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Volume 8 Issue 1
Jan.  2021

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Yirui Wang, Shangce Gao, Mengchu Zhou and Yang Yu, "A Multi-Layered Gravitational Search Algorithm for Function Optimization and Real-World Problems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 94-109, Jan. 2021. doi: 10.1109/JAS.2020.1003462
Citation: Yirui Wang, Shangce Gao, Mengchu Zhou and Yang Yu, "A Multi-Layered Gravitational Search Algorithm for Function Optimization and Real-World Problems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 94-109, Jan. 2021. doi: 10.1109/JAS.2020.1003462

A Multi-Layered Gravitational Search Algorithm for Function Optimization and Real-World Problems

doi: 10.1109/JAS.2020.1003462
Funds:  This research was partially supported by National Natural Science Foundation of China (61872271, 61673403, 61873105, 11972115), the Fundamental Research Funds for the Central Universities (22120190208), and JSPS KAKENHI (JP17K12751)
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  • A gravitational search algorithm (GSA) uses gravitational force among individuals to evolve population. Though GSA is an effective population-based algorithm, it exhibits low search performance and premature convergence. To ameliorate these issues, this work proposes a multi-layered GSA called MLGSA. Inspired by the two-layered structure of GSA, four layers consisting of population, iteration-best, personal-best and global-best layers are constructed. Hierarchical interactions among four layers are dynamically implemented in different search stages to greatly improve both exploration and exploitation abilities of population. Performance comparison between MLGSA and nine existing GSA variants on twenty-nine CEC2017 test functions with low, medium and high dimensions demonstrates that MLGSA is the most competitive one. It is also compared with four particle swarm optimization variants to verify its excellent performance. Moreover, the analysis of hierarchical interactions is discussed to illustrate the influence of a complete hierarchy on its performance. The relationship between its population diversity and fitness diversity is analyzed to clarify its search performance. Its computational complexity is given to show its efficiency. Finally, it is applied to twenty-two CEC2011 real-world optimization problems to show its practicality.


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  • [1]
    Y. Yu, S. C. Gao, Y. R. Wang, and Y. Todo, “Global optimum-based search differential evolution,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 379–394, Mar. 2019. doi: 10.1109/JAS.2019.1911378
    S. C. Gao, Y. Yu, Y. R. Wang, J. H. Wang, J. J. Cheng, and M. C. Zhou, “Chaotic local search-based differential evolution algorithms for optimization,” IEEE Trans. Syst., Man, Cybern.: Syst., 2019, to be published. DOI: 10.1109/TSMC.2019.2956121.
    S. C. Gao, S. B. Song, J. J. Cheng, Y. Todo, and M. C. Zhou, “Incorporation of solvent effect into multi-objective evolutionary algorithm for improved protein structure prediction,” IEEE/ACM Trans. Comput. Biol. Bioinformatics, vol. 15, no. 4, pp. 1365–1378, Jul.-Aug. 2018. doi: 10.1109/TCBB.2017.2705094
    Z. M. Lv, L. Q. Wang, Z. Y. Han, J. Zhao, and W. Wang, “Surrogate-assisted particle swarm optimization algorithm with Pareto active learning for expensive multi-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 838–849, May 2019. doi: 10.1109/JAS.2019.1911450
    P. Champasak, N. Panagant, N. Pholdee, S. Bureerat, and A. R. Yildiz, “Self-adaptive many-objective meta-heuristic based on decomposition for many-objective conceptual design of a fixed wing unmanned aerial vehicle,” Aerosp. Sci. Technol., vol. 100, Article ID 105783, May 2020.
    F. Hamza, H. Abderazek, S. Lakhdar, D. Ferhat, and A. R. Yildiz, “Optimum design of cam-roller follower mechanism using a new evolutionary algorithm,” Int. J. Adv. Manuf. Technol., vol. 99, no. 5–8, pp. 1267–1282, Nov. 2018. doi: 10.1007/s00170-018-2543-3
    S. G. Gao, Y. R. Wang, J. J. Cheng, Y. Inazumi, and Z. Tang, “Ant colony optimization with clustering for solving the dynamic location routing problem,” Appl. Math. Comput., vol. 285, pp. 149–173, Jul. 2016.
