In this paper, a multi-objective optimization (MOO) of wavy fin-and-elliptical tube heat exchangers has been performed by using Computational Fluid Dynamics (CFD), Artificial Neural Network (ANN) of Group Method of Data Handling (GMDH) type, and Non-Dominated Sorting Genetic Algorithm II (NSGA-II). This multi-objective optimization is aimed at achieving maximum heat transfer and minimum pressure drop. For this purpose, the considered objective functions, Colburn factor (j) and friction factor (f) are optimized with regards to the design variables (four variables). The CFD results are validated by means of experimental findings. Polynomials of the GMDH type neural network are formed based on the CFD results. These polynomials relate the objective functions to the design variables. Ultimately, the NSGA-II algorithm obtains the Pareto optimal points by using the input data from the neural network. From among the optimal points, several points with unique features are introduced and explained. The investigation of optimal points indicates that with a slight reduction in heat transfer, pressure drop can be reduced considerably. By combining and simultaneously using the CFD, neural network and NSGA-II optimization algorithm, very useful and valuable results are obtained; which otherwise couldn’t be achieved without the mutual use of these techniques.