This paper proposes a novel metaheuristic algorithm named fractal damping optimization (FDO), which is rooted in fractional-order damped vibration systems. By creatively integrating fractal geometry with fractional-order dynamics theory, alongside the Weierstrass–Mandelbrot fractal resonance model and fractional-order damping regulation mechanism, the developed algorithm dynamically balances global exploration and local exploitation within complex search landscapes. Empirical results demonstrate that FDO surpasses competitors across the majority of test functions, showcasing exceptional deep search capabilities.
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