    Y. R. Wang, S. C. Gao, and Y. Todo, “Ant colony systems for optimization problems in dynamic environments,” in Swarm Intelligence - Volume 1: Principles, Current Algorithms and Methods, Y. Tan, Ed. IET, London, UK: The Institution of Engineering and Technology, 2018, pp. 85−120.
    H. Abderazek, A. R. Yildiz, and S. Mirjalili, “Comparison of recent optimization algorithms for design optimization of a cam-follower mechanism,” Knowl.-Based Syst., vol. 191, Article ID 105237, Mar. 2020.
    E. Kurtuluş, A. R. Yildiz, S. M. Sait, and S. Bureerat, “A novel hybrid Harris hawks-simulated annealing algorithm and RBF-based metamodel for design optimization of highway guardrails,” Mater. Test., vol. 62, no. 3, pp. 251–260, Mar. 2020. doi: 10.3139/120.111478
    S. C. Gao, M. C. Zhou, Y. R. Wang, J. J. Cheng, H. Yachi, and J. H. Wang, “Dendritic neuron model with effective learning algorithms for classification, approximation, and prediction,” IEEE Trans. Neural Networks Learn. Syst., vol. 30, no. 2, pp. 601–614, Feb. 2019. doi: 10.1109/TNNLS.2018.2846646
    L. Wang and J. W. Lu, “A memetic algorithm with competition for the capacitated green vehicle routing problem,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 2, pp. 516–526, Mar. 2019. doi: 10.1109/JAS.2019.1911405
    A. R. Yildiz, B. S. Yildiz, S. M. Sait, S. Bureerat, and N. Pholdee, “A new hybrid Harris hawks-Nelder-Mead optimization algorithm for solving design and manufacturing problems,” Mater. Test., vol. 61, no. 8, pp. 735–743, Aug. 2019. doi: 10.3139/120.111378
    B. S. Yildiz and A. R. Yildiz, “Moth-flame optimization algorithm to determine optimal machining parameters in manufacturing processes,” Mater. Test., vol. 59, no. 5, pp. 425–429, May 2017. doi: 10.3139/120.111024
    A. R. Yildiz, “A novel hybrid whale–Nelder–Mead algorithm for optimization of design and manufacturing problems,” Int. J. Adv. Manuf. Technol., vol. 105, no. 12, pp. 5091–5104, Dec. 2019. doi: 10.1007/s00170-019-04532-1
    B. S. Yildiz, A. R. Yildiz, N. Pholdee, S. Bureerat, S. M. Sait, and V. Patel, “The Henry gas solubility optimization algorithm for optimum structural design of automobile brake components,” Mater. Test., vol. 62, no. 3, pp. 261–264, Mar. 2020. doi: 10.3139/120.111479
    B. S. Yildiz and A. R. Yildiz, “The Harris hawks optimization algorithm, salp swarm algorithm, grasshopper optimization algorithm and dragonfly algorithm for structural design optimization of vehicle components,” Mater. Test., vol. 61, no. 8, pp. 744–748, Aug. 2019. doi: 10.3139/120.111379
    B. S. Yildiz and A. R. Yildiz, “Comparison of grey wolf, whale, water cycle, ant lion and sine-cosine algorithms for the optimization of a vehicle engine connecting rod,” Mater. Test., vol. 60, no. 3, pp. 311–315, Mar. 2018. doi: 10.3139/120.111153
    A. R. Yildiz, H. Abderazek, and S. Mirjalili, “A comparative study of recent non-traditional methods for mechanical design optimization,” Arch. Comput. Methods Eng., vol. 27, no. 4, pp. 1031–1048, Sep. 2020. doi: 10.1007/s11831-019-09343-x
    Y. R. Wang, Y. Yu, S. Y. Cao, X. Y. Zhang, and S. C. Gao, “A review of applications of artificial intelligent algorithms in wind farms,” Artif. Intell. Rev., vol. 53, no. 5, pp. 3447–3500, Jun. 2020. doi: 10.1007/s10462-019-09768-7
