A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming
It addresses the challenge of distributed MILP solving for multi-agent systems with shared resources, offering theoretical guarantees on suboptimality.
This paper proposes a fully distributed primal decomposition algorithm for solving Mixed-Integer Linear Programs (MILPs) with a coupling constraint. The algorithm provides feasible solutions with asymptotic and finite-time suboptimality bounds, and numerical simulations demonstrate its efficacy.
In this paper we deal with a network of agents seeking to solve in a distributed way Mixed-Integer Linear Programs (MILPs) with a coupling constraint (modeling a limited shared resource) and local constraints. MILPs are NP-hard problems and several challenges arise in a distributed framework, so that looking for suboptimal solutions is of interest. To achieve this goal, the presence of a linear coupling calls for tailored decomposition approaches. We propose a fully distributed algorithm based on a primal decomposition approach and a suitable tightening of the coupling constraints. Agents repeatedly update local allocation vectors, which converge to an optimal resource allocation of an approximate version of the original problem. Based on such allocation vectors, agents are able to (locally) compute a mixed-integer solution, which is guaranteed to be feasible after a sufficiently large time. Asymptotic and finite-time suboptimality bounds are established for the computed solution. Numerical simulations highlight the efficacy of the proposed methodology.