32,812 research outputs found

    Solving the Uncapacitated Single Allocation p-Hub Median Problem on GPU

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    A parallel genetic algorithm (GA) implemented on GPU clusters is proposed to solve the Uncapacitated Single Allocation p-Hub Median problem. The GA uses binary and integer encoding and genetic operators adapted to this problem. Our GA is improved by generated initial solution with hubs located at middle nodes. The obtained experimental results are compared with the best known solutions on all benchmarks on instances up to 1000 nodes. Furthermore, we solve our own randomly generated instances up to 6000 nodes. Our approach outperforms most well-known heuristics in terms of solution quality and time execution and it allows hitherto unsolved problems to be solved

    A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems

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    We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the subdomains are solved in parallel to obtain local primal-dual trajectories that are assembled to obtain the global trajectories. We provide a sufficient condition that guarantees convergence of the proposed scheme. This condition states that the effect of perturbations on the boundary conditions (i.e., initial state and terminal dual/adjoint variable) should decay asymptotically as one moves away from the boundaries. This condition also reveals that the scheme converges if the size of the overlap is sufficiently large and that the convergence rate improves with the size of the overlap. We prove that linear quadratic problems satisfy the asymptotic decay condition, and we discuss numerical strategies to determine if the condition holds in more general cases. We draw upon a non-convex optimal control problem to illustrate the performance of the proposed scheme

    A hierarchical time-splitting approach for solving finite-time optimal control problems

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    We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the prediction horizon. Each subproblem is solved in parallel and further split into three by separating the objective from the equality and inequality constraints respectively, such that an analytic solution can be achieved for each subproblem. The proposed solution approach leads to a nested decomposition scheme, which is highly parallelizable. We present a numerical comparison with standard state-of-the-art solvers, and provide analytic solutions to several elements of the algorithm, which enhances its applicability in fast large-scale applications

    PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers

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    The interpretation of the intensity and polarization of the spectral line radiation produced in the atmosphere of the Sun and of other stars requires solving a radiative transfer problem that can be very complex, especially when the main interest lies in modeling the spectral line polarization produced by scattering processes and the Hanle and Zeeman effects. One of the difficulties is that the plasma of a stellar atmosphere can be highly inhomogeneous and dynamic, which implies the need to solve the non-equilibrium problem of the generation and transfer of polarized radiation in realistic three-dimensional (3D) stellar atmospheric models. Here we present PORTA, an efficient multilevel radiative transfer code we have developed for the simulation of the spectral line polarization caused by scattering processes and the Hanle and Zeeman effects in 3D models of stellar atmospheres. The numerical method of solution is based on the non-linear multigrid iterative method and on a novel short-characteristics formal solver of the Stokes-vector transfer equation which uses monotonic B\'ezier interpolation. Therefore, with PORTA the computing time needed to obtain at each spatial grid point the self-consistent values of the atomic density matrix (which quantifies the excitation state of the atomic system) scales linearly with the total number of grid points. Another crucial feature of PORTA is its parallelization strategy, which allows us to speed up the numerical solution of complicated 3D problems by several orders of magnitude with respect to sequential radiative transfer approaches, given its excellent linear scaling with the number of available processors. The PORTA code can also be conveniently applied to solve the simpler 3D radiative transfer problem of unpolarized radiation in multilevel systems.Comment: 15 pages, 15 figures, to appear in Astronomy and Astrophysic
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