl and %Pt are the percentage of exploration and exploitation corresponding to each iteration.

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Ghasemi, M., Zare, M., Zahedi, A. et al. Geyser Inspired Algorithm: A New Geological-inspired Meta-heuristic for Real-parameter and Constrained Engineering Optimization. J Bionic Eng 21, 374–408 (2024). https://doi.org/10.1007/s42235-023-00437-8

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