The precise manipulation of gantry cranes is inherently complicated by underactuated nonlinear dynamics, where a single input must simultaneously regulate trolley positioning and suppress multi-mode oscillations. Traditional Linear Quadratic Regulator (LQR) approaches often yield steady-state errors due to the absence of integral action, while parameter tuning via standard Sine Cosine Algorithms (SCA) is prone to premature convergence in high-dimensional search spaces. This work addresses these limitations by developing an Integral LQR (ILQR) controller tuned via an Improved Sine Cosine Algorithm (ISCA). Distinguished by a linear search path and empirical best-history retention, the ISCA mechanism balances exploration and exploitation to avoid local optima stagnation, ensuring precise gain optimization. Numerical validations confirm the superiority of the proposed ISCA-ILQR scheme, demonstrating a 12.5% reduction in payload sway compared to standard SCA-tuned counterparts in nominal operations. Moreover, the controller exhibits robust disturbance rejection; under combined parametric uncertainties involving significant cable extension (0.40 m) and payload mass variations (0.50 kg), the system effectively confines residual sway within \(\pm 1 {\circ }\) limits, ensuring operational safety in dynamic industrial environments.