Publications

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Discrete models of large, complex systems like national infrastructures and complex logistics frameworks naturally incorporate many modeling uncertainties. Consequently, there is a clear need for optimization techniques that can robustly account for risks associated with modeling uncertainties. This report summarizes the progress of the Late-Start LDRD 'Robust Analysis of Largescale Combinatorial Applications'. This project developed new heuristics for solving robust optimization models, and developed new robust optimization models for describing uncertainty scenarios.

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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.

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We have found that developing a computational framework for reconstructing error control codes for engineered data and ultimately for deciphering genetic regulatory coding sequences is a challenging and uncharted area that will require advances in computational technology for exact solutions. Although exact solutions are desired, computational approaches that yield plausible solutions would be considered sufficient as a proof of concept to the feasibility of reverse engineering error control codes and the possibility of developing a quantitative model for understanding and engineering genetic regulation. Such evidence would help move the idea of reconstructing error control codes for engineered and biological systems from the high risk high payoff realm into the highly probable high payoff domain. Additionally this work will impact biological sensor development and the ability to model and ultimately develop defense mechanisms against bioagents that can be engineered to cause catastrophic damage. Understanding how biological organisms are able to communicate their genetic message efficiently in the presence of noise can improve our current communication protocols, a continuing research interest. Towards this end, project goals include: (1) Develop parameter estimation methods for n for block codes and for n, k, and m for convolutional codes. Use methods to determine error control (EC) code parameters for gene regulatory sequence. (2) Develop an evolutionary computing computational framework for near-optimal solutions to the algebraic code reconstruction problem. Method will be tested on engineered and biological sequences.

We consider the accuracy of predictions made by integer programming (IP) models of sensor placement for water security applications. We have recently shown that IP models can be used to find optimal sensor placements for a variety of different performance criteria (e.g. minimize health impacts and minimize time to detection). However, these models make a variety of simplifying assumptions that might bias the final solution. We show that our IP modeling assumptions are similar to models developed for other sensor placement methodologies, and thus IP models should give similar predictions. However, this discussion highlights that there are significant differences in how temporal effects are modeled for sensor placement. We describe how these modeling assumptions can impact sensor placements.

In recent years, several integer programming models have been proposed to place sensors in municipal water networks in order to detect intentional or accidental contamination. Although these initial models assumed that it is equally costly to place a sensor at any place in the network, there clearly are practical cost constraints that would impact a sensor placement decision. Such constraints include not only labor costs but also the general accessibility of a sensor placement location. In this paper, we extend our integer program to explicitly model the cost of sensor placement. We partition network locations into groups of varying placement cost, and we consider the public health impacts of contamination events under varying budget constraints. Thus our models permit cost/benefit analyses for differing sensor placement designs. As a control for our optimization experiments, we compare the set of sensor locations selected by the optimization models to a set of manually-selected sensor locations.

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We present a model for optimizing the placement of sensors in municipal water networks to detect maliciously injected contaminants. An optimal sensor configuration minimizes the expected fraction of the population at risk. We formulate this problem as a mixed-integer program, which can be solved with generally available solvers. We find optimal sensor placements for three test networks with synthetic risk and population data. Our experiments illustrate that this formulation can be solved relatively quickly and that the predicted sensor configuration is relatively insensitive to uncertainties in the data used for prediction.

We introduce a filter-based evolutionary algorithm (FEA) for constrained optimization. The filter used by an FEA explicitly imposes the concept of dominance on a partially ordered solution set. We show that the algorithm is provably robust for both linear and nonlinear problems and constraints. FEAs use a finite pattern of mutation offsets, and our analysis is closely related to recent convergence results for pattern search methods. We discuss how properties of this pattern impact the ability of an FEA to converge to a constrained local optimum.

A fundamental challenge for all communication systems, engineered or living, is the problem of achieving efficient, secure, and error-free communication over noisy channels. Information theoretic principals have been used to develop effective coding theory algorithms to successfully transmit information in engineering systems. Living systems also successfully transmit biological information through genetic processes such as replication, transcription, and translation, where the genome of an organism is the contents of the transmission. Decoding of received bit streams is fairly straightforward when the channel encoding algorithms are efficient and known. If the encoding scheme is unknown or part of the data is missing or intercepted, how would one design a viable decoder for the received transmission? For such systems blind reconstruction of the encoding/decoding system would be a vital step in recovering the original message. Communication engineers may not frequently encounter this situation, but for computational biologists and biotechnologist this is an immediate challenge. The goal of this work is to develop methods for detecting and reconstructing the encoder/decoder system for engineered and biological data. Building on Sandia's strengths in discrete mathematics, algorithms, and communication theory, we use linear programming and will use evolutionary computing techniques to construct efficient algorithms for modeling the coding system for minimally errored engineered data stream and genomic regulatory DNA and RNA sequences. The objective for the initial phase of this project is to construct solid parallels between biological literature and fundamental elements of communication theory. In this light, the milestones for FY2003 were focused on defining genetic channel characteristics and providing an initial approximation for key parameters, including coding rate, memory length, and minimum distance values. A secondary objective addressed the question of determining similar parameters for a received, noisy, error-control encoded data set. In addition to these goals, we initiated exploration of algorithmic approaches to determine if a data set could be approximated with an error-control code and performed initial investigations into optimization based methodologies for extracting the encoding algorithm given the coding rate of an encoded noise-free and noisy data stream.

