DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's reference manual.

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a reference manual for the commands specification for the DAKOTA software, providing input overviews, option descriptions, and example specifications. DAKOTA Version 5.0 Reference Manual generated on May 7, 2010

[1]  J. Barthelemy,et al.  Two point exponential approximation method for structural optimization , 1990 .

[2]  A. Giunta,et al.  Use of data sampling, surrogate models, and numerical optimization in engineering design , 2002 .

[3]  Thomas Gerstner,et al.  Dimension–Adaptive Tensor–Product Quadrature , 2003, Computing.

[4]  Laura Painton Swiler,et al.  A user's guide to Sandia's latin hypercube sampling software : LHS UNIX library/standalone version. , 2004 .

[5]  T. Tsuchiya,et al.  On the formulation and theory of the Newton interior-point method for nonlinear programming , 1996 .

[6]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[7]  Michael A. Saunders,et al.  User''s guide for NPSOL (Ver-sion 4.0): A FORTRAN package for nonlinear programming , 1984 .

[8]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[9]  Todd D. Plantenga,et al.  HOPSPACK 2.0 user manual. , 2009 .

[10]  Rekha Ranjana Rao,et al.  GOMA - A full-Newton finite element program for free and moving boundary problems with coupled fluid/solid momentum, energy, mass, and chemical species transport: User`s guide , 1996 .

[11]  Stefano Tarantola,et al.  Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models , 2004 .

[12]  Mark Richards,et al.  The surfpack software library for surrogate modeling of sparse irregularly spaced multidimensional data. , 2006 .

[13]  Rüdiger Rackwitz,et al.  Optimization and risk acceptability based on the Life Quality Index , 2002 .

[14]  R. Rackwitz,et al.  Sensitivity and importance measures in structural reliability , 1986 .

[15]  John Mark,et al.  Introduction to radial basis function networks , 1996 .

[16]  R. Haftka.  Combining global and local approximations , 1991 .

[17]  R. Tapia,et al.  Numerical Comparisons of Path-Following Strategies for a Primal-Dual Interior-Point Method for Nonlinear Programming , 2002 .

[18]  Douglas C. Montgomery,et al.  Response Surface Methodology: Process and Product Optimization Using Designed Experiments , 1995 .

[19]  W. J. Whiten,et al.  Computational investigations of low-discrepancy sequences , 1997, TOMS.

[20]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[21]  T. W. Layne,et al.  A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models , 1998 .

[22]  Laura Painton Swiler,et al.  Efficient algorithms for mixed aleatory-epistemic uncertainty quantification with application to radiation-hardened electronics. Part I, algorithms and benchmark results. , 2009 .

[23]  Michael S. Eldred,et al.  DAKOTA , A Multilevel Parallel Object-Oriented Framework for Design Optimization , Parameter Estimation , Uncertainty Quantification , and Sensitivity Analysis Version 4 . 0 User ’ s Manual , 2006 .

[24]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[25]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[26]  Garret N. Vanderplaats,et al.  Numerical Optimization Techniques for Engineering Design: With Applications , 1984 .

[27]  Jack Dongarra,et al.  MPI: The Complete Reference , 1996 .

[28]  D. Higdon,et al.  Computer Model Calibration Using High-Dimensional Output , 2008 .

[29]  Sankaran Mahadevan,et al.  Uncertainty analysis for computer simulations through validation and calibration , 2008 .

[30]  Rüdiger Rackwitz,et al.  Two basic problems in reliability-based structural optimization , 1997, Math. Methods Oper. Res..

[31]  Jay D. Johnson,et al.  A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory , 2007 .

[32]  Qiang Du,et al.  Centroidal Voronoi Tessellations: Applications and Algorithms , 1999, SIAM Rev..

[33]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[34]  Michael S. Eldred,et al.  DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification, and Sensitivity Analysis Version 3.0 Reference Manual , 2001 .

[35]  Michael S Eldred,et al.  Specifying and Reading Program Input with NIDR. , 2008 .

[36]  Laura Swiler,et al.  Importance Sampling: Promises and Limitations , 2010 .

[37]  Fabio Nobile,et al.  A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data , 2008, SIAM J. Numer. Anal..

[38]  P. J. Williams,et al.  OPT++: An object-oriented toolkit for nonlinear optimization , 2007, TOMS.

[39]  M. Eldred,et al.  Solving the Infeasible Trust-region Problem Using Approximations. , 2004 .

[40]  Jasbir S. Arora,et al.  Introduction to Optimum Design , 1988 .

[41]  Sophia Lefantzi,et al.  DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. , 2011 .

[42]  R. Grandhi,et al.  Effective Two-Point Function Approximation for Design Optimization , 1998 .

