7,003 research outputs found
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
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
Distributed Mixed-Integer Linear Programming via Cut Generation and Constraint Exchange
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
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