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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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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Novel Geometric Operations for Linear Programming

This report summarizes the work performed under the project "Linear Programming in Strongly Polynomial Time." Linear programming (LP) is a classic combinatorial optimization problem heavily used directly and as an enabling subroutine in integer programming (IP). Specifically IP is the same as LP except that some solution variables must take integer values (e.g. to represent yes/no decisions). Together LP and IP have many applications in resource allocation including general logistics, and infrastructure design and vulnerability analysis. The project was motivated by the PI's recent success developing methods to efficiently sample Voronoi vertices (essentially finding nearest neighbors in high-dimensional point sets) in arbitrary dimension. His method seems applicable to exploring the high-dimensional convex feasible space of an LP problem. Although the project did not provably find a strongly-polynomial algorithm, it explored multiple algorithm classes. The new medial simplex algorithms may still lead to solvers with improved provable complexity. We describe medial simplex algorithms and some relevant structural/complexity results. We also designed a novel parallel LP algorithm based on our geometric insights and implemented it in the Spoke-LP code. A major part of the computational step is many independent vector dot products. Our parallel algorithm distributes the problem constraints across processors. Current commercial and high-quality free LP solvers require all problem details to fit onto a single processor or multicore. Our new algorithm might enable the solution of problems too large for any current LP solvers. We describe our new algorithm, give preliminary proof-of-concept experiments, and describe a new generator for arbitrarily large LP instances.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

SPAROW: Stochastic Programming and Related Optimization Workflows

SAND2026-16703O SPAROW: Stochastic Programming and Related Optimization Workflows is a Python library tool that facilitates the development and solution of stochastic programming problems. It provides a user-friendly class structure for defining stochastic programs through scenario-based representations of uncertainties. SPAROW incorporates multiple optimization strategies, including integer programming with all scenarios, progressive hedging, Benders decomposition, and Snoglode, a novel technique developed by Carnegie Mellon University. It also features interfaces to external solvers and functions that are commonly used in analysis workflows, making it applicable to a wide range of scientific and engineering design challenges, particularly in power grid planning. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Hart, William [Sandia National Lab. (SNL-NM), Albu↗
DOE OSTI2024

A Mixed Integer Linear Programming-basedDistributed Energy Management for Three-phaseUnbalanced Active Distribution Network

A mixed integer linear programming (MILP)–baseddistributed energy management for three-phase unbalancedactive distribution network is proposed. Modern distributionnetworks have becoming more and more active with increasingdeployment of microgrids, distributed energy resources (DERs)as well as controllable loads. Considering various ownership andcontrol models of microgrids, DERs and controllable loads, adistributed energy management was formulated using the alternatingdirection method of multipliers (ADMM) algorithm. ByADMM, the distribution management system (DMS) and theseactive components are coordinated through price signals, whichare adjusted according to the generation-load mismatch per nodeper phase. To enable resolution of the ADMM-based distributedoptimization using more accessible and popular MILP solver,different linearization techniques were proposed to linearize theaugmented Lagrangian terms and other nonlinear terms. Resultsof case studies on a three-phase active distribution network withthree microgrids and several DERs and controllable loads validatedthe effectiveness of proposed MILP-based distributed energymanagement. In addition, the capability of proposed method inmitigating phase power unbalance has been demonstrated.

Liu, Guodong↗
DOE OSTI2021

Optimizing design and dispatch of a renewable energy system

Renewable energy technologies are becoming increasingly important due to their cost-competitiveness, and because of enhanced climate concerns. We demonstrate the capabilities of an integer-programming optimization model that minimizes capital (investment) and operational costs, and utility charges, while adhering to system sizing constraints, demand requirements, and interoperability characteristics of the systems chosen. Furthermore, the model recommends an optimally sized mix of renewable energy, conventional generation, and energy storage technologies, while simultaneously optimizing the corresponding dispatch strategy. Our case studies explore several venues, i.e., a small campus and a local hospital, with complex utility rate tariffs, multi-technology integration opportunities, and incentives for renewable power production. Using an optimization model, versus applying rules of thumb, can produce millions of dollars in savings over a 25-year time horizon and result in thousands of kilowatts of installed renewable energy.