[43]  S. S. Wilks.  Determination of Sample Sizes for Setting Tolerance Limits , 1941 .

[44]  Paula M. Ferguson,et al.  Python in a Nutshell , 2003 .

[45]  M. Eldred,et al.  Multimodal Reliability Assessment for Complex Engineering Applications using Efficient Global Optimization , 2007 .

[46]  Jon C. Helton,et al.  Sampling-based methods for uncertainty and sensitivity analysis. , 2000 .

[47]  Henryk Wozniakowski,et al.  Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems , 1995, J. Complex..

[48]  R. M. Roberts,et al.  Confidence region estimation techniques for nonlinear regression in groundwater flow: Three case studies , 2007 .

[49]  Sai Hung Cheung,et al.  PARALLEL ADAPTIVE MULTILEVEL SAMPLING ALGORITHMS FOR THE BAYESIAN ANALYSIS OF MATHEMATICAL MODELS , 2012 .

[50]  J. Freidman,et al.  Multivariate adaptive regression splines , 1991 .

[51]  N. Zheng,et al.  Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models , 2006, J. Glob. Optim..

[52]  Menner A Tatang,et al.  Direct incorporation of uncertainty in chemical and environmental engineering systems , 1995 .

[53]  Yih‐Tsuen Wu,et al.  New Algorithm for Structural Reliability Estimation , 1987 .

[54]  Daniel Gilly,et al.  UNIX in a Nutshell , 2006 .

[55]  Gary Tang,et al.  Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation , 2011, Reliab. Eng. Syst. Saf..

[56]  Max Gunzburger,et al.  UNIFORMITY MEASURES FOR POINT SAMPLES IN HYPERCUBES , 2004 .

[57]  Laura Painton Swiler,et al.  Evaluation of Sampling Methods in Constructing Response Surface Approximations , 2006 .

[58]  Garret N. Vanderplaats,et al.  CONMIN: A FORTRAN program for constrained function minimization: User's manual , 1973 .

[59]  F. Jose,et al.  Convergence of Trust Region Augmented Lagrangian Methods Using Variable Fidelity Approximation Data , 1997 .

[60]  L. Tvedt.  Distribution of quadratic forms in normal space-application to structural reliability , 1990 .

[61]  R. Haftka,et al.  Elements of Structural Optimization , 1984 .

[62]  William J. Rider,et al.  Sensitivity analysis techniques applied to a system of hyperbolic conservation laws , 2012, Reliab. Eng. Syst. Saf..

[63]  G. D. Wyss,et al.  A user`s guide to LHS: Sandia`s Latin Hypercube Sampling Software , 1998 .

[64]  A. Stroud.  Approximate calculation of multiple integrals , 1973 .

[65]  Robert J. Vanderbei,et al.  An Interior-Point Algorithm for Nonconvex Nonlinear Programming , 1999, Comput. Optim. Appl..

[66]  M. Hohenbichler,et al.  Improvement Of Second‐Order Reliability Estimates by Importance Sampling , 1988 .

[67]  C. Cornell,et al.  Sensitivity estimation within first and second order reliability methods , 1992 .

[68]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2005, SIAM Rev..

[69]  J. Halton.  On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals , 1960 .

[70]  R. Lewis,et al.  A MULTIGRID APPROACH TO THE OPTIMIZATION OF SYSTEMS GOVERNED BY DIFFERENTIAL EQUATIONS , 2000 .

[71]  David J. Thuente,et al.  Line search algorithms with guaranteed sufficient decrease , 1994, TOMS.

[72]  M. Eldred,et al.  Second-Order Reliability Formulations in DAKOTA/UQ , 2006 .

[73]  Daniel M. Dunlavy,et al.  Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, and Reduced-Order Models , 2006 .

[74]  Richard H. Byrd,et al.  Parallel quasi-Newton methods for unconstrained optimization , 1988, Math. Program..

[75]  Tamara G. Kolda,et al.  Asynchronous Parallel Generating Set Search for Linearly Constrained Optimization , 2008, SIAM J. Sci. Comput..

[76]  Jeroen A. S. Witteveen,et al.  Modeling Arbitrary Uncertainties Using Gram-Schmidt Polynomial Chaos , 2006 .

[77]  Michael S. Eldred,et al.  Second-Order Corrections for Surrogate-Based Optimization with Model Hierarchies , 2004 .

[78]  D. Xiu.  Numerical integration formulas of degree two , 2008 .

[79]  Eldred,et al.  Discrete optimization of isolator locations for vibration isolation systems: An analytical and experimental investigation , 1996 .

[80]  Fabio Nobile,et al.  An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data , 2008, SIAM J. Numer. Anal..

