Cooperative Optimization of Dual Multiagent System for Optimal Resource Allocation

Abstract

In this paper, a continuous-time multiagent system is proposed for solving optimal resource allocation problems with local allocation feasible constraints. In the system, all the primal agents are divided into different groups. We use dual variables which describe the dual agents to represent the groups of the original agents. The groups of dual agents are used to communicate with others on behalf of the primal agents to reduce communication costs. That is to say, primal agents aim to seek their own optimal solutions by using local information. And dual agents represent primal agents to communicate with other agents in different groups by using the whole group information. The two kinds of agents cooperate to find the optimal solution of the problem. In this way, we only need to know the connections of dual agents to design the multiagent network, and do not need to consider the connections of the primal agents. So the communication cost and the amount of variables will be largely reduced especially for large-scale problem. Furthermore, it is proved that the multiagent system can reach consensus with respect to the dual variables. At the same time, the primal variables are convergent to the optimal solutions of the optimization problem under some certain assumptions on the communication network. For large-scale problem if we take the groups as areas, then the system is suitable for multiarea problem. Simulation results are presented to demonstrate the performance of the proposed multiagent system.