Physics-informed machine learning with optimization-based guarantees: Applications to AC power flow
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97 MATHEMATICS AND COMPUTING↗
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Results for “integer programming”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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Proactive Frequency Stability Scheme Based on Bayesian Filters and Spectral Clustering
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ACOPF Transmission Switching Using Open-Source MINLP Solvers
The optimal transmission switching (OTS) problem with AC physics represents a mixed integer non-linear non-convex optimization problem which can provide benefits to transmission level power system operations. In this paper we benchmark a set of open-source mixed integer non-linear programming (MINLP) solvers on the OTS problem with AC physics using the pglib set of power system test cases. Results characterizing the performance of the different solvers are reported and discussed.
ACOPF↗
Mathematical Optimization Techniques
The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND.
Bellman, R.↗
Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint
With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.
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A vehicle scheduling algorithm using non-serial discrete dynamic programming with space shuttle applications
Description of the development and operation of a vehicle-scheduling algorithm which has applications to the NASA problem of assigning payloads to space delivery vehicles. The algorithm is based on a discrete, integer-valued, nonserial, dynamic-programming solution to the classical problem of developing resource utilization plans with limited resources. The algorithm places special emphasis on incorporating interpayload (precedence) relationships; maintaining optimal alternate schedule definitions (a unique feature of dynamic programming) in the event of contingencies (namely, resource inventory changes) without problem resolution; and, by using a special information storage technique, reducing the computational complexity of solving realistic problems.
Dupnick, E.↗
Hyperplane decision trees as piecewise linear surrogate models for chemical process design
Recent trends in chemical engineering research point towards an increasing reliance on data-driven modeling approaches. Neural networks, for instance, have proven to be accurate when data is plentiful and high-dimensional, but in many cases, they require computationally-intensive training procedures. Here, in this work, we describe hyperplane decision trees (HT) as a highly expressive and low-compute machine learning model architecture. These models are locally linear and have linear decision boundaries, resulting in a piecewise linear model of the data. This property allows them to be converted into mixed-integer linear constraints which can be globally optimized. Our open-source PyTorch implementation of this method is a fast, flexible, and accessible way to build accurate piecewise linear models of data.
Decision trees↗
Endogenous Interface Pricing for Consistent Transmission–Distribution Co-Optimization With Discrete Distribution Controls
This paper proposes an endogenous interface pricing model for day-ahead transmission–distribution co-optimization that co-determines the interface locational marginal price (LMP) and the transmission–distribution exchange, ensuring price–dispatch consistency while optimally scheduling discrete distribution controls. The formulation couples a DC optimal power flow (OPF) with a branch-flow AC OPF that schedules distributed energy resources (DERs), tap-changer settings, capacitor banks (CBs), and multi-period energy storage systems (ESSs) under feeder voltage and current limits, and is solved as a mixed-integer second-order cone program (MISOCP). In a T14–D33 system, coordinated device scheduling recovers about 90% of the distribution-to-transmission export achievable in a reference case that ignores distribution network (DN) limits, while satisfying a 1.05 p.u. voltage upper bound. In a T39–D34/D37/D123 system, a sequential decoupled benchmark produces interface LMP distortions up to 12.5% and a 7.28% mismatch in net export energy, whereas the proposed model removes these distortions and the associated settlement mismatches. Second-order cone (SOC) relaxation gaps remain below $10^{-3}$ in all cases.
Noh, Seung-Gil↗
Optimal reconfiguration strategy for a degradable multimodule computing system
The present quantitative approach to the problem of reconfiguring a degradable multimode system assigns some modules to computation and arranges others for reliability. By using expected total reward as the optimal criterion, there emerges an active reconfiguration strategy based not only on the occurrence of failure but the progression of the given mission. This reconfiguration strategy requires specification of the times at which the system should undergo reconfiguration, and the configurations to which the system should change. The optimal reconfiguration problem is converted to integer nonlinear knapsack and fractional programming problems.
Lee, Yann-Hang↗
Generalized Symbolic Execution for Model Checking and Testing
Modern software systems, which often are concurrent and manipulate complex data structures must be extremely reliable. We present a novel framework based on symbolic execution, for automated checking of such systems. We provide a two-fold generalization of traditional symbolic execution based approaches: one, we define a program instrumentation, which enables standard model checkers to perform symbolic execution; two, we give a novel symbolic execution algorithm that handles dynamically allocated structures (e.g., lists and trees), method preconditions (e.g., acyclicity of lists), data (e.g., integers and strings) and concurrency. The program instrumentation enables a model checker to automatically explore program heap configurations (using a systematic treatment of aliasing) and manipulate logical formulae on program data values (using a decision procedure). We illustrate two applications of our framework: checking correctness of multi-threaded programs that take inputs from unbounded domains with complex structure and generation of non-isomorphic test inputs that satisfy a testing criterion. Our implementation for Java uses the Java PathFinder model checker.
