23,896 research outputs found
Mixed Integer Linear Programming For Exact Finite-Horizon Planning In Decentralized Pomdps
We consider the problem of finding an n-agent joint-policy for the optimal
finite-horizon control of a decentralized Pomdp (Dec-Pomdp). This is a problem
of very high complexity (NEXP-hard in n >= 2). In this paper, we propose a new
mathematical programming approach for the problem. Our approach is based on two
ideas: First, we represent each agent's policy in the sequence-form and not in
the tree-form, thereby obtaining a very compact representation of the set of
joint-policies. Second, using this compact representation, we solve this
problem as an instance of combinatorial optimization for which we formulate a
mixed integer linear program (MILP). The optimal solution of the MILP directly
yields an optimal joint-policy for the Dec-Pomdp. Computational experience
shows that formulating and solving the MILP requires significantly less time to
solve benchmark Dec-Pomdp problems than existing algorithms. For example, the
multi-agent tiger problem for horizon 4 is solved in 72 secs with the MILP
whereas existing algorithms require several hours to solve it
Free and regular mixed-model sequences by a linear program-assisted hybrid algorithm GRASP-LP
A linear program-assisted hybrid algorithm (GRASP-LP) is presented to solve a mixed-model sequencing problem in an assembly line. The issue of the problem is to obtain manufacturing sequences of product models with the minimum work overload, allowing the free interruption of operations at workstations and preserving the production mix. The implemented GRASP-LP is compared with other procedures through a case study linked with the Nissan’ Engine Plant from Barcelona.Peer ReviewedPostprint (author's final draft
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
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