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The maximum contact map overlap (MAX-CMO) between a pair of protein structures can be used as a measure of protein similarity. It is a purely topological measure and does not depend on the sequence of the pairs involved in the comparison. More importantly, the MAX-CMO present a very favorable mathematical structure which allows the formulation of integer, linear and Lagrangian models that can be used to obtain guarantees of optimality. It is not the intention of this paper to discuss the mathematical properties of MAX-CMO in detail as this has been dealt elsewhere. In this paper we compare three algorithms that can be used to obtain maximum contact map overlaps between protein structures. We will point to the weaknesses and strengths of each one. It is our hope that this paper will encourage researchers to develop new and improve methods for protein comparison based on MAX-CMO.

We consider the convergence properties of a non-elitist self-adaptive evolutionary strategy (ES) on multi-dimensional problems. In particular, we apply our recent convergence theory for a discretized (1,{lambda})-ES to design a related (1,{lambda})-ES that converges on a class of seperable, unimodal multi-dimensional problems. The distinguishing feature of self-adaptive evolutionary algorithms (EAs) is that the control parameters (like mutation step lengths) are evolved by the evolutionary algorithm. Thus the control parameters are adapted in an implicit manner that relies on the evolutionary dynamics to ensure that more effective control parameters are propagated during the search. Self-adaptation is a central feature of EAs like evolutionary stategies (ES) and evolutionary programming (EP), which are applied to continuous design spaces. Rudolph summarizes theoretical results concerning self-adaptive EAs and notes that the theoretical underpinnings for these methods are essentially unexplored. In particular, convergence theories that ensure convergence to a limit point on continuous spaces have only been developed by Rudolph, Hart, DeLaurentis and Ferguson, and Auger et al. In this paper, we illustrate how our analysis of a (1,{lambda})-ES for one-dimensional unimodal functions can be used to ensure convergence of a related ES on multidimensional functions. This (1,{lambda})-ES randomly selects a search dimension in each iteration, along which points generated. For a general class of separable functions, our analysis shows that the ES searches along each dimension independently, and thus this ES converges to the (global) minimum.

This document provides a user manual for the SGOPT software library. SGOPT is a C++ class library for nonlinear optimization. This library uses an object-oriented design that allows the software to be extended to a new problem domains. Furthermore, this library was designed to that the interface is straightforward while providing flexibility to allow new algorithms to be easily added to this library. The SGOPT library has been used by several software projects at Sandia, and it is integrated into the DAKOTA design and analysis toolkit. This report provides a high-level description of the optimization algorithms provided by SGOPT and describes the C++ class hierarchy in which they are implemented. Finally, installation instructions are included.

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We consider the problem of placing sensors in a network to detect and identify the source of any contamination. We consider two variants of this problem: (1) sensor-constrained: we are allowed a fixed number of sensors and want to minimize contamination detection time; and (2) time-constrained: we must detect contamination within a given time limit and want to minimize the number of sensors required. Our main results are as follows. First, we give a necessary and sufficient condition for source identification. Second, we show that the sensor and time constrained versions of the problem are polynomially equivalent. Finally, we show that the sensor-constrained version of the problem is polynomially equivalent to the asymmetric k-center problem and that the time-constrained version of the problem is polynomially equivalent to the dominating set problem.

We present a model for optimizing the placement of sensors in municipal water networks to detect maliciously-injected contaminants. An optimal sensor configuration minimizes the expected fraction of the population at risk. We formulate this problem as an integer program, which can be solved with generally available IP solvers. We find optimal sensor placements for three real networks with synthetic risk and population data. Our experiments illustrate that this formulation can be solved relatively quickly, and that the predicted sensor configuration is relatively insensitive to uncertainties in the data used for prediction.

We describe COLIN, a Common Optimization Library INterface for C++. COLIN provides C++ template classes that define a generic interface for both optimization problems and optimization solvers. COLIN is specifically designed to facilitate the development of hybrid optimizers, for which one optimizer calls another to solve an optimization subproblem. We illustrate the capabilities of COLIN with an example of a memetic genetic programming solver.

