A Finite-Time Cutting Plane Algorithm for Distributed Mixed Integer Linear Programming

Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. In the proposed algorithm, at each communication round, agents solve locally a small LP, generate suitable cutting planes, namely intersection cuts and cost-based cuts, and communicate a fixed number of active constraints, i.e., a candidate optimal basis. We prove that, if the cost is integer, the algorithm converges to the lexicographically minimal optimal solution in a finite number of communication rounds. Finally, through numerical computations, we analyze the algorithm convergence as a function of the network size.Comment: 6 pages, 3 figure

Decomposition Methods for Global Solutions of Mixed-Integer Linear Programs

This paper introduces two decomposition-based methods for two-block mixed-integer linear programs (MILPs), which break the original problem into a sequence of smaller MILP subproblems. The first method is based on the l1-augmented Lagrangian. The second method is based on the alternating direction method of multipliers. When the original problem has a block-angular structure, the subproblems of the first block have low dimensions and can be solved in parallel. We add reverse-norm cuts and augmented Lagrangian cuts to the subproblems of the second block. For both methods, we show asymptotic convergence to globally optimal solutions and present iteration upper bounds. Numerical comparisons with recent decomposition methods demonstrate the exactness and efficiency of our proposed methods