<![CDATA[Real-world applications frequently necessitate optimization of chaotic response surfaces and constrained functions, which present difficult challenges for conventional methods. In order to effectively manage constraints and uncertainty, these complexities necessitate sophisticated algorithms. The objective of this research is to optimize the Rider Optimization Algorithm (ROA) by incorporating chaotic maps—namely, Logistic, Sinusoidal, and Iterative—to enhance exploration and exploitation. The chaotic ROA consistently outperforms the standard ROA in convergence speed, accuracy, and robustness, as evidenced by benchmark evaluations. For instance, in the multiple disk clutch brake design problem, the chaotic ROA obtained the highest objective value of 0.2352, which was equivalent to or greater than the leading algorithms TSO, MFO, and WOA. The chaotic ROA variants (ROAC1, ROAC2, ROAC3) exhibited superior stability by achieving low standard deviations (e.g., 0.3321 in the Branin function at high noise levels) across noisy response surface benchmarks. The integration of constraint-handling mechanisms guaranteed that practicable solutions were achieved without sacrificing optimality. The chaotic ROA is established as a robust and adaptable solution for complex, noisy, and constrained optimization challenges in industrial scheduling, resource allocation, and engineering design by the proposed approach.]]>
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