[81]  E. Omojokun.  Trust region algorithms for optimization with nonlinear equality and inequality constraints , 1990 .

[82]  Kyung K. Choi,et al.  A NEW STUDY ON RELIABILITY-BASED DESIGN OPTIMIZATION , 1999 .

[83]  M. Eldred,et al.  Efficient Global Reliability Analysis for Nonlinear Implicit Performance Functions , 2008 .

[84]  Joos Vandewalle,et al.  A Multilinear Singular Value Decomposition , 2000, SIAM J. Matrix Anal. Appl..

[85]  Heikki Haario,et al.  DRAM: Efficient adaptive MCMC , 2006, Stat. Comput..

[86]  W. E. Hart,et al.  A performance analysis of evolutionary pattern search with generalized mutation steps , 1999, Proceedings of the 1999 Congress on Evolutionary Computation-CEC99 (Cat. No. 99TH8406).

[87]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[88]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[89]  John Red-Horse,et al.  Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach , 1999 .

[90]  C. D. Perttunen,et al.  Lipschitzian optimization without the Lipschitz constant , 1993 .

[91]  Lloyd N. Trefethen,et al.  Barycentric Lagrange Interpolation , 2004, SIAM Rev..

[92]  T. Kolda,et al.  Nonlinearly-constrained optimization using asynchronous parallel generating set search. , 2007 .

[93]  Achintya Haldar,et al.  Probability, Reliability and Statistical Methods in Engineering Design (Haldar, Mahadevan) , 1999 .

[94]  J. Renaud,et al.  New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 2 , 1998 .

[95]  Stephen J. Wright.  Primal-Dual Interior-Point Methods , 1997, Other Titles in Applied Mathematics.

[96]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[97]  Thomas Gerstner,et al.  Numerical integration using sparse grids , 2004, Numerical Algorithms.

[98]  D. Robinson,et al.  COMPARISON OF QUASI- AND PSEUDO-MONTE CARLO SAMPLING FOR RELIABILITY AND UNCERTAINTY ANALYSIS , 1999 .

[99]  Tamara G. Kolda,et al.  Algorithm 856: APPSPACK 4.0: asynchronous parallel pattern search for derivative-free optimization , 2006, TOMS.

[100]  Dongbin Xiu,et al.  High-Order Collocation Methods for Differential Equations with Random Inputs , 2005, SIAM J. Sci. Comput..

[101]  K Schittkowski.  NLPQLP: A Fortran Implementation of a Sequential Quadratic Programming Algorithm with Distributed and Non-Monotone Line Search , 2005 .

[102]  L. Watson,et al.  An interior-point sequential approximate optimization methodology , 2004 .

[103]  A. O'Hagan,et al.  Bayesian calibration of computer models , 2001 .

[104]  R. Ghanem,et al.  Quantifying uncertainty in chemical systems modeling , 2004 .

[105]  Paul Anderson,et al.  The UNIX C shell field guide , 1986 .

[106]  Raphael T. Haftka,et al.  Sensitivity-based scaling for approximating. Structural response , 1993 .

[107]  Jon C. Helton,et al.  Evidence Theory for Engineering Applications , 2004 .

[108]  N. Higham.  The numerical stability of barycentric Lagrange interpolation , 2004 .

[109]  H. Hong.  Simple Approximations for Improving Second-Order Reliability Estimates , 1999 .

[110]  Y.-T. Wu,et al.  Safety-Factor Based Approach for Probability-Based Design Optimization , 2001 .

[111]  Philip E. Gill,et al.  Practical optimization , 1981 .

[112]  J. Mount.  Importance Sampling , 2005 .

[113]  J. E. Renaud,et al.  Investigation of reliability method formulations in DAKOTA/UQ , 2004 .

[114]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[115]  Anthony Skjellum,et al.  Using MPI - portable parallel programming with the message-parsing interface , 1994 .

[116]  Brian W. Kernighan,et al.  The C Programming Language , 1978 .

[117]  Kemper Lewis,et al.  Effective generation of Pareto sets using genetic programming , 2001 .

[118]  Donald R. Jones,et al.  Efficient Global Optimization of Expensive Black-Box Functions , 1998, J. Glob. Optim..

[119]  H. H. Rosenbrock,et al.  An Automatic Method for Finding the Greatest or Least Value of a Function , 1960, Comput. J..

[120]  Max D. Morris,et al.  Factorial sampling plans for preliminary computational experiments , 1991 .

[121]  J. Murzewski,et al.  Probability, Reliability and Statistical Methods in Engineering Design: A. Halder and S. Mahadevan, John Wiley & Sons, New York, 2000, xi+304 pp , 2001 .