The paper proposes an energy management system, which considers the efficiency of the reversible pump/turbin-e that varies nonlinearly depending on the water flow rate during the pump/turbine modes of operation. A vibration avoidance strategy of the reversible pump hydro storage is developed. A probabilistic approach based on artificial neural networks and Naive-based is used. Through minimizing the levelized Cost of Energy (COE), this study shows the optimal size and reconfiguration of the HMG system as well as purchased/sold energy. Two novel modified optimizers based on the Particle Swarm Optimization (PSO) and the Aquila Optimizer (AO), namely: AO initialized PSO and AO updated PSO are developed. The results via the PSO and AO optimizers are compared in terms of reducing the COE and attaining a low execution time. Based on the results, a COE of 0.22 $/kWh through the developed strategy could be obtained with CO2 emissions of 1974 ton/year against 0.24 $/kWh and 2460 ton/year using the PSO, which saves 24.6% of the yearly CO2 emissions. Furthermore, the vibration avoidance strategy avoids the dead zones and enables the reversible pump/turbine machine to operate at higher efficiencies — both of which are impossible to achieve in the occurrence of vibrations.