    J. L. Payne, M. Giacobini, and J. H. Moore, “Complex and dynamic population structures: Synthesis, open questions, and future directions,” Soft Comput., vol. 17, no. 7, pp. 1109–1120, Jul. 2013. doi: 10.1007/s00500-013-0994-x
    B. Allen, G. Lippner, Y. T. Chen, B. Fotouhi, N. Momeni, S. T. Yau, and M. A. Nowak, “Evolutionary dynamics on any population structure,” Nature, vol. 544, no. 7649, pp. 227–230, Apr. 2017. doi: 10.1038/nature21723
    J. J. Cheng, X. Wu, M. C. Zhou, S. C. Gao, Z. H. Huang, and C. Liu, “A novel method for detecting new overlapping community in complex evolving networks,” IEEE Trans. Syst.,Man,Cybern.:Syst., vol. 49, no. 9, pp. 1832–1844, Sep. 2019. doi: 10.1109/TSMC.2017.2779138
    B. Dorronsoro and P. Bouvry, “Improving classical and decentralized differential evolution with new mutation operator and population topologies,” IEEE Trans. Evol. Comput., vol. 15, no. 1, pp. 67–98, Feb. 2011. doi: 10.1109/TEVC.2010.2081369
    E. Alba and M. Tomassini, “Parallelism and evolutionary algorithms,” IEEE Trans. Evol. Comput., vol. 6, no. 5, pp. 443–462, Oct. 2002. doi: 10.1109/TEVC.2002.800880
    N. Lynn, M. Z. Ali, and P. N. Suganthan, “Population topologies for particle swarm optimization and differential evolution,” Swarm Evol. Comput., vol. 39, pp. 24–35, Apr. 2018. doi: 10.1016/j.swevo.2017.11.002
    E. Cantú-Paz, Efficient and Accurate Parallel Genetic Algorithms. Boston, USA: Springer, 2001.
    E. Alba and B. Dorronsoro, Cellular Genetic Algorithms. Boston, USA: Springer, 2008.
    A. Sharifi, V. Noroozi, M. Bashiri, A. B. Hashemi, and M. R. Meybodi, “Two phased cellular PSO: A new collaborative cellular algorithm for optimization in dynamic environments,” in Proc. 2012 IEEE Congr. Evolutionary Computation, Brisbane, Australia, pp. 1−8.
    S. Nabizadeh, A. Rezvanian, and M. R. Meybodi, “A multi-swarm cellular PSO based on clonal selection algorithm in dynamic environments,” in Proc. 2012 Int. Conf. Informatics, Electronics & Vision, Dhaka, Bangladesh, pp. 482−486.
    W. Fang, J. Sun, H. H. Chen, and X. J. Wu, “A decentralized quantum-inspired particle swarm optimization algorithm with cellular structured population,” Inf. Sci., vol. 330, pp. 19–48, Feb. 2016. doi: 10.1016/j.ins.2015.09.055
    B. Dorronsoro and P. Bouvry, “Differential evolution algorithms with cellular populations,” in Proc. 11th Int. Conf. Parallel Problem Solving from Nature, Kraków, Poland, 2010, pp. 320−330.
    J. L. Liao, Y. Q. Cai, T. Wang, H. Tian, and Y. H. Chen, “Cellular direction information based differential evolution for numerical optimization: An empirical study,” Soft Comput., vol. 20, no. 7, pp. 2801–2827, Jul. 2016. doi: 10.1007/s00500-015-1682-9
    A. El Dor, M. Clerc, and P. Siarry, “A multi-swarm PSO using charged particles in a partitioned search space for continuous optimization,” Comput. Optim. Appl., vol. 53, no. 1, pp. 271–295, Sep. 2012. doi: 10.1007/s10589-011-9449-4
    J. J. Liang and P. N. Suganthan, “Dynamic multi-swarm particle swarm optimizer,” in Proc. 2005 IEEE Swarm Intelligence Symp., Pasadena, USA, pp. 124−129.
    Y. Jiang, W. Huang, and L. Chen, “Applying multi-swarm accelerating particle swarm optimization to dynamic continuous functions,” in Proc. 2009 Second Int. Workshop on Knowledge Discovery and Data Mining, Moscow, Russia, pp. 710−713.
