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DOE OSTI2021

Progress toward favorable landscapes in quantum combinatorial optimization

The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. Here, we study how these quantum and classical components interrelate. In particular, we focus on algorithms for solving the combinatorial optimization problem MaxCut, and study how the structure of the classical optimization landscape relates to the quantum circuit used to evaluate the MaxCut objective function. In order to analytically characterize the impact of quantum features on the critical points of the landscape, we consider a family of quantum circuit ansätze composed of mutually commuting elements. We identify multiqubit operations as a key resource and show that overparameterization allows for obtaining favorable landscapes. Namely, we prove that an ansatz from this family containing exponentially many variational parameters yields a landscape free of local optima for generic graphs. However, we further prove that these ansätze do not offer superpolynomial advantages over purely classical MaxCut algorithms. Here, we then present a series of numerical experiments illustrating that noncommutativity and entanglement are important features for improving algorithm performance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Avoiding excess computation in asynchronous evolutionary algorithms

Abstract Asynchronous evolutionary algorithms are becoming increasingly popular as a means of making full use of many processors while solving computationally expensive search and optimization problems. These algorithms excel at keeping large clusters fully utilized, but may sometimes inefficiently sample an excess of fast‐evaluating solutions at the expense of higher‐quality, slow‐evaluating ones. We have previously introduced a steady‐state parent selection strategy, SWEET (“Selection whilE EvaluaTing”), that sometimes selects individuals that are still being evaluated and allows them to reproduce early. We perform a takeover‐time analysis that confirms that this strategy gives slow‐evaluating individuals that have higher fitnesses an increased ability to multiply in the population. We also find that SWEET appears effective at improving optimization performance on problems in which solution quality is positively correlated with evaluation time. We evaluate our approach on six simulated real‐valued optimization problems and three real‐world applications: an autonomous vehicle controller problem that involves tuning a spiking neural network and two adversarial EA problems. We further evaluate SWEET versus a basic asynchronous process in a simulated setting. We present evidence that SWEET outperforms basic asynchronous processes in a use‐case in which performance is positively correlated with evaluation time, and performs comparably (and often better) than basic asynchronous processes in several use‐cases where performance is negatively correlated with evaluation time. That said, in the cases where performance and evaluation time are negatively correlated the variance of outcomes for SWEET is notably high.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Adaptive Optimizer for Measurement-Frugal Variational Algorithms

Variational hybrid quantum-classical algorithms (VHQCAs) have the potential to be useful in the era of near-term quantum computing. However, recently there has been concern regarding the number of measurements needed for convergence of VHQCAs. Here, we address this concern by investigating the classical optimizer in VHQCAs. We introduce a novel optimizer called individual Coupled Adaptive Number of Shots (iCANS). This adaptive optimizer frugally selects the number of measurements (i.e., number of shots) both for a given iteration and for a given partial derivative in a stochastic gradient descent. We numerically simulate the performance of iCANS for the variational quantum eigensolver and for variational quantum compiling, with and without noise. In all cases, and especially in the noisy case, iCANS tends to out-perform state-of-the-art optimizers for VHQCAs. We therefore believe this adaptive optimizer will be useful for realistic VHQCA implementations, where the number of measurements is limited.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Optimal well placement and brine extraction for pressure management during CO 2 sequestration

Large-scale pressure increases resulting from carbon dioxide (CO 2 ) injection in the subsurface can potentially impact caprock integrity, induce reactivation of critically stressed faults, and drive CO 2 or brine through conductive features into shallow groundwater. Pressure management involving the extraction of native fluids from storage formations can be used to reduce such pressure increases. However, dealing with large volumes of extracted brine can be technically challenging and expensive. Selection of optimal well locations and pumping rates are critical for maximizing CO 2 storage and minimizing brine extraction during geologic CO 2 sequestration (GCS). Robust and efficient computerized algorithms combining reservoir models and optimization methods are needed to make proper decisions on well placement and pumping rates. This work presents a constrained differential evolution (CDE) algorithm for solving global optimization problems involving pressure management of GCS projects. Application of the CDE optimization methodology was demonstrated for a hypothetical CO 2 storage scenario in a deep sandstone reservoir in the Southern San Joaquin Basin in California, USA. Industrial-scale storage of CO 2 would generate significant pressure buildup in this formation, which in turn would raise concerns about induced seismicity due to presence of multiple faults surrounding the injection site. Through the CDE optimization algorithm coupled to a vertically-averaged reservoir simulator, we successfully estimated optimal solutions for brine extraction wells in the reservoir that would limit the local pressure along the faults to a prescribed threshold. Multiple realizations of the reservoir permeability field were created to understand the impact of reservoir heterogeneity on optimization results. Our results indicate that the reservoir slope and heterogeneity have significant impact on optimum extraction rates. Reservoir heterogeneity is also a significant factor for extraction well locations, suggesting that in practice decisions about extraction well placement through optimization should be made at later project stages when data from a few years of CO 2 injection have allowed iterative updating and refining of the reservoir forward models. Although the study focused on optimization of brine extraction, the CDE optimization methodology presented in this paper has also potential to solve other complex optimization problems related to GCS, such as increasing storage efficiency by enhancing injectivity and capillary and dissolution trapping.

