Q-Learning-Based Dumbo Octopus Algorithm for Parameter Tuning of Fractional-Order PID Controller for AVR Systems

The tuning of fractional-order proportional-integral-derivative (FOPID) controllers for automatic voltage regulator (AVR) systems presents a complex challenge, necessitating the solution of real-order integral and differential equations. This study introduces the Dumbo Octopus Algorithm (DOA), a novel metaheuristic inspired by machine learning with animal behaviors, as an innovative approach to address this issue. For the first time, the DOA is invented and employed to optimize FOPID parameters, and its performance is rigorously evaluated against 11 existing metaheuristic algorithms using 23 classical benchmark functions and CEC2019 test sets. The evaluation includes a comprehensive quantitative analysis and qualitative analysis. Statistical significance was assessed using the Friedman’s test, highlighting the superior performance of the DOA compared to competing algorithms. To further validate its effectiveness, the DOA was applied to the FOPID parameter tuning of an AVR system, demonstrating exceptional performance in practical engineering applications. The results indicate that the DOA outperforms other algorithms in terms of convergence accuracy, robustness, and practical problem-solving capability. This establishes the DOA as a superior and promising solution for complex optimization problems, offering significant advancements in the tuning of FOPID for AVR systems.