A Metaheuristic Algorithm Based on Incomplete Differential Proportional-Integral-Derivative Control

Optimization plays a critical role in various domains, but traditional deterministic methods often falter when ad-dressing complex, high-dimensional problems. Metaheuristic algorithms have emerged as a robust alternative, but many struggle with balancing exploration and exploitation, thus limiting their adaptability. To address these challenges, this study introduces the Incomplete Differential Proportional-Integral-Derivative Optimization Algorithm (IDPOA). Inspired by incremental PID control, the IDPOA employs historical deviation data, an exponential dynamic tuning mechanism, and a smoothing coefficient to enhance optimization efficiency and convergence. The algorithm is evaluated using CEC2017 benchmark functions and real-world engineering problems, demonstrating superior performance in achieving global optima while avoiding local traps. Statistical tests affirm the robustness and computational efficiency of the IDPOA algorithm compared to state-of-the-art algorithms. This work contributes a novel, mathematically grounded approach to optimization, promising broad applicability and effectiveness for solving complex global optimization problems.