Hybridization of the weighted distance method with directional bat algorithm for NMPC tuning

This work presents a hybrid optimization algorithm that combines the Weighted Distance Method and the Directional Bat Algorithm to improve the efficiency and robustness of solving nonlinear model predictive control problems. The proposed hybrid framework integrates the global exploration capability of the Directional Bat Algorithm with the local exploitation and adaptive refinement properties of the Weighted Distance Method. In the first stage, the Directional Bat Algorithm generates a diverse set of candidate solutions by using adaptive mechanisms for frequency, amplitude, and random movement, thereby ensuring broad coverage of the search space and preventing premature convergence to local minima. Subsequently, the Weighted Distance Method refines these solutions by computing weighted directional vectors, which are updated at each iteration based on the population mean distance and each agent’s proximity to the global best individual. The sequential combination of both strategies achieves an effective balance between exploration and exploitation, resulting in greater stability, improved convergence performance, and higher-quality optimal solutions. On a standard suite of thirty benchmark functions in dimensions 10, 30, and 50, the hybrid ranks third among five optimizers: it outperforms both of its constituent algorithms but does not surpass the Differential Evolution and Particle Swarm baselines, confirming that the sequential coupling yields a stronger optimizer than either component alone. On the tuning of a nonlinear model predictive controller for a Van de Vusse reactor, the proposed hybrid scheme achieves competitive closed-loop tracking performance compared with the standalone methods while improving convergence stability and robustness to initialization, highlighting its potential for complex nonlinear control applications.