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Advances in surrogate based modeling, feasibility analysis, and optimization: A review

Investigation of entropy generation in MHD and slip flow over a rotating porous disk with variable properties

Surrogate-based optimization proceeds in cycles. Each cycle consists of analyzing a number of designs, fitting a surrogate, performing optimization based on the surrogate, and finally analyzing a candidate solution. Algorithms that use the surrogate uncertainty estimator to guide the selection of the next sampling candidate are readily available, e.g., the efficient global optimization (EGO) algorithm. However, adding one single point at a time may not be efficient when the main concern is wall-clock time (rather than number of simulations) and simulations can run in parallel. Also, the need for uncertainty estimates limits EGO-like strategies to surrogates normally implemented with such estimates (e.g., kriging and polynomial response surface). We propose the multiple surrogate efficient global optimization (MSEGO) algorithm, which adds several points per optimization cycle with the help of multiple surrogates. We import uncertainty estimates from one surrogate to another to allow use of surrogates that do not provide them. The approach is tested on three analytic examples for nine basic surrogates including kriging, radial basis neural networks, linear Shepard, and six different instances of support vector regression. We found that MSEGO works well even with imported uncertainty estimates, delivering better results in a fraction of the optimization cycles needed by EGO.

Efficient global optimization algorithm assisted by multiple surrogate techniques

We compute the Bayesian evidence and complexity of 193 slow-roll single-field models of inflation using the Planck 2013 Cosmic Microwave Background data, with the aim of establishing which models are favoured from a Bayesian perspective Our calculations employ a new numerical pipeline interfacing an inflationary effective likelihood with the slow-roll library ASPIC and the nested sampling algorithm MULTINEST The models considered represent a complete and systematic scan of the entire landscape of inflationary scenarios proposed so far Our analysis singles out the most probable models (from an Occam's razor point of view) that are compatible with Planck data, while ruling out with very strong evidence 34% of the models considered We identify 26% of the models that are favoured by the Bayesian evidence, corresponding to 15 different potential shapes If the Bayesian complexity is included in the analysis, only 9% of the models are preferred, corresponding to only 9 different potential shapes These shapes are all of the plateau type

The Best Inflationary Models After Planck

Scattered data interpolation problems arise in many applications. Shepard’s method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust fit, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard’s algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data.

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Algorithm 905: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data

Magnetohydrodynamic flow and heat transfer about a rotating disk with suction and injection at the disk

Magnetohydrodynamic Flow Between a Solid Rotating Disk and a Porous Stationary Disk

This paper presents a massively parallel global deterministic direct search method VTDIRECT for solving nonconvex quadratic minimization problems with either box or±1 integer constraints. Using the canonical dual transformation, these well-known NP-hard problems can be reformulated as perfect dual stationary problems with zero duality gap. Under certain conditions, these dual problems are equivalent to smooth concave maximization over a convex feasible space. Based on a perturbation method proposed by Gao, the integer programming problem is shown to be equivalent to a continuous unconstrained Lipschitzian global optimization problem. The parallel algorithm VTDIRECT is then applied to solve these dual problems to obtain global minimizers. Parallel performance results for several nonconvex quadratic integer programming problems are reported.

William I. Thacker

Papers

Algorithm 905: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data

Magnetohydrodynamic flow and heat transfer about a rotating disk with suction and injection at the disk

Magnetohydrodynamic Flow Between a Solid Rotating Disk and a Porous Stationary Disk

Solving the canonical dual of box-and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm

Magnetohydroynamic Free Convection from a Disk Rotating in a Vertical Plane