25 ENERGY STORAGE↗
DOE OSTI2014

SU-F-BRD-08: Guaranteed Epsilon-Optimal Treatment Plans with Minimum Number of Beams for SBRT Using RayStation

Purpose: To efficiently find quality-guaranteed treatment plans with the minimum number of beams for stereotactic body radiation therapy using RayStation. Methods: For a pre-specified pool of candidate beams we use RayStation (a treatment planning software for clinical use) to identify the deliverable plan which uses all the beams with the minimum dose to organs at risk (OARs) and dose to the tumor and other structures in specified ranges. Then use the dose matrix information for the generated apertures from RayStation to solve a linear program to find the ideal plan with the same objective and constraints allowing use of all beams. Finally we solve a mixed integer programming formulation of the beam angle optimization problem (BAO) with the objective of minimizing the number of beams while remaining in a predetermined epsilon-optimality of the ideal plan with respect to the dose to OARs. Since the treatment plan optimization is a multicriteria optimization problem, the planner can exploit the multicriteria optimization capability of RayStation to navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus OARs sparing, and then use the proposed technique to reduce the number of beams while guaranteeing quality. For the numerical experiments two liver cases and one lung case with 33 non-coplanar beams are considered. Results: The ideal plan uses an impractically large number of beams. The proposed technique reduces the number of beams to the range of practical application (5 to 9 beams) while remaining in the epsilon-optimal range of 1% to 5% optimality gap. Conclusion: The proposed method can be integrated into a general algorithm for fast navigation of the ideal dose distribution Pareto surface and finding the treatment plan with the minimum number of beams, which corresponds to the delivery time, in epsilon-optimality range of the desired ideal plan. The project was supported by the Federal Share of program income earned by Massachusetts General Hospital on C06 CA059267, Proton Therapy Research and Treatment Center and partially by RaySearch Laboratories.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2023

Mathematical Programming Models for Shale Oil & Gas Development: A Review and Perspective

Here, in this paper, we provide a comprehensive review of mathematical programming models for shale oil & gas development, and we offer a perspective on outstanding research opportunities. We distinguish contributions in five major topic areas, namely: (1) development planning, (2) water management, (3) production optimization, (4) supplies, gathering & processing, and (5) life cycle analysis & sustainability. We highlight how various types of mathematical programming models (i.e., linear programs, nonlinear programs, mixed-integer linear programs, mixed-integer nonlinear programs) have been proposed primarily by the Process Systems Engineering community to address the respective decision-making problems, and we highlight instances of successful deployment in industry. Finally, based on a critical assessment of the existing body of work, we identify opportunities for future research across the major topic areas.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

INDDGO: Integrated Network Decomposition & Dynamic programming for Graph Optimization

It is well-known that dynamic programming algorithms can utilize tree decompositions to provide a way to solve some NP -hard problems on graphs where the complexity is polynomial in the number of nodes and edges in the graph, but exponential in the width of the underlying tree decomposition. However, there has been relatively little computational work done to determine the practical utility of such dynamic programming algorithms. We have developed software to construct tree decompositions using various heuristics and have created a fast, memory-efficient dynamic programming implementation for solving maximum weighted independent set. We describe our software and the algorithms we have implemented, focusing on memory saving techniques for the dynamic programming. We compare the running time and memory usage of our implementation with other techniques for solving maximum weighted independent set, including a commercial integer programming solver and a semi-definite programming solver. Our results indicate that it is possible to solve some instances where the underlying decomposition has width much larger than suggested by the literature. For certain types of problems, our dynamic programming code runs several times faster than these other methods.

Groër, Christopher S.↗
DOE OSTI2011

Final Report---Optimization Under Nonconvexity and Uncertainty: Algorithms and Software

the goal of this work was to develop new algorithmic techniques for solving large-scale numerical optimization problems, focusing on problems classes that have proven to be among the most challenging for practitioners: those involving uncertainty and those involving nonconvexity. This research advanced the state-of-the-art in solving mixed integer linear programs containing symmetry, mixed integer nonlinear programs, and stochastic optimization problems. The focus of the work done in the continuation was on Mixed Integer Nonlinear Programs (MINLP)s and Mixed Integer Linear Programs (MILP)s, especially those containing a great deal of symmetry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A shared-mobility-based framework for evacuation planning and operations under forecast uncertainty

