Multi-Objective Fitted Q-Iteration: Random sampling for enhanced weights simplex exploration

This work explores the application of the Multi-Objective Fitted Q-Iteration (MOFQI) algorithm in water systems control, and introduces the random sampling to maximise the exploration of the weights simplex. MOFQI, as an offline, model-free, and multi-objective control algorithm, mitigates the challenges of dimensionality, modeling complexity, and multiple objectives encountered by traditional dynamic programming approaches. We explore the construction of the training dataset and leverage the Extra-Trees regressor for the continuous Q-function approximation. We compared MOFQI to Stochastic Dynamic Programming (SDP) on the Lake Como case study, which is characterized by three conflicting objectives: flood and drought control and water supply.