Optimizing ternary hybrid nanofluids using neural networks, gene expression programming, and multi-objective particle swarm optimization: a computational intelligence strategy

The performance of nanofluids is largely determined by their thermophysical properties. Optimizing these properties can significantly enhance nanofluid performance. This study introduces a hybrid strategy based on computational intelligence to determine the optimal conditions for ternary hybrid nanofluids. The goal is to minimize dynamic viscosity and maximize thermal conductivity by varying the volume fraction, temperature, and nanomaterial mixing ratio. The proposed strategy integrates machine learning, multi-objective optimization, and multi-criteria decision-making. Three machine learning techniques—GMDH-type neural network, gene expression programming, and combinatorial algorithm—are applied to model dynamic viscosity and thermal conductivity as functions of the input variables. Then, the high-performing models provide the foundation for optimization using the well-established multi-objective particle swarm optimization algorithm. Finally, the decision-making technique TOPSIS is employed to identify the most desirable points from the Pareto front, based on various design scenarios. To validate the proposed strategy, a ternary hybrid nanofluid composed of graphene oxide (GO), iron oxide (Fe₃O₄), and titanium dioxide (TiO₂) was employed as a case study. The results demonstrated that the combinatorial approach excelled in accurately modeling ( R = 0.99964–0.99993). The optimization process revealed that optimal VFs span a broad range across all mixing ratios, while optimal temperatures were consistently near the maximum value (65 °C). The decision-making outcomes indicated that the mixing ratio was consistent across all design scenarios, with the volume fraction serving as the key differentiating factor.