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<p>The standard Whale Optimization Algorithm (WOA) is simple and widely used, but it can lose population diversity and converge prematurely when solving complex, multimodal, or high-dimensional optimization problems. This weakness is important because unstable optimization can reduce the reliability of benchmark-function solutions and neural network classification models. To address this problem, this study proposes a Gaussian mutation-based Improved Whale Optimization Algorithm (IWOA). The proposed mutation operator introduces controlled random perturbation into the search process so that search agents can escape stagnant regions while preserving the simple structure of the original WOA. IWOA was evaluated on 19 benchmark functions with dimensions of 10, 20, 30, 40, and 50 and was compared under identical conditions with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Bat Algorithm (BA), Seagull Optimization Algorithm (SOA), and standard WOA. The results show that IWOA achieved the best overall average rank and improved the standard WOA on 66 out of 95 function-dimensional cases, with 11 ties. Friedman testing confirmed significant differences among algorithms (<InlineEquation ID="IEq1"><EquationSource Format="TEX">\(\chi ^2 = 71.30\)</EquationSource></InlineEquation>, <InlineEquation ID="IEq2"><EquationSource Format="TEX">\(p = 2.21 \times 10^{-13}\)</EquationSource></InlineEquation>), and Wilcoxon signed-rank testing confirmed a significant improvement of IWOA over WOA (<InlineEquation ID="IEq3"><EquationSource Format="TEX">\(p = 0.0060\)</EquationSource></InlineEquation>). IWOA was also applied to train feedforward artificial neural networks on 14 classification datasets. The IWOA-ANN model achieved competitive or improved classification performance compared with BA-ANN, PSO-ANN, and WOA-ANN. The findings indicate that Gaussian mutation improves the exploration capability of WOA and provides a competitive optimizer for numerical optimization and neural network classification, although it is not universally superior on every function or dataset.</p>

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Gaussian Mutation-based Whale Optimization Algorithm for Benchmark Function Optimization and Neural Network Classification

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月14日

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  • Ali Raza,
  • Waqas Haider Bangyal,
  • Adnan Ashraf,
  • Zia Ul-Qayyum,
  • Shujaat Ali,
  • Dilawar Shah,
  • Muhammad Haleem

摘要

The standard Whale Optimization Algorithm (WOA) is simple and widely used, but it can lose population diversity and converge prematurely when solving complex, multimodal, or high-dimensional optimization problems. This weakness is important because unstable optimization can reduce the reliability of benchmark-function solutions and neural network classification models. To address this problem, this study proposes a Gaussian mutation-based Improved Whale Optimization Algorithm (IWOA). The proposed mutation operator introduces controlled random perturbation into the search process so that search agents can escape stagnant regions while preserving the simple structure of the original WOA. IWOA was evaluated on 19 benchmark functions with dimensions of 10, 20, 30, 40, and 50 and was compared under identical conditions with Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Bat Algorithm (BA), Seagull Optimization Algorithm (SOA), and standard WOA. The results show that IWOA achieved the best overall average rank and improved the standard WOA on 66 out of 95 function-dimensional cases, with 11 ties. Friedman testing confirmed significant differences among algorithms (\(\chi ^2 = 71.30\), \(p = 2.21 \times 10^{-13}\)), and Wilcoxon signed-rank testing confirmed a significant improvement of IWOA over WOA (\(p = 0.0060\)). IWOA was also applied to train feedforward artificial neural networks on 14 classification datasets. The IWOA-ANN model achieved competitive or improved classification performance compared with BA-ANN, PSO-ANN, and WOA-ANN. The findings indicate that Gaussian mutation improves the exploration capability of WOA and provides a competitive optimizer for numerical optimization and neural network classification, although it is not universally superior on every function or dataset.