58 GEOSCIENCES↗
DOE OSTI2016

TH-EF-BRB-05: 4pi Non-Coplanar IMRT Beam Angle Selection by Convex Optimization with Group Sparsity Penalty

Purpose: Integrated beam orientation and fluence map optimization is expected to be the foundation of robust automated planning but existing heuristic methods do not promise global optimality. We aim to develop a new method for beam angle selection in 4π non-coplanar IMRT systems based on solving (globally) a single convex optimization problem, and to demonstrate the effectiveness of the method by comparison with a state of the art column generation method for 4π beam angle selection. Methods: The beam angle selection problem is formulated as a large scale convex fluence map optimization problem with an additional group sparsity term that encourages most candidate beams to be inactive. The optimization problem is solved using an accelerated first-order method, the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The beam angle selection and fluence map optimization algorithm is used to create non-coplanar 4π treatment plans for several cases (including head and neck, lung, and prostate cases) and the resulting treatment plans are compared with 4π treatment plans created using the column generation algorithm. Results: In our experiments the treatment plans created using the group sparsity method meet or exceed the dosimetric quality of plans created using the column generation algorithm, which was shown superior to clinical plans. Moreover, the group sparsity approach converges in about 3 minutes in these cases, as compared with runtimes of a few hours for the column generation method. Conclusion: This work demonstrates the first non-greedy approach to non-coplanar beam angle selection, based on convex optimization, for 4π IMRT systems. The method given here improves both treatment plan quality and runtime as compared with a state of the art column generation algorithm. When the group sparsity term is set to zero, we obtain an excellent method for fluence map optimization, useful when beam angles have already been selected. NIH R43CA183390, NIH R01CA188300, Varian Medical Systems; Part of this research took place while D. O’Connor was a summer intern at RefleXion Medical.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

Status on the Development of a Modeling and Simulation Framework for the Economic Assessment of Nuclear Hybrid Energy Systems

An effort to design and build a modeling and simulation framework to assess the economic viability of Nuclear Hybrid Energy Systems (NHES) was undertaken in fiscal year 2015 (FY15). The purpose of this report is to document the various tasks associated with the development of such a framework and to provide a status on its progress. Several tasks have been accomplished. First, starting from a simulation strategy, a rigorous mathematical formulation has been achieved in which the economic optimization of a Nuclear Hybrid Energy System is presented as a constrained robust (under uncertainty) optimization problem. Some possible algorithms for the solution of the optimization problem are presented. A variation of the Simultaneous Perturbation Stochastic Approximation algorithm has been implemented in RAVEN and preliminary tests have been performed. The development of the software infrastructure to support the simulation of the whole NHES has also moved forward. The coupling between RAVEN and an implementation of the Modelica language (OpenModelica) has been implemented, migrated under several operating systems and tested using an adapted model of a desalination plant. In particular, this exercise was focused on testing the coupling of the different code systems; testing parallel, computationally expensive simulations on the INL cluster; and providing a proof of concept for the possibility of using surrogate models to represent the different NHES subsystems. Another important step was the porting of the RAVEN code under the Windows™ operating system. This accomplishment makes RAVEN compatible with the development environment that is being used for dynamic simulation of NHES components. A very simplified model of a NHES on the electric market has been built in RAVEN to confirm expectations on the analysis capability of RAVEN to provide insight into system economics and to test the capability of RAVEN to identify limit surfaces even for stochastic constraints. This capability will be needed in the future to enforce the stochastic constraints on the electric demand coverage from the NHES. The development team gained experience with many of the tools that are currently envisioned for use in the economic analysis of NHES and completed several important steps. Given the complexity of the project, preference has been given to a structural approach in which several independent efforts have been used to build the cornerstone of the simulation framework. While this is good approach in establishing such a complex framework, it may delay reaching more complete results on the performance of analyzed system configurations. The integration of the previously reported exergy analysis approach was initially proposed as part of this milestone. However, in reality, the exergy-based apportioning of cost will take place only in a second stage of the implementation since it will be used to properly allocate cost among the different NHES subsystems. Therefore, exergy does not appear at the level of the main drivers in the analysis framework; the latter development of the base framework is the focus of this report.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2014