To meet evacuation needs from carless populations who need personalized assistance to evacuate safely, in this article we propose a ridesharing-based evacuation program that recruits volunteer drivers before a disaster strikes, and then matches volunteer drivers with evacuees once demand is realized. Here we optimize resource planning and evacuation operations under uncertain spatiotemporal demand, and construct a two-stage stochastic mixed-integer program to ensure high demand fulfillment rates. We consider three formulations to improve the number of evacuees served, by minimizing an expected penalty cost, imposing a probabilistic constraint, and enforcing a constraint on the conditional value at risk of the total number of unserved evacuees, respectively. We discuss the benefits and disadvantages of the different risk measures used in the three formulations, given certain carless population sizes and the variety of evacuation modes available. We also develop a heuristic approach to provide quick, dynamic and conservative solutions. We demonstrate the performance of our approaches using five different networks of varying sizes based on regions of Charleston County, South Carolina, an area that experienced a mandatory evacuation order during Hurricane Florence, and utilize real demographic data and hourly traffic count data to estimate the demand distribution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

A scalable stochastic programming approach for the design of flexible systems

We study the problem of designing systems in order to minimize cost while meeting a given flexibility target. Flexibility is attained by enforcing a joint chance constraint, which ensures that the system will exhibit feasible operation with a given target probability level. Unfortunately, joint chance constraints are complicated mathematical objects that often need to be reformulated using mixed-integer programming (MIP) techniques. In this work, we cast the design problem as a conflict resolution problem that seeks to minimize cost while maximizing flexibility. We propose a purely continuous relaxation of this problem that provides a significantly more scalable approach relative to MIP methods and show that the formulation delivers solutions that closely approximate the Pareto set of the original joint chance-constrained problem.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Model Predictive Control of Discrete-Continuous Energy Systems via Generalized Disjunctive Programming

Generalized Disjunctive Programming (GDP) provides an alternative framework to model optimization problems with both discrete and continuous variables. The key idea behind GDP involves the use of logical disjunctions to represent discrete decisions in the continuous space, and logical propositions to denote algebraic constraints in the discrete space. Compared to traditional mixed-integer programming (MIP), the inherent logic structure in GDP yields tighter relaxations that are exploited by global branch and bound algorithms to improve solution quality. In this paper, we present a general GDP model for optimal control of hybrid systems that exhibit both discrete and continuous dynamics. Specifically, we use GDP to formulate a model predictive control (MPC) model for piecewise-affine systems with implicit switching logic. As an example, the GDP-based MPC approach is used as a supervisory control to improve energy efficiency in residential buildings with binary on/off, relay-based thermostats. A simulation study is used to demonstrate the validity of the proposed approach, and the improved solution quality compared to existing MIPbased control approaches.

Bhattacharya, Arnab↗
DOE OSTI2021

Multi-Period Active Distribution Network Planning Using Multi-Stage Stochastic Programming and Nested Decomposition by SDDIP

This paper presents a multi-period active distribution network planning (ADNP) with distributed generation (DG). The objective of the proposed ADNP is to minimize the total planning cost, subject to both investment and operation constraints. The paper proposes a multi-stage stochastic optimization model to address DG uncertainties over several periods, in which the decisions are made sequentially by only using the present-stage information. A nested decomposition method is proposed which applies the stochastic dual dynamic integer programming (SDDIP) method to address computational intractabilities of the proposed ADNP approach. The presented numerical results and discussions on a 33-bus distribution system and a large-scale 906-bus system verify the effectiveness of the proposed ADNP method and its solution method.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Modeling Road Vulnerability to Snow Using Mixed Integer Optimization

As the number and severity of snowfall events continue to grow, the need to intelligently direct road maintenance during these snowfall events will also grow. In several locations, local governments lack the resources to completely treat all roadways during snow events. Furthermore, some governments utilize only traffic data to determine which roads should be treated. As a result, many schools, businesses, and government offices must be unnecessarily closed, which directly impacts the social, educational, and economic well-being of citizens and institutions. In this work, we propose a mixed integer programming formulation to optimally allocate resources to manage snowfall on roads using meteorological, geographical, and environmental parameters. Additionally, we evaluate the impacts of an increase in budget for winter road maintenance on snow control resources.

