Hybrid white shark optimizer with differential evolution for training multi-layer perceptron neural network

This study presents a novel hybrid optimization algorithm combining the white shark optimizer (WSO) with differential evolution (DE), referred to as WSODE, for training multi-layer perceptron (MLP) neural networks and solving systems design problems. The structure of WSO, while effective in exploitation due to its wavy motion-based search, suffers from limited exploration capability. This limitation arises from WSO’s reliance on local search behaviors, where it tends to focus on a narrow region of the search space, reducing the diversity of solutions and increasing the likelihood of premature convergence. To address this, DE is integrated with WSO (WSODE) to enhance exploration by introducing mutation and crossover operations, which increase diversity and enable the algorithm to escape local optima. The performance of WSODE is evaluated on the CEC2022, CEC2021, and CEC2017 benchmark functions and compared against several state-of-the-art optimizers. The results demonstrate that WSODE consistently achieves superior or competitive performance, with faster convergence rates and higher solution quality across diverse benchmarks. Specifically, on the CEC2022 suite, WSODE ranked first or second across multiple functions, including high-dimensional, multi-modal, and deceptive landscapes and significantly outperforming other algorithms like WOA and SHO. On the CEC2021 suite, WSODE ranked first in several complex functions, such as C6 and C10, with mean values of 3.32×10⁻¹ and 4.90×10¹, respectively, showcasing its robustness in handling deceptive and rugged landscapes. Additionally, WSODE has been applied to the training of multi-layer perceptrons using various datasets with different levels of complexity and attribute counts. The results indicate that WSODE achieves lower mean squared error and higher classification accuracy compared to existing methods across most datasets, reinforcing its effectiveness and reliability in both benchmark and practical applications.