A Cutting Surface Algorithm for Semi-Infinite Convex Programming with an Application to Moment Robust Optimization

In this paper, we present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set consists of probability distributions with given bounds on their moments. Moments of arbitrary order, as well as nonpolynomial moments, can be included in the formulation. We show that this gives rise to a hierarchy of optimization problems with decreasing levels of risk-aversion, with classic robust optimization at one end of the spectrum and stochastic programming at the other. Although our primary motivation is to solve distributionally robust optimization problems with moment uncertainty, the cutting surface method for general semi-infinite convex programs is also of independent interest. The proposed method is applicable to problems with nondifferentiable semi-infinite constraints indexed by an infinite dimensional index set. Examples comparing the cutting surface algorithm to the central cutting plane algorithm of Kortanek and No demonstrate the potential of our algorithm even in the solution of traditional semi-infinite convex programming problems, whose constraints are differentiable, and are indexed by an index set of low dimension. After the rate of convergence analysis of the cutting surface algorithm, we extend the authors' moment matching scenario generation algorithm to a probabilistic algorithm that finds optimal probability distributions subject to moment constraints. The combination of this distribution optimization method and the central cutting surface algorithm yields a solution to a family of distributionally robust optimization problems that are considerably more general than the ones proposed to date.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A parallel evolutionary multiple-try metropolis Markov chain Monte Carlo algorithm for sampling spatial partitions

We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large, complex, and constrained spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as optimization heuristics for state space traversal and the theoretical convergence properties of Markov Chain Monte Carlo algorithms for sampling from unknown distributions. Local optimality information that is identified via a directed search by our optimization heuristic is used to adaptively update a Markov chain in a promising direction within the framework of a Multiple-Try Metropolis Markov Chain model that incorporates a generalized Metropolis-Hastings ratio. We further expand the reach of our EMCMC algorithm by harnessing the computational power afforded by massively parallel computing architecture through the integration of a parallel EA framework that guides Markov chains running in parallel.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An algorithm for physics informed scan path optimization in additive manufacturing

Site specific microstructure control is a critical research area within the field of additive manufacturing due to its potential to revolutionize part performance. One way to achieve site specific microstructure control is through control of the solidification conditions via the construction of intricate scan paths; however, the search space for such a problem is large. Previous attempts only considered the solidification conditions at the top surface while also requiring either lots of manual-fine tuning or large amounts of computational resources. This paper introduces a general method for scan path optimization which considers the solidification conditions in the bulk of the material without an increase in computational expense. This method consists of three core components:1. A heat transfer model for simulating the temperature field at a given time.2. A surrogate model which takes scan pattern information and temperature data and predicts the solidification conditions of the bulk as well as the meltpool depths for a spot melt.3. A decision algorithm to decide which spot melt should be printed next based on the outputs of the surrogate model.Each of these components can be changed without changing the overall method. Within this work, this method is applied in the creation of an algorithm containing a semi-analytic heat transfer model to simulate the temperature field, a fully convolutional neural network (FCNN) as the surrogate model, and a greedy decision algorithm. The resulting algorithm produced complex scan patterns which gave strong results for simulated microstructure control.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Efficient Distributed Optimization of Wind Farms Using Proximal Primal-Dual Algorithms

This paper presents a distributed approach to performing real-time optimization of large wind farms. Wind turbines in a wind farm typically operate individually to maximize their own performance regardless of the impact of aerodynamic interactions on neighboring turbines. This paper optimizes the overall power produced by a wind farm by formulating and solving a nonconvex optimization problem where the yaw angles are optimized to allow some turbines to operate in misaligned conditions and shape the aerodynamic interactions in a favorable way. The solution of the nonconvex smooth problem is tackled using a proximal primal-dual gradient method, which provably identifies a first-order stationary solution in a global sublinear manner. By adding auxiliary optimization variables for every pair of turbines that are coupled aerodynamically, and properly adding consensus constraints into the underlying problem, a distributed algorithm with turbine-to-turbine message passing is obtained; this allows for turbines to be optimized in parallel using local information rather than information from the whole wind farm. This algorithm is computationally light, as it involves closed-form updates. This approach is demonstrated on a large wind farm with 60 turbines. The results indicate that similar performance can be achieved as with finite-difference gradient-based optimization at a fraction of the computational time and thus approaching real-time control/optimization.

