A chaotic zebra optimization algorithm for numerical and constrained engineering applications: a case study on MLP classification challenges

Optimization search algorithms plays a crucial role in resolving complex constrained engineering and Multi Layer Perceptron (MLP) classification problems, often requiring efficacious and robust search strategies. This study introduces the Chaotic Zebra Optimization Algorithm (CZOA), an enriched version of the classical Zebra Optimization Algorithm (ZOA), incorporating chaotic maps to enhance search efficiency and convergence speed. The CZOA variants (CZOA1, CZOA2, CZOA3, and CZOA4) are evaluated using 23 standard benchmark functions across multiple dimensions (10D, 30D, 50D, and 100D), the CEC 2022 benchmark test suite, and three constrained engineering optimal design problems (three-bar truss, pressure vessel, and multi-disk clutch optimization). Furthermore, CZOA’s effectiveness is evaluated on four MLP classification datasets (Balloon, Iris, Breast Cancer, and XOR dataset). Simulation results reveal that CZOA1 consistently outperforms other variants and classical ZOA, achieving the lowest fitness values, lowered standard deviations, and enriched convergence rates. Specifically, in F1 (10D), CZOA1 reduces computation time from 4559.9 s (ZOA) to just 0.1563 s, achieving faster speed up. In CEC 2022 functions test suit, CZOA1 delivers the best performance with an average fitness of 333.86 and a standard deviation of 0.69, surpassing state-of-the-art metaheuristics such as GWO, WOA, and TLBO. Engineering optimal design results confirm CZOA1’s superior fitness values, with 263.8965 in the three-bar truss problem and 6849.485 in pressure vessel optimization, outperforming classical methods like GWO, DE, and PSO. For MLP classification tasks, CZOA1 achieves a 99.00% classification rate in breast cancer detection, highlighting its superior ability in handling high-dimensional search spaces. Comparative evaluations demonstrate that chaotic maps significantly enhance exploration–exploitation balance, reduce computational search complexity, and improve solution accuracy. The findings establish CZOA as a promising optimization technique for real-world engineering and classification challenges.