This article presents a new approach to modeling and optimizing individual decision-making strategies in multi-agent socio-economic systems (MSES). This approach is based on the synthesis of agent-based modeling methods, machine learning and genetic optimization algorithms. A procedure for the synthesis and training of artificial neural networks (ANNs) that simulate the functionality of MSES and provide an approximation of the values ​​of its objective characteristics has been developed. The feature of the two-step procedure is the combined use of particle swarm optimization methods (to determine the optimal values ​​of hyperparameters) and the Adam machine learning algorithm (to compute weight coefficients of the ANN). The use of such ANN-based surrogate models in parallel multi-agent real-coded genetic algorithms (MA-RCGA) makes it possible to raise substantially the time-efficiency of the evolutionary search for optimal solutions. We have conducted numerical experiments that confirm a significant improvement in the performance of MA-RCGA, which periodically uses the ANN-based surrogate-model to approximate the values ​​of the objective and fitness functions. A software framework has been designed that consists of the original (reference) agent-based model of trade interactions, the ANN-based surrogate model and the MA-RCGA genetic algorithm. At the same time, the software libraries FLAME GPU, OpenNN (Open Neural Networks Library), etc., agent-based modeling and machine learning methods are used. The system we developed can be used by responsible managers.