    I. De Falco, A. Della Cioppa, D. Maisto, U. Scafuri, and E. Tarantino, “Biological invasion–inspired migration in distributed evolutionary algorithms,” Inf. Sci., vol. 207, pp. 50–65, Nov. 2012. doi: 10.1016/j.ins.2012.04.027
    J. X. Cheng, G. X. Zhang, and F. Neri, “Enhancing distributed differential evolution with multicultural migration for global numerical optimization,” Inf. Sci., vol. 247, pp. 72–93, Oct. 2013. doi: 10.1016/j.ins.2013.06.011
    Y. J. Gong, W. N. Chen, Z. H. Zhan, J. Zhang, Y. Li, Q. F. Zhang, and J. J. Li, “Distributed evolutionary algorithms and their models: A survey of the state-of-the-art,” Appl. Soft Comput., vol. 34, pp. 286–300, Sep. 2015. doi: 10.1016/j.asoc.2015.04.061
    S. Janson and M. Middendorf, “A hierarchical particle swarm optimizer and its adaptive variant,” IEEE Trans. Syst.,Man,Cybern.,Part B (Cybern.), vol. 35, no. 6, pp. 1272–1282, Dec. 2005. doi: 10.1109/TSMCB.2005.850530
    F. Herrera, M. Lozano, and C. Moraga, “Hierarchical distributed genetic algorithms,” Int. J. Intell. Syst., vol. 14, no. 11, pp. 1099–1121, Nov. 1999. doi: 10.1002/(SICI)1098-111X(199911)14:11<1099::AID-INT3>3.0.CO;2-O
    M. Giacobini, M. Preuss, and M. Tomassini, “Effects of scale-free and small-world topologies on binary coded self-adaptive CEA,” in Proc. 6th European Conf. Evolutionary Computation in Combinatorial Optimization, Budapest, Hungary, 2006, pp. 86−98.
    C. G. Zhang and Z. Yi, “Scale-free fully informed particle swarm optimization algorithm,” Inf. Sci., vol. 181, no. 20, pp. 4550–4568, Oct. 2011. doi: 10.1016/j.ins.2011.02.026
    E. Lieberman, C. Hauert, and M. A. Nowak, “Evolutionary dynamics on graphs,” Nature, vol. 433, no. 7023, pp. 312–316, Jan. 2005. doi: 10.1038/nature03204
    S. C. Gao, Y. R. Wang, J. H. Wang, and J. J. Cheng, “Understanding differential evolution: A Poisson law derived from population interaction network,” J. Comput. Sci., vol. 21, pp. 140–149, Jul. 2017. doi: 10.1016/j.jocs.2017.06.007
    Y. R. Wang, S. C. Gao, Y. Yu, and Z. Xu, “The discovery of population interaction with a power law distribution in brain storm optimization,” Memetic Comput., vol. 11, no. 1, pp. 65–87, Mar. 2019. doi: 10.1007/s12293-017-0248-z
    E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, “GSA: A gravitational search algorithm,” Inf. Sci., vol. 179, no. 13, pp. 2232–2248, Jun. 2009. doi: 10.1016/j.ins.2009.03.004
    S. Sarafrazi, H. Nezamabadi-Pour, and S. Saryazdi, “Disruption: A new operator in gravitational search algorithm,” Sci. Iran., vol. 18, no. 3, pp. 539–548, Jun. 2011. doi: 10.1016/j.scient.2011.04.003
    H. Nobahari, M. Nikusokhan, and P. Siarry, “A multi-objective gravitational search algorithm based on non-dominated sorting,” Int. J. Swarm Intell. Res., vol. 3, no. 3, pp. 32–49, Jul. 2012. doi: 10.4018/jsir.2012070103
    S. C. Gao, C. Vairappan, Y. Wang, Q. P. Cao, and Z. Tang, “Gravitational search algorithm combined with chaos for unconstrained numerical optimization,” Appl. Math. Comput., vol. 231, pp. 48–62, Mar. 2014.
