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Solving nonlinear systems and unconstrained optimization problems by hybridizing whale optimization algorithm and flower pollination algorithm

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  • Tawhid, M.A.
  • Ibrahim, A.M.

Abstract

This paper suggests a new hybrid algorithm by integrating two population-based algorithms: Whale Optimization Algorithm (WOA) and Flower Pollination Algorithm (FPA), to solve complex nonlinear systems and unconstrained optimization problems. WOFPA denotes the suggested algorithm, a hybrid Whale Optimization Algorithm and Flower Pollination Algorithm. Nonlinear systems can be cast into unconstrained optimization problems, called merit functions, where the optimal solutions for the merit functions are equivalent to the solutions of nonlinear systems. WOFPA aims to decrease the execution time and the complexity of WOA and FPA. WOFPA has the advantages of WOA and FPA; WOFPA is a high-quality algorithm to solve both problems, nonlinear systems and unconstrained optimization problems. For example, FPA may have a premature convergence in the local optima, and WOFPA subdues the disadvantage of FPA. Numerical experiments of 14 benchmarks nonlinear systems and 30 CEC 2014 benchmarks unconstrained optimization functions with various dimensions are employed to test the performance of WOFPA. To have a further investigation for the performance of WOFPA, WOFPA is compared with WOA, FPA, and other existing algorithms from the literature. Two non-parametric statistical tests, Wilcoxon statistical test and the Friedman test, are conducted for this study to check the performance of the proposed algorithms and other compared algorithms and the significance of our results. The experiment results demonstrate that WOFPA performs better than other algorithms in the literature by getting the optimum solutions for most nonlinear systems and optimization problems and proves its efficiency compared with other existing algorithms.

Suggested Citation

  • Tawhid, M.A. & Ibrahim, A.M., 2021. "Solving nonlinear systems and unconstrained optimization problems by hybridizing whale optimization algorithm and flower pollination algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1342-1369.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:1342-1369
    DOI: 10.1016/j.matcom.2021.07.010
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    References listed on IDEAS

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    1. Mohamed A. Tawhid & Ahmed F. Ali, 2017. "Multi-directional bat algorithm for solving unconstrained optimization problems," OPSEARCH, Springer;Operational Research Society of India, vol. 54(4), pages 684-705, December.
    2. Abdelaziz, A.Y. & Ali, E.S. & Abd Elazim, S.M., 2016. "Implementation of flower pollination algorithm for solving economic load dispatch and combined economic emission dispatch problems in power systems," Energy, Elsevier, vol. 101(C), pages 506-518.
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    Cited by:

    1. Deng, Huaijun & Liu, Linna & Fang, Jianyin & Qu, Boyang & Huang, Quanzhen, 2023. "A novel improved whale optimization algorithm for optimization problems with multi-strategy and hybrid algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 794-817.
    2. Tawhid, Mohamed A. & Ibrahim, Abdelmonem M., 2022. "Improved salp swarm algorithm combined with chaos," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 202(C), pages 113-148.
    3. Zhang, Jinzhong & Zhang, Gang & Kong, Min & Zhang, Tan & Wang, Duansong & Chen, Rui, 2023. "CWOA: A novel complex-valued encoding whale optimization algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 151-188.

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