Search

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 algorithmic framework to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. At each communication round, agents locally solve a small linear program, generate suitable cutting planes, and communicate a fixed number of active constraints. Within the distributed framework, we first propose an algorithm that, under the assumption of integer-valued optimal cost, guarantees finite-time convergence to an optimal solution. Second, we propose an algorithm for general problems that provides a suboptimal solution up to a given tolerance in a finite number of communication rounds. Both algorithms work under asynchronous, directed, unreliable networks. Finally, through numerical computations, we analyze the algorithm scalability in terms of the network size. Moreover, for a multi-agent multi-task assignment problem, we show, consistently with the theory, its robustness to packet loss. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of stochastic resource allocation problems where resources assigned to a task may fail probabilistically to complete assigned tasks. Failures to complete a task are observed before new resource allocations are selected. The resulting temporal resource allocation problem is a stochastic control problem, with a discrete state space and control space that grow in cardinality exponentially with the number of tasks. We modify this optimal control problem by expanding the admissible control space, and show that the resulting control problem can be solved exactly by efficient algorithms in time that grows nearly linear with the number of tasks. The approximate control problem also provides a bound on the achievable performance for the original control problem. The approximation is used as part of a model predictive control (MPC) algorithm to generate resource allocations over time in response to information on task completion status. We show in computational experiments that, for single resource class problems, the resulting MPC algorithm achieves nearly the same performance as the optimal dynamic programming algorithm while reducing computation time by over four orders of magnitude. In multiple resource class experiments involving 1000 tasks, the model predictive control performance is within 4% of the performance bound obtained by the solution of the expanded control space problem. [ABSTRACT FROM AUTHOR]