    M. Khatibinia and S. Khosravi, “A hybrid approach based on an improved gravitational search algorithm and orthogonal crossover for optimal shape design of concrete gravity dams,” Appl. Soft Comput., vol. 16, pp. 223–233, Mar. 2014. doi: 10.1016/j.asoc.2013.12.008
    U. Güvenç and F. Katircioğlu, “Escape velocity: A new operator for gravitational search algorithm,” Neural Comput. Appl., vol. 31, no. 1, pp. 27–42, Jan. 2019. doi: 10.1007/s00521-017-2977-9
    P. Haghbayan, H. Nezamabadi-Pour, and S. Kamyab, “A niche GSA method with nearest neighbor scheme for multimodal optimization,” Swarm Evol. Comput., vol. 35, pp. 78–92, Aug. 2017. doi: 10.1016/j.swevo.2017.03.002
    M. Doraghinejad and H. Nezamabadi-Pour, “Black hole: A new operator for gravitational search algorithm,” Int. J. Comput. Intell. Syst., vol. 7, no. 5, pp. 809–826, Oct. 2014. doi: 10.1080/18756891.2014.966990
    S. Sarafrazi, H. Nezamabadi-Pour, and S. R. Seydnejad, “A novel hybrid algorithm of GSA with kepler algorithm for numerical optimization,” J. King Saud Univ.-Comput. Inf. Sci., vol. 27, no. 3, pp. 288–296, Jul. 2015.
    B. Shaw, V. Mukherjee, and S. P. Ghoshal, “A novel opposition-based gravitational search algorithm for combined economic and emission dispatch problems of power systems,” Int. J. Electr. Power Energy Syst., vol. 35, no. 1, pp. 21–33, Feb. 2012. doi: 10.1016/j.ijepes.2011.08.012
    E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, “BGSA: Binary gravitational search algorithm,” Nat. Comput., vol. 9, no. 3, pp. 727–745, Sep. 2010. doi: 10.1007/s11047-009-9175-3
    S. C. Gao, Y. Todo, T. Gong, G. Yang, and Z. Tang, “Graph planarization problem optimization based on triple-valued gravitational search algorithm,” IEEJ Trans. Electr. Electron. Eng., vol. 9, no. 1, pp. 39–48, Jan. 2014. doi: 10.1002/tee.21934
    M. Soleimanpour-Moghadam, H. Nezamabadi-Pour, and M. M. Farsangi, “A quantum inspired gravitational search algorithm for numerical function optimization,” Inf. Sci., vol. 267, pp. 83–100, May 2014. doi: 10.1016/j.ins.2013.09.006
    S. Duman, U. Güvenç, Y. Sönmez, and N. Yörükeren, “Optimal power flow using gravitational search algorithm,” Energy Convers. Manag., vol. 59, pp. 86–95, Jul. 2012. doi: 10.1016/j.enconman.2012.02.024
    B. González, F. Valdez, P. Melin, and G. Prado-Arechiga, “Fuzzy logic in the gravitational search algorithm for the optimization of modular neural networks in pattern recognition,” Expert Syst. Appl., vol. 42, no. 14, pp. 5839–5847, Aug. 2015. doi: 10.1016/j.eswa.2015.03.034
    R. E. Precup, R. C. David, E. M. Petriu, M. B. Radac, and S. Preitl, “Adaptive GSA-based optimal tuning of PI controlled servo systems with reduced process parametric sensitivity, robust stability and controller robustness,” IEEE Trans. Cybern., vol. 44, no. 11, pp. 1997–2009, Nov. 2014. doi: 10.1109/TCYB.2014.2307257
    S. Al-Zubaidi, J. A. Ghani, and C. H. C. Haron, “Optimization of cutting conditions for end milling of Ti6Al4V Alloy by using a gravitational search algorithm (GSA),” Meccanica, vol. 48, no. 7, pp. 1701–1715, Sep. 2013. doi: 10.1007/s11012-013-9702-2
    E. Rashedi, E. Rashedi, and H. Nezamabadi-Pour, “A comprehensive survey on gravitational search algorithm,” Swarm Evol. Comput., vol. 41, pp. 141–158, Aug. 2018. doi: 10.1016/j.swevo.2018.02.018
    A. R. Yildiz, E. Kurtuluş, E. Demirci, B. S. Yildiz, and S. Karagöz, “Optimization of thin-wall structures using hybrid gravitational search and Nelder-Mead algorithm,” Mater. Test., vol. 58, no. 1, pp. 75–78, Jan. 2016. doi: 10.3139/120.110823
    B. S. Yildiz, H. Lekesiz, and A. R. Yildiz, “Structural design of vehicle components using gravitational search and charged system search algorithms,” Mater. Test., vol. 58, no. 1, pp. 79–81, Jan. 2016. doi: 10.3139/120.110819
    G. Y. Sun, A. Z. Zhang, Z. J. Wang, Y. J. Yao, J. S. Ma, and G. D. Couples, “Locally informed gravitational search algorithm,” Knowl.-Based Syst., vol. 104, pp. 134–144, Jul. 2016. doi: 10.1016/j.knosys.2016.04.017
    Z. Y. Lei, S. C. Gao, S. Gupta, J. J. Cheng, and G. Yang, “An aggregative learning gravitational search algorithm with self-adaptive gravitational constants,” Expert Syst. Appl., vol. 152, Article ID 113396, Aug. 2020.
