Distributed Bilevel Constrained Optimization via Multiagent System Approaches

In this article, two types of multiagent systems (MASs) are developed for distributed bilevel constrained optimization. Within the framework of the distributed bilevel optimization modeling, the objective function is in a summation manner of local objective functions. Multiple agents connected via a communication network are harnessed for optimizing the local objective functions cooperatively while adhering to coupled constraints with global information, and each agent is tasked with solving an individual inner problem and it is subject to multiple local constraints. To address challenges posed by the distributed computation requirement of the proposed bilevel optimization models and multiple complex constraints, first and second-order MASs are customized and proven to converge to the optimal solution. Three examples involving two numerical simulations and an economic dispatch problem are elaborated to verify and demonstrate the optimality, enhanced robustness to communication blocking, and fast convergence of the proposed approaches.