Evolutionary Multi-Objective Direct Policy Search (EMODPS) is a prominent framework for designing control policies in multi-purpose environmental systems, combining direct policy search with multi-objective evolutionary algorithms (MOEAs) to identify Pareto approximate control policies. While EMODPS is effective, the choice of functions within its global approximator networks remains underexplored, despite their potential to significantly influence both solution quality and MOEA performance. This study conducts a rigorous assessment of a suite of Radial Basis Functions (RBFs) as candidates for these networks. We critically evaluate their ability to map system states to control actions, and assess their influence on Pareto efficient control policies. We apply this analysis to two contrasting case studies: the Conowingo Reservoir System, which balances competing water demands including hydropower, environmental flows, urban supply, power plant cooling, and recreation; and The Shallow Lake Problem, where a city navigates the trade-off between environmental and economic objectives when releasing anthropogenic phosphorus. Our findings reveal that the choice of RBF functions substantially impacts model outcomes. In complex scenarios like multi-objective reservoir control, this choice is critical, while in simpler contexts, such as the Shallow Lake Problem, the influence is less pronounced, though distinctive differences emerge in the characteristics of the prescribed control strategies.

Efficient multi-purpose reservoir control policies are crucial in the face of frequent and severe floods and droughts, and to balance water allocation across conflicting demands. Evolutionary Multi-Objective Direct Policy Search (EMODPS) is a popular approach to design control policies for multi-purpose reservoir systems. EMODPS, however, relies on experimental choices within the key components of the framework particularly when coupling multi-objective evolutionary optimization with nonlinear approximation networks. This study explores a suite of radial basis functions (RBFs) used to map the system's states to control actions in a flexible manner as time-varying, non-linear relationships. We provide a systematic assessment of different RBF functions to explore their suitability to obtain Pareto efficient control policies. We use the Susquehanna river basin case study in which competing water demands for hydropower, environment, urban water supply, atomic power plant cooling and recreation need to be met. Our findings suggest that the choice of RBF functions have a large impact on the model outcomes and the search behavior of the optimization algorithm.