Neighborhood centroid opposition-based flood algorithm for optimizing fractional-order PID control in nonlinear heat exchanger dynamics

This study presents a novel neighborhood centroid opposition-based flood algorithm (NCO-FLA) for optimizing fractional-order proportional-integral-derivative (FOPID) controllers aimed at precise temperature regulation in nonlinear shell-and-tube heat exchanger systems. By integrating opposition-based learning (OBL) and neighborhood centroid mechanisms into the conventional flood algorithm (FLA), the proposed NCO-FLA significantly improves global search efficiency and mitigates premature convergence in high-dimensional parameter spaces. The FOPID controller, with its five tunable parameters, provides a more flexible and robust framework than traditional PID structures, especially under nonlinear and dynamic conditions commonly encountered in industrial heat exchange processes. Extensive simulations conducted in MATLAB/Simulink demonstrate that NCO-FLA outperforms benchmark metaheuristic algorithms, including the marine predators algorithm (MPA), reptile search algorithm (RSA), catch fish optimization algorithm (CFOA), and the original FLA as well as classical algorithms such as differential evolution (DE), particle swarm optimization (PSO), evolution strategy with covariance matrix adaptation (CMA-ES), DE variants with linear population size reduction (L-SHADE) and NCO-PSO. Quantitative results show that he proposed NCO-FLA achieved 10–15 % lower ITAE values compared to the other optimizers, confirming its enhanced control accuracy and convergence stability. The proposed NCO-FLA also exhibited a smoother and faster convergence trend compared to other algorithms, as confirmed by the convergence profiles, and achieved the lowest standard deviation (0.9183), indicating superior consistency and reliability. Additionally, the NCO-FLA-tuned FOPID controller achieves zero overshoot, near-zero steady-state error, and significantly shorter rise (5.16 s) and settling times (19.05 s). Statistical significance was confirmed through Friedman and Wilcoxon signed-rank tests, as well as Mann-Whitney U test where all p-values were below 0.05, affirming the superiority and robustness of the proposed method. These findings underscore the algorithm's strong potential for real-world deployment in complex thermal systems where high accuracy, stability, and adaptive control are critical. The proposed NCO-FLA represents a promising advancement in metaheuristic optimization for industrial control systems. Future work will focus on integrating the algorithm with machine learning models and evaluating its performance in large-scale, real-time environments.