## 1 Introduction
Differential Grouping Cooperative Coevolution (DGCC) implements a decomposition strategy that minimizes the interdependence between groups of variables [16], Multi-Level Cooperative Coevolution (MLCC) [17] uses the size of a group of parameters as an optimized parameter. Hierarchical Coevolution Model, a model of coevolution of symbiotic species [18], takes into account homogeneous and heterogeneous aspects of co-evolution to maintain diversity, accelerates convergence, preserves diversity and prevents premature convergence of the process of finding optimal solutions. Competitive coevolution uses the following types of interactions of subpopulations: interaction according to the \"host-parasite\" scheme; interaction of subpopulations with different search areas; and interaction of subpopulations that differ in search strategies (algorithms or algorithm settings). The latter type of coevolution is used to adapt the parameter settings of search algorithms that ensure the dominance of algorithms with the best settings. In particular, [19] considers a co-evolutionary \"cultural\" particle swarm algorithm that implements the concept of improving population algorithms based on taking into account the experience gained during solving the problem. Examples of using co-evolutionary particle swarm algorithms for solving optimal design problems with constraints and minimax problems are considered in [20; 21]. In addition, competitive evolution can be used as a tool for effective dynamic distribution of computing resources between subpopulations [22; 23] in the process of solving the problem. In [24; 25; 26], co-evolutionary technologies for solving multi-criteria problems are developed using cooperative, competitive and combined coevolution schemes. It is shown that the combined coevolution schemes look more preferable, since they allow solving quite complex problems of multi-criteria optimization, providing a representative approximation of the Pareto set and adaptive configuration of the algorithm for a specific task. A co-evolutionary algorithm for solving the multi-criteria optimization problem under uncertainty is considered in [27]. However, the assumption of the probabilistic nature of the uncertainty limits the possibilities of using this algorithm. Thus, co-evolutionary optimization technologies make it possible, in general, to solve the problem of finding a set of globally optimal solutions under multimodality and multicriteriality quite effectively. At the same time, the complexity of the MOU problem is that when solving it, it is fundamentally necessary to take into account the presence and conflicting nature of the interaction of two types of uncertain factors: the uncertainty of the goal (interpreted as multi-criteria) and the uncertainty of the environment. It is assumed that the uncertainty is known only that it belongs to a certain area, and there are no statistical characteristics. Therefore, the spread of co-evolutionary technology to the MOU tasks requires the develop ment of new models of coevolution that take into account the conflict nature of the problem being solved and, as a result, the conflict nature of the interaction of subpopulations. The purpose of this article is to develop hierarchical game models of coevolution that take into account the conflict nature of the MOU problem, as well as the structure of the optimality principles used to find a set of optimal solutions.