Mathematical methods of planning in systems consisted of rational agents

The paper is devoted to mathematical methods of planning in systems consisting of rational agents. An agent is an autonomous object that has sources of information about the environment and influences this environment. A rational agent is an agent who has a goal and uses optimal behavioral strategies to achieve it. It is assumed that there is a utility function, which is defined on the set of possible sequences of actions of the agent and takes values in the set of real numbers. A rational agent acts to maximize the utility function. If rational agents form a system, then they have a common goal and act in an optimal way to achieve it. Agents use the optimal solution of the extreme problem, which corresponds to the goal of the system. The problem of linear programming is considered, in which the number of product sets produced by the system is maximized. To solve the nonlinear problem of optimizing the production plan, the conditional gradient method is used, which at each iteration allows a posteriori estimation of the error of the solution and allows stopping the calculation process after reaching the required accuracy. Since the rational agents that are part of the system can have separate optimality criteria, multi-criteria optimization problems appear. The article considers a humanmachine procedure for solving such problems, which is connected with the conditional gradient method and uses information from the decision-maker (DM) at each iteration. The difficulties of this approach are that the DM is not able to make decisions many times under the condition of a significant number of iterations of the nonlinear programming method. The article proposes to replace OPR with an artificial neural network. Nonlinear and stochastic programming methods are used to find optimal parameters of this network.