17 WIND ENERGY↗
DOE OSTI2015

Optimizing Approximate Weighted Matching on Nvidia Kepler K40

Matching is a fundamental graph problem with numerous applications in science and engineering. While algorithms for computing optimal matchings are difficult to parallelize, approximation algorithms on the other hand generally compute high quality solutions and are amenable to parallelization. In this paper, we present efficient implementations of the current best algorithm for half-approximate weighted matching, the Suitor algorithm, on Nvidia Kepler K-40 platform. We develop four variants of the algorithm that exploit hardware features to address key challenges for a GPU implementation. We also experiment with different combinations of work assigned to a warp. Using an exhaustive set of $269$ inputs, we demonstrate that the new implementation outperforms the previous best GPU algorithm by $10$ to $100\times$ for over $100$ instances, and from $100$ to $1000\times$ for $15$ instances. We also demonstrate up to $20\times$ speedup relative to $2$ threads, and up to $5\times$ relative to $16$ threads on Intel Xeon platform with $16$ cores for the same algorithm. The new algorithms and implementations provided in this paper will have a direct impact on several applications that repeatedly use matching as a key compute kernel. Further, algorithm designs and insights provided in this paper will benefit other researchers implementing graph algorithms on modern GPU architectures.

GPU↗
DOE OSTI2022

KSSOLV 2.0: An efficient MATLAB toolbox for solving the Kohn-Sham equations with plane-wave basis set

KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new algorithms. Furthermore, it includes new functionalities such as new iterative diagonalization algorithms, k-point sampling for electron band structures, geometry optimization and advanced algorithms for performing DFT calculations with local, semi-local, and hybrid exchange-correlation functionals. It can be used to study the electronic structures of both molecules and solids. So, we describe these new capabilities in this work through a few use cases. We also demonstrate the numerical accuracy and computational efficiency of KSSOLV on a variety of examples.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Economical and Engineering Aspects of Proactive Demand Participation: Centralized versus Bilateral Control Structure

The electric grid of the U.S. is evolving from a system characterized by large and centralized fossil-fueled power plants and passive customers to a network with high penetration of distributed energy resources and proactive customers. This project facilitated the evolution of the U.S. electric power grid by enabling proactive participation of demands in electricity market at the power distribution system level. This project has three major achievements. First, we designed a centralized distribution system operator managed electricity market and developed a three-phase alternating current optimal power flow algorithm to coordinate the operation of large-scale flexible loads and distributed energy resources. Second, we designed a decentralized bilateral coordinate framework for retail electricity market, where each participating customer is capable of making decisions regarding energy production and consumption based on information received from transactive neighbors. Third, the impacts of centralized and decentralized demand-side participation scheme on power system operations were evaluated with both large-scale simulations and hardware-in-the-loop demonstrations. The major activities and specific accomplishments of the technical tasks are summarized in Section II. The detailed design of centralized/hierarchical and decentralized/bilateral retail electricity markets and the comparison between the two markets are described in Section III. The accomplishments and conclusions of the project are presented in Section IV. The major findings of the project falls into three areas, hierarchical distribution system operator managed electricity market, bilateral electricity market and decentralized market coordination, and comparison of centralized and decentralized market coordination mechanisms. In the area of hierarchical distribution system operator managed electricity market design, an integrated wholesale and retail electricity market was shown to be highly effective in extracting the operational flexibility from distributed energy resources to provide services to the wholesale market. A chordal conversion based convex iteration algorithm is not only computationally efficiency but also achieves global optimal solution in coordinating the operations of a large number of heterogeneous distributed energy resources.In the area of decentralized market coordination approach, we showed that bilateral transactions among proactive customers and decentralized transaction clearing mechanism based on simultaneous second-price sealed-bid auction can encourage truthful bidding strategies from the market participations. In addition, the individual customers can rely on a portfolio optimization approach to maximize their returns while minimizing risks. In the area of comparison of centralized and decentralized market coordination mechanisms, we found that the centralized market design results in higher social welfare and lower wholesale market clearing price for electricity. In general, centralized market design favors distributed energy resources and fixed loads. The decentralized market design mostly benefits flexible loads and conventional generators.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

