Nanoparticles can enhance the thermophysical properties of base fluids, leading to increased efficiency, especially in heat transfer applications. Therefore, achieving optimized thermophysical properties of nanofluids is of particular importance. In this study, two multilayer feedforward artificial neural networks (ANN) were designed and trained to predict the relative viscosity and thermal conductivity ratio of a water-based hybrid nanofluid MWCNT-Y2O3 (with a nanoparticle weight ratio of 80:20). The nanofluid samples studied contained varying volume concentrations of MWCNT-Y2O3 nanoparticles (from 0.01 to 0.2 percent) in the base fluid. Experimental data for relative viscosity and thermal conductivity ratio at different temperatures (from 25°C to 60°C) were available. For each ANN designed to estimate either the relative viscosity or the thermal conductivity ratio outputs, regression plots corresponding to the training, validation, and testing data sets demonstrated the networks' excellent performance. The mean and maximum relative percentage errors obtained for the testing data were as follows: for relative viscosity output, 0.5120% mean error and 2.5450% maximum error; for thermal conductivity ratio output, 0.1733% mean error and 0.2874% maximum error. Moreover, based on the developed model, a multi-objective optimization problem was formulated to simultaneously determine the minimum relative viscosity and maximum thermal conductivity ratio of the nanofluid. This problem was solved using the multi-objective particle swarm optimization (MOPSO) metaheuristic method. Consequently, the optimal objective function values and input parameters were obtained, and the Pareto optimal points were graphically illustrated.