A decentralized approach to multi-agent MILPs: Finite-time feasibility and performance guarantees

Abstract

We address the optimal design of a large scale multi-agent system where each agent has discrete and/or continuous decision variables that need to be set so as to optimize the sum of linear local cost functions, in presence of linear local and global constraints. The problem reduces to a Mixed Integer Linear Program (MILP) that is here addressed according to a decentralized iterative scheme based on dual decomposition, where each agent determines its decision vector by solving a smaller MILP involving its local cost function and constraint given some dual variable, whereas a central unit enforces the global coupling constraint by updating the dual variable based on the tentative primal solutions of all agents. An appropriate tightening of the coupling constraint through iterations allows to obtain a solution that is feasible for the original MILP. The proposed approach is inspired by a recent method to the MILP approximate solution via dual decomposition and constraint tightening, and presents the advantage of guaranteeing feasibility in finite-time and providing better performance guarantees. The two approaches are compared on a numerical example on plug-in electric vehicles optimal charging.

A Primal Decomposition Method with Suboptimality Bounds for Distributed Mixed-Integer Linear Programming

“…In Figure 3, comparison histograms of the relative suboptimality of both methods and of the relative restriction magnitude are shown. A further investigation to be carried out consists of comparing the restriction magnitude of DiP-FEAS-MILP with the time-varying restriction proposed in [16].…”

“…Here the key idea is to tighten the coupling constraint and then apply a dual decomposition method to get mixed-integer points violating the restricted coupling constraint but not the original one. In [16], an improved iterative tightening procedure has been proposed to obtain enhanced performance guarantees. In both works [15,16], a master processing unit is needed.…”

“…In [16], an improved iterative tightening procedure has been proposed to obtain enhanced performance guarantees. In both works [15,16], a master processing unit is needed. The first, fully distributed implementation of the above dual decomposition based methodology is proposed in [17].…”

“…In this paper we pursue the same main goal as in [15][16][17], namely to provide a fast algorithm to compute a feasible mixed-integer solution of (1) with guaranteed suboptimality bounds. In particular, we consider a distributed computation framework over networks, even though we will point out how to implement the method in a parallel architecture.…”

Distributed Mixed-Integer Linear Programming via Cut Generation and Constraint Exchange

“…In [14] a parallel dual decomposition method, relying on a suitable tightening of the constraints, is proposed to approximately solve structured MILPs with local and coupling constraints. The algorithm is improved in [15] by means of an iterative tightening procedure. The methods are applied to charging control of electric vehicles.…”