A Distributed Algorithm for Large-Scale Multi-Agent MINLPs - Dong, Sheng; Xia, Weiguo (Proceedings of the IEEE Conference on Decision & Control, 2024)
In this paper, we focus on the optimization of large-scale multi-agent systems, where agents collaboratively optimize the sum of local objective functions through their own continuous and/or discrete decision variables, subject to global coupling constraints and local constraints. The resulting Mixed-Integer Nonlinear Programmings (MINLPs) are NP-hard, non-convex, and large-scale. Therefore, this paper aims to design distributed algorithms to find feasible suboptimal solutions with a guaranteed bound. To this end, considering dual decomposition as an effective method to decompose large-scale constraint-coupled optimization problems, we first show, based on the convexification effects of large-scale MINLPs, that the primal solutions from the dual are near-optimal under certain conditions. This expands recent results in Mixed-Integer Linear Programmings (MILPs) to the nonlinear case but requires additional efforts on the proof. Utilizing this result to tighten the coupling constraints, we develop a fully distributed algorithm for the tightened problem, based on dual decomposition and consensus protocols. The algorithm is guaranteed to provide feasible solutions for the original MINLP. Moreover, asymptotic suboptimality bounds are established for the obtained solution. Finally, the efficacy of the method is verified through numerical simulations.