Mixed integer optimization↗
DOE OSTI2019

Stochastic Optimization for Grid Resilience. FY18 Final Technical Report

The optimal restoration problem lies at the foundation of the evaluation and improvement of resilience in power systems. In this report we present a scalable decomposition algorithm for solving this problem for realistic power systems. The algorithm has been developed in three major research threads, corresponding to the chapters in the present report. Chapter 1 studies mixed-integer programming (MIP) formulations for the requirement that each electrical island that appears after a recon guration must have at least one energized generator. We provide three alternative MIP formulations for this restriction, show their equivalence, and prove that two of them are stronger in terms of their linear programming relaxation than the formulation most commonly used in the power systems literature. Since the time to solve MIPs can vary signi cantly between equivalent formulations, we also present computational experiments on IEEE test systems for the Intentional Controlled Islanding (ICI) and the Black Start Allocation (BSA) problems. We observe that a polynomially separable, exponential in size, strong formulation yields the best performance for the BSA problem and exhibits a comparable performance to a linear in size, weak formulation for the ICI problem. Chapter 2 presents a methodology to generate mixed-integer linear approximations of the AC power ow equations governing lines, transformers (including tap regulators and phase shifters), shunt and series compensators, and consumption responsive to voltage. Our approximations are capable of capturing limitations for power grids under abnormal or uncommon operating conditions where common assumptions used in power ow relaxations may not hold. Particularly, the approximation captures overvoltages under almost no load, which is a major concern when energizing lines after a blackout. The method constructs piecewise linear approximations of the non-linear power ow equations by minimizing the squared approximation error over a subset of the feasible domain. We test the method using a realistic database for the Chilean system (1548 buses, 1114 lines, 564 transformers). The resulting approximations yield root mean square errors in the order of 0.05pu and are successfully applied to solve a transmission switching instance for the Chilean system. Chapter 3 presents our algorithm for optimal restoration. The algorithm works by partitioning the problem into a master problem and a slave problem. The master problem optimizes over energization sequences of generators, buses and branches, for the entire restoration horizon, while respecting the energization requiments studied in Chapter 1. The slave problem veri es that there exist power ow solutions supporting the energization sequences proposed by the master problem, adding cuts to the master if an infeasible sequence is detected.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Allocating limited deicing resources in winter snow events

As the number and severity of snowfall events continue to grow, the need to direct road maintenance intelligently during these snowfall events will also grow. In several locations, local governments lack the resources to treat all roadways completely during snow events. Furthermore, some governments utilize only traffic data to determine which roads should be treated. As a result, many schools, businesses, and government offices must be unnecessarily closed, which directly impacts the social, educational, and economic well-being of citizens and institutions. In this work, we propose a mixed integer programming (MIP) formulation to allocate resources to manage snowfall on roads using meteorological, geographical, and environmental parameters. Furthermore, given that MIPs often scale poorly with problem size, we also present a constructive heuristic designed for the problem. Finally, we evaluate the impacts of an increase in budget for winter road maintenance on snow control resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Domain Decomposition for Integer Optimal Control with Total Variation Regularization

Total variation integer optimal control problems admit solutions and necessary optimality conditions via geometric variational analysis. In spite of the existence of said solutions, algorithms which solve the discretized objective suffer from high numerical cost associated with the combinatorial nature of integer programming. Hence, such methods are often limited to small and medium-sized problems. We propose a globally convergent, coordinate descent–inspired algorithm that allows tractable subproblem solutions restricted to a partition of the domain. Our decomposition method solves relatively small trust-region subproblems that modify the control variable on a subdomain only. Given nontrivial subdomain overlap, we prove that a global first-order necessary optimality condition is equivalent to a first-order necessary optimality condition per subdomain. We additionally show that a sufficient decrease is achieved on a single subdomain by way of a trust-region subproblem solver using geometric measure–theoretic arguments, which we integrate with a greedy patch selection to prove convergence of our algorithm. In conclusion, we demonstrate the practicality of our algorithm on a benchmark large-scale, PDE-constrained integer optimal control problem and find that our method is faster than the state of the art.

