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Alternated superior chaotic variants of gravitational search algorithm for optimization problems

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  • Kumar, Deepak
  • Rani, Mamta

Abstract

Nature inspired algorithms like Gravitational Search Algorithm (GSA) has been able to solve complex optimization problems with a reasonable performance. But still there is problem of premature convergence to the local optimal solutions due to lack of appropriate balancing between exploration and exploitation procedures. In the literature, chaotic maps have been successful in diversifying the population to a greater level to avoid the entrapment of the solutions in local region(s), and provide better convergence speed with high precision. Recent developments in nonlinear dynamical systems, especially discrete alternated systems, have proved their worth in enhancing the functionality of the metaheuristic algorithms to a great extent (Kumar and Rani, 2019). We have integrated alternated discrete dynamical systems in superior orbit with GSA for more diversification of the population with the aim of increasing the chances for the candidate solutions to arrive at global solutions which otherwise remain stagnant in local optimal points. From the obtained results, we have verified that the proposed methods have outperformed the competing algorithms significantly as they have been able to arrive at global optimal points with much improved optimization rates. In some cases, the improvement in optimization values (mean and standard deviation) have reduced to less than twice the optimization values of the chaotic GSA.

Suggested Citation

  • Kumar, Deepak & Rani, Mamta, 2022. "Alternated superior chaotic variants of gravitational search algorithm for optimization problems," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:chsofr:v:159:y:2022:i:c:s0960077922003629
    DOI: 10.1016/j.chaos.2022.112152
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    References listed on IDEAS

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    1. Arturo Valdivia-González & Daniel Zaldívar & Erik Cuevas & Marco Pérez-Cisneros & Fernando Fausto & Adrián González, 2017. "A Chaos-Embedded Gravitational Search Algorithm for the Identification of Electrical Parameters of Photovoltaic Cells," Energies, MDPI, vol. 10(7), pages 1-25, July.
    2. Yadav, Anju & Rani, Mamta, 2015. "Alternate superior Julia sets," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 1-9.
    3. Mamta Rani & Deepak Kumar, 2019. "Alternated Chaotic Biogeography Based Algorithm for Optimization Problems," International Journal of Applied Evolutionary Computation (IJAEC), IGI Global, vol. 10(4), pages 39-50, October.
    4. Levinsohn, Erik A. & Mendoza, Steve A. & Peacock-López, Enrique, 2012. "Switching induced complex dynamics in an extended logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 426-432.
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