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NASA NTRS1986

The expanded LaGrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

NASA NTRS1988

The expanded Lagrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

NASA NTRS2012

Application of an Optimal Tuner Selection Approach for On-Board Self-Tuning Engine Models

An enhanced design methodology for minimizing the error in on-line Kalman filter-based aircraft engine performance estimation applications is presented in this paper. It specific-ally addresses the under-determined estimation problem, in which there are more unknown parameters than available sensor measurements. This work builds upon an existing technique for systematically selecting a model tuning parameter vector of appropriate dimension to enable estimation by a Kalman filter, while minimizing the estimation error in the parameters of interest. While the existing technique was optimized for open-loop engine operation at a fixed design point, in this paper an alternative formulation is presented that enables the technique to be optimized for an engine operating under closed-loop control throughout the flight envelope. The theoretical Kalman filter mean squared estimation error at a steady-state closed-loop operating point is derived, and the tuner selection approach applied to minimize this error is discussed. A technique for constructing a globally optimal tuning parameter vector, which enables full-envelope application of the technology, is also presented, along with design steps for adjusting the dynamic response of the Kalman filter state estimates. Results from the application of the technique to linear and nonlinear aircraft engine simulations are presented and compared to the conventional approach of tuner selection. The new methodology is shown to yield a significant improvement in on-line Kalman filter estimation accuracy.

Simon, Donald L.↗

DOE OSTI2021

Multiscale Control of Generic Second Order Traffic Models by Driver-Assist Vehicles

We study the derivation of generic high order macroscopic traffic models from a follow-the-leader particle description via a kinetic approach. First, we recover a third order traffic model as the hydrodynamic limit of an Enskog-type kinetic equation. Next, we introduce in the vehicle interactions a binary control modeling the automatic feedback provided by driver-assist vehicles and we upscale such a new particle description by means of another Enskog-based hydrodynamic limit. The resulting macroscopic model is now a generic second order model (GSOM), which contains in turn a control term inherited from the microscopic interactions. We show that such a control may be chosen so as to optimize global traffic trends, such as the vehicle flux or the road congestion, constrained by the GSOM dynamics. By means of numerical simulations, we investigate the effect of this control hierarchy in some specific case studies, which exemplify the multiscale path from the vehiclewise implementation of a driver-assist control to its optimal hydrodynamic design.

GSOM↗

NASA NTRS1981

Minimum fuel horizontal flightpaths in the terminal area

The problem of minimum fuel airplane trajectories from arbitrary initial states to be fixed final state is considered. There are four state variables (two position coordinates, heading, and constrained velocity) and two constrained controls (thrust and bank angle). The fuel optimality of circular and straight line flightpaths is examined. Representative extremals (trajectories satisfying the necessary conditions of the minimum principle) of various types are computed and used to evaluate trajectories generated by an on line algorithm. Attention is paid to the existence of Darboux points (beyond which an extremal ceases to be globally optimal). One fuel flow rate model includes a term quadratic in thrust; hence, the optimal thrust is continuous and nonsingular. The other fuel flow rate model is linear in thrust, and consequently the optimal thrust is discontinuous and singular.

Kreindler, E.↗

NASA NTRS2006

Genetic Algorithm for Optimization: Preprocessing with n Dimensional Bisection and Error Estimation

A knowledge of the appropriate values of the parameters of a genetic algorithm (GA) such as the population size, the shrunk search space containing the solution, crossover and mutation probabilities is not available a priori for a general optimization problem. Recommended here is a polynomial-time preprocessing scheme that includes an n-dimensional bisection and that determines the foregoing parameters before deciding upon an appropriate GA for all problems of similar nature and type. Such a preprocessing is not only fast but also enables us to get the global optimal solution and its reasonably narrow error bounds with a high degree of confidence.

