Multi-Objective Grouped Grey Wolf Optimization of PID Controllers Applied to a Water Treatment Plant Model.

A comparison of proportional-integral-derivative (PID) controller tuning for a 2x2 Multiple-Input Multiple-Output (MIMO) water treatment plant model is presented. The PID tuning procedures are based on Multi-Objective Grey Wolf Optimizer (MOGWO) and Multi-Objective Grouped Grey Wolf Optimizer (MOGGWO) are performed under two different initial conditions. The tuning procedure is structured as a multi-objective optimization problem with four objective functions, the integral time-squared error is minimized in each output response, and the integral of the control actions is minimized in each input. MOGWO is a metaheuristic based on the hunting behavior of grey wolves, following the hierarchy and leadership procedures that these animals have, while the proposed MOGGWO is a new version proposed in this study with two different groups with different functionalities. The performance was analyzed by 50 runs based on statistical metrics. MOGGWO can find more local minima since its Pareto front is more dispersed than that found by MOGWO.