The U.S. Department of Energy recently announced the first five grants for the Genomes to Life (GTL) Program. The goal of this program is to ''achieve the most far-reaching of all biological goals: a fundamental, comprehensive, and systematic understanding of life.'' While more information about the program can be found at the GTL website (www.doegenomestolife.org), this paper provides an overview of one of the five GTL projects funded, ''Carbon Sequestration in Synechococcus Sp.: From Molecular Machines to Hierarchical Modeling.'' This project is a combined experimental and computational effort emphasizing developing, prototyping, and applying new computational tools and methods to elucidate the biochemical mechanisms of the carbon sequestration of Synechococcus Sp., an abundant marine cyanobacteria known to play an important role in the global carbon cycle. Understanding, predicting, and perhaps manipulating carbon fixation in the oceans has long been a major focus of biological oceanography and has more recently been of interest to a broader audience of scientists and policy makers. It is clear that the oceanic sinks and sources of CO(2) are important terms in the global environmental response to anthropogenic atmospheric inputs of CO(2) and that oceanic microorganisms play a key role in this response. However, the relationship between this global phenomenon and the biochemical mechanisms of carbon fixation in these microorganisms is poorly understood. The project includes five subprojects: an experimental investigation, three computational biology efforts, and a fifth which deals with addressing computational infrastructure challenges of relevance to this project and the Genomes to Life program as a whole. Our experimental effort is designed to provide biology and data to drive the computational efforts and includes significant investment in developing new experimental methods for uncovering protein partners, characterizing protein complexes, identifying new binding domains. We will also develop and apply new data measurement and statistical methods for analyzing microarray experiments. Our computational efforts include coupling molecular simulation methods with knowledge discovery from diverse biological data sets for high-throughput discovery and characterization of protein-protein complexes and developing a set of novel capabilities for inference of regulatory pathways in microbial genomes across multiple sources of information through the integration of computational and experimental technologies. These capabilities will be applied to Synechococcus regulatory pathways to characterize their interaction map and identify component proteins in these pathways. We will also investigate methods for combining experimental and computational results with visualization and natural language tools to accelerate discovery of regulatory pathways. Furthermore, given that the ultimate goal of this effort is to develop a systems-level of understanding of how the Synechococcus genome affects carbon fixation at the global scale, we will develop and apply a set of tools for capturing the carbon fixation behavior of complex of Synechococcus at different levels of resolution. Finally, because the explosion of data being produced by high-throughput experiments requires data analysis and models which are more computationally complex, more heterogeneous, and require coupling to ever increasing amounts of experimentally obtained data in varying formats, we have also established a companion computational infrastructure to support this effort as well as the Genomes to Life program as a whole.

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, analytic reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity 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, analytic reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity 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, analytic reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity 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.

This report describes the design of PICO, a C++ framework for implementing general parallel branch-and-bound algorithms. The PICO framework provides a mechanism for the efficient implementation of a wide range of branch-and-bound methods on an equally wide range of parallel computing platforms. We first discuss the basic architecture of PICO, including the application class hierarchy and the package's serial and parallel layers. We next describe the design of the serial layer, and its central notion of manipulating subproblem states. Then, we discuss the design of the parallel layer, which includes flexible processor clustering and communication rates, various load balancing mechanisms, and a non-preemptive task scheduler running on each processor. We describe the application of the package to a branch-and-bound method for mixed integer programming, along with computational results on the ASCI Red massively parallel computer. Finally we describe the application of the branch-and-bound mixed-integer programming code to a resource constrained project scheduling problem for Pantex.

The authors describe a convergence theory for evolutionary pattern search algorithms (EPSAs) on a broad class of unconstrained and linearly constrained problems. EPSAs adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSAs is inspired by recent analyses of pattern search methods. The analysis significantly extends the previous convergence theory for EPSAs. The analysis applies to a broader class of EPSAs,and it applies to problems that are nonsmooth, have unbounded objective functions, and which are linearly constrained. Further, they describe a modest change to the algorithmic framework of EPSAs for which a non-probabilistic convergence theory applies. These analyses are also noteworthy because they are considerably simpler than previous analyses of EPSAs.

Crystal lattices are infinite periodic graphs that occur naturally in a variety of geometries and which are of fundamental importance in polymer science. Discrete models of protein folding use crystal lattices to define the space of protein conformations. Because various crystal lattices provide discretizations of the same physical phenomenon, it is reasonable to expect that there will exist invariants across lattices related to fundamental properties of the protein folding process. This paper considers whether performance-guaranteed approximability is such an invariant for HP lattice models. The authors define a master approximation algorithm that has provable performance guarantees provided that a specific sublattice exists within a given lattice. They describe a broad class of crystal lattices that are approximable, which further suggests that approximability is a general property of HP lattice models.

The authors describe a naturalistic behavioral model for the simulation of small unit combat. This model, Klein's recognition-primed decision making (RPD) model, is driven by situational awareness rather than a rational process of selecting from a set of action options. They argue that simulated combatants modeled with RPD will have more flexible and realistic responses to a broad range of small-scale combat scenarios. Furthermore, they note that the predictability of a simulation using an RPD framework can be easily controlled to provide multiple evaluations of a given combat scenario. Finally, they discuss computational issues for building an RPD-based behavior engine for fully automated combatants in small conflict scenarios, which are being investigated within Sandia's Next Generation Site Security project.

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