domain decomposition↗
DOE OSTI2012

Model Based Optimal Sensor Network Design for Condition Monitoring in an IGCC Plant

This report summarizes the achievements and final results of this program. The objective of this program is to develop a general model-based sensor network design methodology and tools to address key issues in the design of an optimal sensor network configuration: the type, location and number of sensors used in a network, for online condition monitoring. In particular, the focus in this work is to develop software tools for optimal sensor placement (OSP) and use these tools to design optimal sensor network configuration for online condition monitoring of gasifier refractory wear and radiant syngas cooler (RSC) fouling. The methodology developed will be applicable to sensing system design for online condition monitoring for broad range of applications. The overall approach consists of (i) defining condition monitoring requirement in terms of OSP and mapping these requirements in mathematical terms for OSP algorithm, (ii) analyzing trade-off of alternate OSP algorithms, down selecting the most relevant ones and developing them for IGCC applications (iii) enhancing the gasifier and RSC models as required by OSP algorithms, (iv) applying the developed OSP algorithm to design the optimal sensor network required for the condition monitoring of an IGCC gasifier refractory and RSC fouling. Two key requirements for OSP for condition monitoring are desired precision for the monitoring variables (e.g. refractory wear) and reliability of the proposed sensor network in the presence of expected sensor failures. The OSP problem is naturally posed within a Kalman filtering approach as an integer programming problem where the key requirements of precision and reliability are imposed as constraints. The optimization is performed over the overall network cost. Based on extensive literature survey two formulations were identified as being relevant to OSP for condition monitoring; one based on LMI formulation and the other being standard INLP formulation. Various algorithms to solve these two formulations were developed and validated. For a given OSP problem the computation efficiency largely depends on the “size” of the problem. Initially a simplified 1-D gasifier model assuming axial and azimuthal symmetry was used to test out various OSP algorithms. Finally these algorithms were used to design the optimal sensor network for condition monitoring of IGCC gasifier refractory wear and RSC fouling. The sensors type and locations obtained as solution to the OSP problem were validated using model based sensing approach. The OSP algorithm has been developed in a modular form and has been packaged as a software tool for OSP design where a designer can explore various OSP design algorithm is a user friendly way. The OSP software tool is implemented in Matlab/Simulink© in-house. The tool also uses few optimization routines that are freely available on World Wide Web. In addition a modular Extended Kalman Filter (EKF) block has also been developed in Matlab/Simulink© which can be utilized for model based sensing of important process variables that are not directly measured through combining the online sensors with model based estimation once the hardware sensor and their locations has been finalized. The OSP algorithm details and the results of applying these algorithms to obtain optimal sensor location for condition monitoring of gasifier refractory wear and RSC fouling profile are summarized in this final report.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2015

A Parallel Computing Framework for Finding the Supported Solutions to a Biobjective Network Optimization Problem

Abstract Solving multi‐objective combinatorial optimization problems can quickly become computationally challenging when applied to large networks generated from big data. Present‐day first‐rate Mixed Integer Programming (MIP) solvers have parallelism built‐in to take advantage of multicore architectures; but specialized network optimization algorithms that can often solve graph problems more efficiently than a general MIP solver are typically programmed serially. Thus, these network algorithm implementations do not take full advantage of modern multicore computer capabilities. Many parallel computing languages include a fork/join framework into their concurrency packages that allow for simple conversion of recursive serial algorithms to operate in parallel without having to use complicated low‐level message‐passing interfaces. Fork/join is particularly well suited to divide and conquer algorithms such as Non‐Inferior Set Estimation (NISE) method for computing the supported Pareto front of a multi‐objective optimization problem. This work develops a simple general parallel NISE (pNISE) implementation using the Java 7 concurrency tools, and then offers results from a specific implementation of solving a bi‐objective shortest path problem. The results indicate that this method is capable of sizeable speed‐ups on both small‐scale personal computers as well as large‐scale shared memory supercomputers. Finally, other network problems suitable to this method are discussed, including multi‐objective variants of the minimum spanning tree problem, transportation problem, assignment problem, maximum flow problem, and the minimum‐cost flow problem. Copyright © 2015 John Wiley & Sons, Ltd.

Medrano, Fernando Antonio↗