Ongoing research at Sandia National Laboratories has been in the area of developing models and simulation methods that can be used to uncover and illuminate the material defects created during He bubble growth in aging bulk metal tritides. Previous efforts have used molecular dynamics calculations to examine the physical mechanisms by which growing He bubbles in a Pd metal lattice create material defects. However, these efforts focused only on the growth of He bubbles in pure Pd and not on bubble growth in the material of interest, palladium tritide (PdT), or its non-radioactive isotope palladium hydride (PdH). The reason for this is that existing inter-atomic potentials do not adequately describe the thermodynamics of the Pd-H system, which includes a miscibility gap that leads to phase separation of the dilute (alpha) and concentrated (beta) alloys of H in Pd at room temperature. This document will report the results of research to either find or develop inter-atomic potentials for the Pd-H and Pd-T systems, including our efforts to use experimental data and density functional theory calculations to create an inter-atomic potential for this unique metal alloy system.
Many optimization problems in computational science and engineering (CS&E) are characterized by expensive objective and/or constraint function evaluations paired with a lack of derivative information. Direct search methods such as generating set search (GSS) are well understood and efficient for derivative-free optimization of unconstrained and linearly-constrained problems. This paper addresses the more difficult problem of general nonlinear programming where derivatives for objective or constraint functions are unavailable, which is the case for many CS&E applications. We focus on penalty methods that use GSS to solve the linearly-constrained problems, comparing different penalty functions. A classical choice for penalizing constraint violations is {ell}{sub 2}{sup 2}, the squared {ell}{sub 2} norm, which has advantages for derivative-based optimization methods. In our numerical tests, however, we show that exact penalty functions based on the {ell}{sub 1}, {ell}{sub 2}, and {ell}{sub {infinity}} norms converge to good approximate solutions more quickly and thus are attractive alternatives. Unfortunately, exact penalty functions are discontinuous and consequently introduce theoretical problems that degrade the final solution accuracy, so we also consider smoothed variants. Smoothed-exact penalty functions are theoretically attractive because they retain the differentiability of the original problem. Numerically, they are a compromise between exact and {ell}{sub 2}{sup 2}, i.e., they converge to a good solution somewhat quickly without sacrificing much solution accuracy. Moreover, the smoothing is parameterized and can potentially be adjusted to balance the two considerations. Since many CS&E optimization problems are characterized by expensive function evaluations, reducing the number of function evaluations is paramount, and the results of this paper show that exact and smoothed-exact penalty functions are well-suited to this task.
We describe an asynchronous parallel derivative-free algorithm for linearly-constrained optimization. Generating set search (GSS) is the basis of ourmethod. At each iteration, a GSS algorithm computes a set of search directionsand corresponding trial points and then evaluates the objective function valueat each trial point. Asynchronous versions of the algorithm have been developedin the unconstrained and bound-constrained cases which allow the iterations tocontinue (and new trial points to be generated and evaluated) as soon as anyother trial point completes. This enables better utilization of parallel resourcesand a reduction in overall runtime, especially for problems where the objec-tive function takes minutes or hours to compute. For linearly-constrained GSS,the convergence theory requires that the set of search directions conform to the3 nearby boundary. The complexity of developing the asynchronous algorithm forthe linearly-constrained case has to do with maintaining a suitable set of searchdirections as the search progresses and is the focus of this research. We describeour implementation in detail, including how to avoid function evaluations bycaching function values and using approximate look-ups. We test our imple-mentation on every CUTEr test problem with general linear constraints and upto 1000 variables. Without tuning to individual problems, our implementationwas able to solve 95% of the test problems with 10 or fewer variables, 75%of the problems with 11-100 variables, and nearly half of the problems with100-1000 variables. To the best of our knowledge, these are the best resultsthat have ever been achieved with a derivative-free method. Our asynchronousparallel implementation is freely available as part of the APPSPACK software.4
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 developers manual for the DAKOTA software and describes the DAKOTA class hierarchies and their interrelationships. It derives directly from annotation of the actual source code and provides detailed class documentation, including all member functions and attributes.
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 user's manual for the DAKOTA software and provides capability overviews and procedures for software execution, as well as a variety of example studies.
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.