This work deals with the problem of a nozzle design addressed through a multi-objective optimization strategy where governing equations of fluid dynamics model the phenomena. The liquid flow rate and the nozzle length are considered as the design criteria. Two Differential Evolution variants are proposed to obtain a set of design configurations that presents numerous and different synergies between the design criteria. The first variant is based on the Hypervolume performance metric (MODE-HVR) and the second one includes the $\epsilon $ -dominance concept (MODE-HV $\epsilon \text{R}$ ). A comparative study is performed with other optimizers from well-established search approaches for multi-objective optimization such as algorithms based on Pareto dominance (NSGA-II and SPEA2), decomposition (MOEA/D), metric (SMS-EMOA) and hybrid (NSGA-III). Based on the Spacing and Hypervolume indicators of the obtained Pareto fronts, the proposed optimization algorithms can provide more design solutions, promoting the reconfigurability (synergy) in the nozzle design. Hence, the multi-objective design strategy allows the designer to have a wide range of solutions and to choose the most suitable one for a particular application, compared with a traditional design where both design criteria are considered as a single aggregate function.

The growing energy demand in rural areas such as the ejido Boca del Cerro, located in Tenosique, Tabasco (Mexico), near the Usumacinta River, calls for sustainable energy solutions such as microgrids. This study proposes an energy management system combining renewable energy forecasting and fuzzy control for a simulated small autonomous rural microgrid scenario designed to supply a fixed priority load of 5 kW and a variable flexible load ranging from 1 to 10 kW. Three LSTM architectures (vanilla, stacked, and bidirectional) are compared for predicting solar irradiance, wind speed, and river flow. The vanilla model is optimized using Hyperband to improve prediction accuracy, particularly for flow rate, which is rarely addressed in similar studies. Forecasts feed into models of photovoltaic, wind, and hydro systems within the microgrid. Energy dispatch is managed through fuzzy logic control. The fuzzy controller supports load prioritization, battery charge/discharge management, and surplus energy redirection to an absorbing load. The final vanilla LSTM achieved RMSE values of 25.741, 0.302, and 12.644 for solar irradiance, wind speed, and river flow, respectively, with NSE values above 0.949 in all cases. These results indicate high forecasting accuracy for solar irradiance and river flow, with limited improvement for wind speed. Overall, the proposed EMS enables effective energy flow management, while the integration of hydrokinetic turbines with AI-based forecasting represents a novel contribution.