MO-G-304-04: Generating Well-Dispersed Representations of the Pareto Front for Multi-Criteria Optimization in Radiation Treatment Planning

Purpose: To present a novel multi-criteria optimization (MCO) solution approach that generates well-dispersed representation of the Pareto front for radiation treatment planning. Methods: Different algorithms have been proposed and implemented in commercial planning software to generate MCO plans for external-beam radiation therapy. These algorithms consider convex optimization problems. We propose a grid-based algorithm to generate well-dispersed treatment plans over Pareto front. Our method is able to handle nonconvexity in the problem to deal with dose-volume objectives/constraints, biological objectives, such as equivalent uniform dose (EUD), tumor control probability (TCP), normal tissue complication probability (NTCP), etc. In addition, our algorithm is able to provide single MCO plan when clinicians are targeting narrow bounds of objectives for patients. In this situation, usually none of the generated plans were within the bounds and a solution is difficult to identify via manual navigation. We use the subproblem formulation utilized in the grid-based algorithm to obtain a plan within the specified bounds. The subproblem aims to generate a solution that maps into the rectangle defined by the bounds. If such a solution does not exist, it generates the solution closest to the rectangle. We tested our method with 10 locally advanced head and neck cancer cases. Results: 8 objectives were used including 3 different objectives for primary target volume, high-risk and low-risk target volumes, and 5 objectives for each of the organs-at-risk (OARs) (two parotids, spinal cord, brain stem and oral cavity). Given tight bounds, uniform dose was achieved for all targets while as much as 26% improvement was achieved in OAR sparing comparing to clinical plans without MCO and previously proposed MCO method. Conclusion: Our method is able to obtain well-dispersed treatment plans to attain better approximation for convex and nonconvex Pareto fronts. Single treatment plan can be achieved when given bounds on the objectives.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗
DOE OSTI2021

A Software Framework for Comparing Training Approaches for Spiking Neuromorphic Systems

There are a wide variety of training approaches for spiking neural networks for neuromorphic deployment. However, it is often not clear how these training algorithms perform or compare when applied across multiple neuromorphic hardware platforms and multiple datasets. In this work, we present a software framework for comparing performance across four neuromorphic training algorithms across three neuromorphic simulators and four simple classification tasks. We introduce an approach for training a spiking neural network using a decision tree, and we compare this approach to training algorithms based on evolutionary algorithms, back-propagation, and reservoir computing. We present a hyperparameter optimization approach to tune the hyperparameters of the algorithm, and show that these optimized hyperparameters depend on the processor, algorithm, and classification task. Finally, we compare the performance of the optimized algorithms across multiple metrics, including accuracy, training time, and resulting network size, and we show that there is not one best training algorithm across all datasets and performance metrics.

Schuman, Catherine↗
DOE OSTI2022

Automating Genetic Algorithm Mutations for Molecules Using a Masked Language Model

Inspired by the evolution of biological systems, genetic algorithms have been applied to generate solutions for optimization problems in a variety of scientific and engineering disciplines. For a given problem, a suitable genome representation must be defined along with a mutation operator to generate subsequent generations. Unlike natural systems which display a variety of complex rearrangements (e.g. mobile genetic elements), mutation for genetic algorithms commonly utilizes only random point-wise changes. Furthermore, generalizing beyond point-wise mutations poses a key difficulty as useful genome rearrangements depend on the representation and problem domain. To move beyond the limitations of manually defined point-wise changes, here we propose the use of techniques from masked language models to automatically generate mutations. As a first step, common subsequences within a given population are used to generate a vocabulary. The vocabulary is then used to tokenize each genome. A masked language model is trained on the tokenized data in order to generate possible rearrangements (i.e. mutations). In order to illustrate the proposed strategy, we use string representations of molecules and use a genetic algorithm to optimize for drug-likeness and synthesizability. Finally, our results show that moving beyond random point-wise mutations accelerates genetic algorithm optimization.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Optimization of a Unipolar Magnetic Bearing

New designs of unipolar magnetic bearings in electrical industrial machines are optimized by means of genetic algorithms. As a result, the optimal geometric dimensions are determined. On that basis, a design is developed for an electric motor with a unipolar active magnetic bearing.

42 ENGINEERING↗