The article considers the problem of implementing a digital industrial ecosystem project in the presence of several acceptable technologies for its implementation and corresponding vector objective functions for assessing of their quality. For a formalized description of optimization of project implementation management, a new formalization in the form of a two-level multi-agent hierarchical network economic and mathematical model is proposed. The identification of parameters, structural balanced interaction and optimization of the result of managing the implementation of processes of the studied digital industrial ecosystem project within the framework of the proposed two-level multi-agent hierarchical network model are described. The paper presents a methodology for solving the problem under consideration, which is implemented in the form of one-step operations that allow their algorithmization.