Primal decomposition and constraint generation for asynchronous distributed mixed-integer linear programming

In this paper, we deal with large-scale Mixed Integer Linear Programs (MILPs) with coupling constraints that must be solved by processors over networks. We propose a finite-time distributed algorithm that computes a feasible solution with suboptimality bounds over asynchronous and unreliable networks. As shown in a previous work of ours, a feasible solution of the considered MILP can be computed by resorting to a primal decomposition of a suitable problem convexification. In this paper we reformulate the primal decomposition resource allocation problem as a linear program with an exponential number of unknown constraints. Then we design a distributed protocol that allows agents to compute an optimal allocation by generating and exchanging only few of the unknown constraints. Each allocation is iteratively used to compute a candidate feasible solution of the original MILP. We establish finite-time convergence of the proposed algorithm under very general assumptions on the communication network. A numerical example corroborates the theoretical results.