The connectionist-metaheuristic approach solved the urgent task of using new approaches to analyze the foreign direct investment and macroeconomic indicators that affect the volume of their attraction to a particular country in the world economy. The proposed connectionist-metaheuristic system makes it possible to improve the quality of the approximation due to: the simplification of structural identification through the use of only one hidden layer of neural network models; reduction of the computational complexity of parametric identification and the ensuring good scalability through the use of batch mode for non-recurrent neural network models and multi-agent metaheuristics for recurrent neural network models; descriptions of non-linear dependencies through the use of neural network models; high approximation accuracy due to the use of recurrent neural network models; resistance to data incompleteness and data noise due to the use of metaheuristics for parametric identification of recurrent neural network models; lack of requirements for knowledge of distribution, homogeneity, weak correlation, and optimal factors’ choice. In the case of a GPU, an LSTM-based neural network with the highest approximation accuracy should be chosen. For LSTM, the coefficient of determination using the gradient method is 0.785, and using metaheuristics (modified wasp colony optimization) is 0.835. The proposed approach makes it possible to expand the scope of approximation methods’ application based on artificial neural networks and metaheuristics, which is confirmed by its adaptation for an economic problem and contributes to an increase in intelligent computer systems efficiency for general and special purposes.