Sen, S. K.↗

DOE OSTI2026

Introduction to and comparison of deep learning and optimization approaches to analytical wake modeling of a tilted wind turbine

This paper introduces innovative optimization and deep learning techniques to enhance the prediction of complex wake dynamics in the downstream wind velocity of tilted wind turbines. Traditional methods for calibrating the Bastankhah wake model often lead to increased errors in wind velocity distribution due to overfitting of the local wake characteristics. To address this issue, we propose an additional global optimization step to reduce errors in wind velocity predictions with respect to various wake parameters. Despite this improvement, the Bastankhah model's axisymmetric Gaussian wake shape limits its accuracy for complex wake structures. Therefore, we also propose a deep learning approach, which demonstrates promising results by accurately modeling complex wake shapes across a broader range of tilt angles with minimal computational cost. The deep learning approach achieves near-identical predictions to high-fidelity large-eddy simulations, representing a promising advancement in wake modeling.

17 WIND ENERGY↗

NASA NTRS2019

End to End Optimization of a Mars Hybrid Transportation Architecture

NASA’s Mars Study Capability Team (MSCT) is developing a reusable Mars hybrid transportation architecture in which both chemical and solar electric propulsion systems are used in a single vehicle design to send crew and cargo to Mars. This paper presents a new integrated framework that combines Earth departure/arrival, heliocentric trajectory, Mars orbit reorientation, and vehicle sizing into a single environment and solves the entire mission from beginning to end in an effort to find a globally optimized solution for the hybrid architecture.

Qu, Min↗

DOE OSTI2023

Optimal Traffic Signal Control Using Priority Metric Based on Real-Time Measured Traffic Information

Optimizing traffic control systems at traffic intersections can reduce network-wide fuel consumption as well as improve traffic flow. While traffic signals have conventionally been controlled based on predetermined schedules, various adaptive control systems have been developed recently using advanced sensors such as cameras, radars, and LiDARs. By utilizing rich traffic information enabled by the advanced sensors, more efficient or optimal traffic signal control is possible in response to varying traffic conditions. This paper proposes an optimal traffic signal control method to minimize network-wide fuel consumption utilizing real-time traffic information provided by advanced sensors. This new method employs a priority metric calculated by a weighted sum of various factors, including the total number of vehicles, total vehicle speed, vehicle waiting time, and road preference. Genetic Algorithm (GA) is used as a global optimization method to determine the optimal weights in the priority metric. In order to evaluate the effectiveness of the proposed method, a traffic simulation model is developed in a high-fidelity traffic simulation environment called SUMO, based on a real-world traffic network. The traffic flow within this model is simulated using actual measured traffic data from the traffic network, enabling a comprehensive assessment of the novel optimal traffic signal control method in realistic conditions. The simulation results show that the proposed priority metric-based real-time traffic signal control algorithm can significantly reduce network-wide fuel consumption compared to the conventional fixed-time control and coordinated actuated control methods that are currently used in the modeled network. Additionally, incorporating truck priority in the priority metric leads to further improvements in fuel consumption reduction.

47 OTHER INSTRUMENTATION↗

DOE OSTI2021

Spatial biases of information influence global estimates of soil respiration: how can we improve global predictions?

Soil respiration (Rs), the efflux of CO2 from soils to the atmosphere, is a major component of the terrestrial carbon cycle, but is poorly constrained from regional to global scales. The global soil respiration database (SRDB) is a compilation of in-situ Rs observations from around the globe that has been consistently updated with new measurements over the past decade. It is unclear whether the addition of data to new versions of the SRDB has produced better-constrained global Rs estimates. We compared two versions of the SRDB (v3.0 n=5173 and v5.0 n=10366) to determine how additional data influenced the global sum and uncertainty of Rs as predicted by a quantile regression forest model. A model parameterized using SRDBv3 yielded a global Rs sum of 88.6 Pg C yr-1, and associated uncertainty of 29.9 (mean absolute error) and 57.9 (standard deviation) Pg C yr-1, whereas parameterization using SRDBv5 yielded 96.5 Pg C yr-1 and associated uncertainty of 30.2 (mean average error) and 73.4 (standard deviation) Pg C yr-1. Empirically estimated global heterotrophic respiration (Rh) from v3 and v5 were 49.9-50.2 (mean 50.1) and 53.3-53.5 (mean 53.4) Pg C yr-1, respectively. Interestingly, SRDBv5’s inclusion of new data from underrepresented regions (e.g., Asia, Africa, South America) thus resulted in overall higher model uncertainty. The SRDBv5 is still biased towards northern latitudes and temperate zones, so we tested that an optimized global distribution of Rs measurements resulted in a global sum of 96.4 ± 21.4 Pg C yr-1 and lower model uncertainty. These results support current global estimates of Rs but highlight spatial inconsistencies that influence model parameterization and interpretation that should be addressed to improve regional- to global-scale predictions.