    F. Q. Zhao, F. L. Xue, Y. Zhang, W. M. Ma, C. Zhang, and H. B. Song, “A hybrid algorithm based on self-adaptive gravitational search algorithm and differential evolution,” Expert Syst. Appl., vol. 113, pp. 515–530, Dec. 2018. doi: 10.1016/j.eswa.2018.07.008
    A. Z. Zhang, G. Y. Sun, J. C. Ren, X. D. Li, Z. J. Wang, and X. P. Jia, “A dynamic neighborhood learning-based gravitational search algorithm,” IEEE Trans. Cybern., vol. 48, no. 1, pp. 436–447, Jan. 2018. doi: 10.1109/TCYB.2016.2641986
    Y. R. Wang, Y. Yu, S. C. Gao, H. Y. Pan, and G. Yang, “A hierarchical gravitational search algorithm with an effective gravitational constant,” Swarm Evol. Comput., vol. 46, pp. 118–139, May 2019. doi: 10.1016/j.swevo.2019.02.004
    H. Mittal, R. Pal, A. Kulhari, and M. Saraswat, “Chaotic kbest gravitational search algorithm (CKGSA),” in Proc. 2016 Ninth Int. Conf. Contemporary Computing, Noida, India, pp. 1−6.
    F. Olivas, F. Valdez, P. Melin, A. Sombra, and O. Castillo, “Interval type-2 fuzzy logic for dynamic parameter adaptation in a modified gravitational search algorithm,” Inf. Sci., vol. 476, pp. 159–175, Feb. 2019. doi: 10.1016/j.ins.2018.10.025
    H. Mittal and M. Saraswat, “An image segmentation method using logarithmic kbest gravitational search algorithm based superpixel clustering,” Evol. Intell., 2018, to be published. DOI: 10.1007/s12065-018-0192-y.
    D. Pelusi, R. Mascella, L. Tallini, J. Nayak, B. Naik, and Y. Deng, “Improving exploration and exploitation via a hyperbolic gravitational search algorithm,” Knowl.-Based Syst., vol. 193, Article ID 105404, Apr. 2020.
    H. Mittal and M. Saraswat, “An optimum multi-level image thresholding segmentation using non-local means 2D histogram and exponential Kbest gravitational search algorithm,” Eng. Appl. Artif. Intell., vol. 71, pp. 226–235, May 2018. doi: 10.1016/j.engappai.2018.03.001
    D. Pelusi, R. Mascella, L. Tallini, J. Nayak, B. Naik, and A. Abraham, “Neural network and fuzzy system for the tuning of gravitational search algorithm parameters,” Expert Syst. Appl., vol. 102, pp. 234–244, Jul. 2018. doi: 10.1016/j.eswa.2018.02.026
    S. Mirjalili and S. Z. M. Hashim, “A new hybrid PSOGSA algorithm for function optimization,” in Proc. 2010 Int. Conf. Computer and Information Application, Tianjin, China, pp. 374−377.
    S. Mirjalili and A. Lewis, “Adaptive gbest-guided gravitational search algorithm,” Neural Comput. Appl., vol. 25, no. 7–8, pp. 1569–1584, Dec. 2014. doi: 10.1007/s00521-014-1640-y
    E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, “Filter modeling using gravitational search algorithm,” Eng. Appl. Artif. Intell., vol. 24, no. 1, pp. 117–122, Feb. 2011. doi: 10.1016/j.engappai.2010.05.007
    A. Bahrololoum, H. Nezamabadi-Pour, H. Bahrololoum, and M. Saeed, “A prototype classifier based on gravitational search algorithm,” Appl. Soft Comput., vol. 12, no. 2, pp. 819–825, Feb. 2012. doi: 10.1016/j.asoc.2011.10.008
    J. K. Ji, S. C. Gao, S. Q. Wang, Y. J. Tang, H. Yu, and Y. Todo, “Self-adaptive gravitational search algorithm with a modified chaotic local search,” IEEE Access, vol. 5, pp. 17881–17895, Sep. 2017. doi: 10.1109/ACCESS.2017.2748957
    N. H. Awad, M. Z. Ali, J. J. Liang, B. Y. Qu, and P. N. Suganthan, “Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective bound constrained real-parameter numerical optimization,” Nanyang Technological University, Singapore, 2016.
