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

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.Comment: 57th IEEE Conference on Decision and Contro

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

Parallel Optimal Control for Cooperative Automation of Large-scale Connected Vehicles via ADMM

This paper proposes a parallel optimization algorithm for cooperative automation of large-scale connected vehicles. The task of cooperative automation is formulated as a centralized optimization problem taking the whole decision space of all vehicles into account. Considering the uncertainty of the environment, the problem is solved in a receding horizon fashion. Then, we employ the alternating direction method of multipliers (ADMM) to solve the centralized optimization in a parallel way, which scales more favorably to large-scale instances. Also, Taylor series is used to linearize nonconvex constraints caused by coupling collision avoidance constraints among interactive vehicles. Simulations with two typical traffic scenes for multiple vehicles demonstrate the effectiveness and efficiency of our method

Collision-free Multiple Unmanned Combat Aerial Vehicles Cooperative Trajectory Planning for Time-critical Missions using Differential Flatness Approach

This paper investigates the cooperative trajectory planning for multiple unmanned combat aerial vehicles in performing autonomous cooperative air-to-ground target attack missions. Firstly, the collision-free cooperative trajectory planning problem for time-critical missions is formulated as a cooperative trajectory optimal control problem (CTP-OCP), which is based on an approximate allowable attack region model, several constraints model, and a multi-criteria objective function. Next, a planning algorithm based on the differential flatness, B-spline curves and nonlinear programming is designed to solve the CTP-OCP. In particular, the notion of the virtual time is introduced to deal with the temporal constraints. Finally, the proposed approach is validated by two typical scenarios and the simulation results show the feasibility and effectiveness of the proposed planning approach.Defence Science Journal, Vol. 64, No. 1, January 2014, DOI:10.14429/dsj.64.299