Stell, Emma↗

DOE OSTI2022

Optimal economic dispatch policy for prosumer with energy storage considering self-consumption demand

This paper analyzed the effects of self-consumption demand on the joint economic dispatch of prosumers (energy consumers who are also producers), particularly for prosumers with both energy storage and distributed energy sources (DERs). Studies in the existing literature on the economic dispatch scheduling policy of energy storage, mostly from the perspective of electricity merchants, do not address the impacts of self-consumption demand. However, due to the intermittent and high levels of uncertainty regarding DERs generation and the dynamic demand of the prosumer, production and consumption are not always simultaneous; there are two possible scenarios in each period depending on whether DERs generation can meet prosumers' self-consumption or not. Incorporating the self-consumption demand will pose modeling challenges since these two scenarios cannot occur simultaneously in each period, and different scenarios require different decisions for prosumers. Further, this paper analyzed the two scenarios separately to find the optimal storage scheduling strategy, and the results were combined to get the optimal global solution. We focused on prosumers' economic decision-making while considering self-consumption demand and the physical constraints of a battery based on dynamic programming. Our study showed that the feasible state of charge (SOC) range of storage can be segmented into several sub-ranges by SOC reference points under the above two scenarios. As a result, a prosumer's optimal scheduling can be uniquely and conveniently selected based on the sub-ranges within which the current SOC falls. The results, therefore, provided multistage decision-making guidance for prosumers with energy storage.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Surrogate modeling and optimization of the leaching process in a rare earth elements recovery plant

Critical minerals (CMs) and Rare Earth Elements (REEs) play a vital role in crucial infrastructure technologies such as renewable energy generation and batteries. Recovering them from waste materials has recently been found to significantly reduce environmental impact and supply chain costs related to these materials. In this work, we investigate surrogate modeling techniques aimed to simplify the modeling, simulation, and optimization of the leaching processes involved in CM and REE recovery flowsheets. As there is currently a lack of systematic studies on this topic, we perform extensive computational testing to ascertain which surrogate models are easier to construct and offer high predictive accuracy. Further, our results suggest that sparse quadratic models balance predictive accuracy and computational efficiency. Training and using these surrogates for global optimization of the leaching process requires two orders of magnitude fewer measurements and is up to four orders of magnitude faster than optimizing the original simulation using equation-oriented optimization or derivative-free optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Pyomo.GDP: an ecosystem for logic based modeling and optimization development

We present three core principles for engineering-oriented integrated modeling and optimization tool sets—intuitive modeling contexts, systematic computer-aided reformulations, and flexible solution strategies—and describe how new developments in Pyomo.GDP for Generalized Disjunctive Programming (GDP) advance this vision. We describe a new logical expression system implementation for Pyomo.GDP allowing for a more intuitive description of logical propositions. The logical expression system supports automated reformulation of these logical constraints to linear constraints. We also describe two new logic-based global optimization solver implementations built on Pyomo.GDP that exploit logical structure to avoid “zero-flow” numerical difficulties that arise in nonlinear network design problems when nodes or streams disappear. These new solvers also demonstrate the capability to link to external libraries for expanded functionality within an integrated implementation. We present these new solvers in the context of a flexible array of solution paths available to GDP models. Finally, we present results on a new library of GDP models demonstrating the value of multiple solution approaches.

42 ENGINEERING↗

DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Optimization of Superconducting Linac for Proton Improvement Plan-II (PIP-II)

PIP-II is an essential upgrade of the Fermilab complex that will enable the worlds most intense high-energy beam of neutrinos for the international Deep Underground Neutrino Experiment at LBNF and support a broad physics program at Fermilab. Ultimately, the PIP-II superconducting linac will be capable of accelerating the $H-$ CW beam to 800 MeV with an average power of 1.6 MW. To operate the linac with such high power, beam losses and beam emittance growth must be tightly controlled. In this paper, we present the results of global optimization of the Linac options towards a robust and efficient physics design for the superconducting section of the PIP-II linac. We also investigate the impact of the nonlinear field of the dipole correctors on the beam quality and derive the requirement on the field quality using statistical analysis. Finally, we assess the need to correct the quadrupole focusing produced by Half Wave, and Single Spoke accelerating cavities. We assess the feasibility of controlling the beam coupling in the machine by changing the polarity of the field of linac focusing solenoids