Khurshid, Sarfraz↗
Optimization of orbital assignment and specification of service areas in satellite communications
The mathematical nature of the orbital and frequency assignment problem for communications satellites is explored, and it is shown that choosing the correct permutations of the orbit locations and frequency assignments is an important step in arriving at values which satisfy the signal-quality requirements. Two methods are proposed to achieve better spectrum/orbit utilization. The first, called the delta S concept, leads to orbital assignment solutions via either mixed-integer or restricted basis entry linear programming techniques; the method guarantees good single-entry carrier-to-interference ratio results. In the second, a basis for specifying service areas is proposed for the Fixed Satellite Service. It is suggested that service areas should be specified according to the communications-demand density in conjunction with the delta S concept in order to enable the system planner to specify more satellites and provide more communications supply.
Wang, Cou-Way↗
Beta distributions: A computer program for probabilities and fractile points
A beta distribution is specified by range parameters a b, and two shape parameters alpha and beta 0. The computer program presented calculates any desired probability and/or fractile point for specified values of a, b, alpha, and beta. This program additionally computes gamma function values for integer and noninteger arguments.
Brownlow, J. D.↗
X10: A FORTRAN direct access data management system
The XIO system is a set of subroutines that provide generalized data management capability for FORTRAN programs using a direct access file. Arrays of integer, real, double precision, and character data may be stored, each logical group of data identified by a unique matrix number. A matrix may be organized and stored as batches to reduce core requirements. Batches may be accessed randomly or sequentially. The file may be checkpointed and retained, allowing for restarts with stored values. The XIO subroutines operate on either IBM 360-370/OS/VS or DEC PDP-11/RSX computing systems.
Roland, D. P.↗
Delivery Ring Spill Characterization and Impulse Study
High-intensity particle physics experiments require uniform beam extraction to prevent instantaneous rate spikes from overwhelming detector systems. By analyzing accelerator parameters and extracted beam dynamics, we directly inform spill regulation systems that make real-time adjustments to minimize non-uniformity. This Department of Energy Visiting Faculty Program project transitioned from characterizing Main Injector half-integer slow extraction for SpinQuest to Delivery Ring third-integer slow extraction for Mu2e. Working alongside the Fast Adaptive Neural Control (FANC) group, we developed an automated pipeline that aligns asynchronous instrument channels, embeds quality metrics, and isolates clean spill populations. Analyzing baseline spills alongside a dedicated quadrupole impulse study allowed us to quantify noise structures while mapping time-varying beam response and transit-delay dynamics. These empirical measurements directly ground digital twin models, supporting FANC’s deployment of real-time, FPGA-based neural network controllers in the Mu2e Spill Regulation System.
Dolen, James William [Purdue U., West Lafayette] (↗
DB90: A Fortran Callable Relational Database Routine for Scientific and Engineering Computer Programs
This report describes a database routine called DB90 which is intended for use with scientific and engineering computer programs. The software is written in the Fortran 90/95 programming language standard with file input and output routines written in the C programming language. These routines should be completely portable to any computing platform and operating system that has Fortran 90/95 and C compilers. DB90 allows a program to supply relation names and up to 5 integer key values to uniquely identify each record of each relation. This permits the user to select records or retrieve data in any desired order.
Wrenn, Gregory A.↗
Interactive Data-Collection And Display Program With Debugging
INFORM program designed to aid assembly language programers of SEL 810B computers in working with scaled-integer applications. INFORM was developed to meet needs of engineers designing real-time digital controls using SEL 810B where time and hardware constraints make use of integer arithmetic and scaled integers necessary. Package includes auxiliary routines that add dynamic data acquisition and high-speed dynamic display to INFORM capabilities.
Cwynar, D. S.↗
An Ada Linear-Algebra Software Package Modeled After HAL/S
New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.
Klumpp, Allan R.↗
A matheuristic for design and dispatch of a utility-connected distributed energy system
Modeling distributed power generation systems often requires complicated mathematical expressions that present challenges for commercial optimization solvers. Here, this paper presents a matheuristic to solve a mixed-integer optimization model that informs decisions regarding the design and dispatch of a utility-connected microgrid. We deploy a genetic algorithm to search the system design space and a linear program to solve the economic dispatch problem. The model is a component of a web tool that requires solutions within a few minutes. Our method yields objective function values within 5% of an exogenously produced optimal in fewer than 30 seconds for 90% of our test cases compared to only 10% of our test cases by a traditional optimization solver in the same amount of time.
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