    J. D. Gibbons and S. Chakraborti, “Nonparametric statistical inference,” in International Encyclopedia of Statistical Science, M. Lovric, Ed. Berlin, Heidelberg, Germany: Springer, 2011, pp. 977−979.
    B. Gu and F. Pan, “Modified gravitational search algorithm with particle memory ability and its application,” Int. J. Innov. Comput.,Inf. Control, vol. 9, no. 11, pp. 4531–4544, 2013.
    Z. Y. Song, S. C. Gao, Y. Yu, J. Sun, and Y. Todo, “Multiple chaos embedded gravitational search algorithm,” IEICE Trans. Inf. Syst., vol. E100-D, no. 4, pp. 888–900, Apr. 2017. doi: 10.1587/transinf.2016EDP7512
    Y. R. Wang, S. C. Gao, Y. Yu, Z. Q. Wang, J. J. Cheng, and T. Yuki, “A gravitational search algorithm with chaotic neural oscillators,” IEEE Access, vol. 8, pp. 25938–25948, Feb. 2020. doi: 10.1109/ACCESS.2020.2971505
    Y. Shi and R. Eberhart, “A modified particle swarm optimizer,” in Proc. 1998 IEEE Int. Conf. Evolutionary Computation Proceedings, Anchorage, USA, pp. 69−73.
    Z. H. Zhan, J. Zhang, Y. Li, and Y. H. Shi, “Orthogonal learning particle swarm optimization,” IEEE Trans. Evol. Comput., vol. 15, no. 6, pp. 832–847, Dec. 2011. doi: 10.1109/TEVC.2010.2052054
    Y. J. Gong, J. J. Li, Y. C. Zhou, Y. Li, H. S. H. Chung, Y. H. Shi, and J. Zhang, “Genetic learning particle swarm optimization,” IEEE Trans. Cybern., vol. 46, no. 10, pp. 2277–2290, Oct. 2016. doi: 10.1109/TCYB.2015.2475174
    R. Cheng and Y. C. Jin, “A competitive swarm optimizer for large scale optimization,” IEEE Trans. Cybern., vol. 45, no. 2, pp. 191–204, Feb. 2015. doi: 10.1109/TCYB.2014.2322602
    S. Das and P. N. Suganthan, “Problem definitions and evaluation criteria for CEC 2011 competition on testing evolutionary algorithms on real world optimization problems,” Jadavpur University, Kolkata, 2010.
    J. Zhao, S. X. Liu, M. C. Zhou, X. W. Guo, and L. Qi, “Modified cuckoo search algorithm to solve economic power dispatch optimization problems,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 4, pp. 794–806, Jul. 2018. doi: 10.1109/JAS.2018.7511138
    K. Z. Gao, Z. G. Cao, L. Zhang, Z. H. Chen, Y. Y. Han, and Q. K. Pan, “A review on swarm intelligence and evolutionary algorithms for solving flexible job shop scheduling problems,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 4, pp. 904–916, Jul. 2019. doi: 10.1109/JAS.2019.1911540
    J. J. Wang and T. Kumbasar, “Parameter optimization of interval Type-2 fuzzy neural networks based on PSO and BBBC methods,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 247–257, Jan. 2019. doi: 10.1109/JAS.2019.1911348


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    • A multi-layered gravitational search algorithm is proposed from the perspective of population structure.
    • Hierarchical interactions among four layers enhance the proposed algorithm’s exploration and exploitation abilities.
    • Population diversity and fitness diversity are discussed to understand the proposed algorithm’s search behavior.
    • The proposed algorithm is applied to function optimization and real-world problems.


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