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

Learning in continuous action space for developing high dimensional potential energy models

Reinforcement learning (RL) approaches that combine a tree search with deep learning have found remarkable success in searching exorbitantly large, albeit discrete action spaces, as in chess, Shogi and Go. Many real-world materials discovery and design applications, however, involve multi-dimensional search problems and learning domains that have continuous action spaces. Exploring high-dimensional potential energy models of materials is an example. Traditionally, these searches are time consuming (often several years for a single bulk system) and driven by human intuition and/or expertise and more recently by global/local optimization searches that have issues with convergence and/or do not scale well with the search dimensionality. Here, in a departure from discrete action and other gradient-based approaches, we introduce a RL strategy based on decision trees that incorporates modified rewards for improved exploration, efficient sampling during playouts and a “window scaling scheme" for enhanced exploitation, to enable efficient and scalable search for continuous action space problems. Using high-dimensional artificial landscapes and control RL problems, we successfully benchmark our approach against popular global optimization schemes and state of the art policy gradient methods, respectively. We demonstrate its efficacy to parameterize potential models (physics based and high-dimensional neural networks) for 54 different elemental systems across the periodic table as well as alloys. We analyze error trends across different elements in the latent space and trace their origin to elemental structural diversity and the smoothness of the element energy surface. Broadly, our RL strategy will be applicable to many other physical science problems involving search over continuous action spaces.

36 MATERIALS SCIENCE↗

NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗

DOE OSTI2022

Scalable deep learning for watershed model calibration

Watershed models such as the Soil and Water Assessment Tool (SWAT) consist of high-dimensional physical and empirical parameters. These parameters often need to be estimated/calibrated through inverse modeling to produce reliable predictions on hydrological fluxes and states. Existing parameter estimation methods can be time consuming, inefficient, and computationally expensive for high-dimensional problems. In this paper, we present an accurate and robust method to calibrate the SWAT model (i.e., 20 parameters) using scalable deep learning (DL). We developed inverse models based on convolutional neural networks (CNN) to assimilate observed streamflow data and estimate the SWAT model parameters. Scalable hyperparameter tuning is performed using high-performance computing resources to identify the top 50 optimal neural network architectures. We used ensemble SWAT simulations to train, validate, and test the CNN models. We estimated the parameters of the SWAT model using observed streamflow data and assessed the impact of measurement errors on SWAT model calibration. We tested and validated the proposed scalable DL methodology on the American River Watershed, located in the Pacific Northwest-based Yakima River basin. Our results show that the CNN-based calibration is better than two popular parameter estimation methods (i.e., the generalized likelihood uncertainty estimation [GLUE] and the dynamically dimensioned search [DDS], which is a global optimization algorithm). For the set of parameters that are sensitive to the observations, our proposed method yields narrower ranges than the GLUE method but broader ranges than values produced using the DDS method within the sampling range even under high relative observational errors. The SWAT model calibration performance using the CNNs, GLUE, and DDS methods are compared using R 2 and a set of efficiency metrics, including Nash-Sutcliffe, logarithmic Nash-Sutcliffe, Kling-Gupta, modified Kling-Gupta, and non-parametric Kling-Gupta scores, computed on the observed and simulated watershed responses. The best CNN-based calibrated set has scores of 0.71, 0.75, 0.85, 0.85, 0.86, and 0.91. The best DDS-based calibrated set has scores of 0.62, 0.69, 0.8, 0.77, 0.79, and 0.82. The best GLUE-based calibrated set has scores of 0.56, 0.58, 0.71, 0.7, 0.71, and 0.8. The scores above show that the CNN-based calibration leads to more accurate low and high streamflow predictions than the GLUE and DDS sets. Our research demonstrates that the proposed method has high potential to improve our current practice in calibrating large-scale integrated hydrologic models.

54 ENVIRONMENTAL SCIENCES↗