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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A Bi-Level Formulation And Solution Method For The Integration Of Process Design And Scheduling

Design and operation decisions of manufacturing plants can often be expressed within a hierarchical structure, where optimal decisions at lower operating level provide constraints for the decision raking at a higher decision level. In this work, we are addressing the case of a hierarchical design and scheduling optimization problem. The integration of design and scheduling decisions can play a big role in designing economically profitable plants and improving their operational performance. This problem can be expressed as a bi-level problem, where design related decisions occur at the upper level and operational scheduling decisions at the lower level. Since discrete decisions are involved in both optimization levels, the resulting formulation typically corresponds to bi-level mixed-integer programming problems (B-MIP). The solution of B-MIP problems is very challenging, and typically requires the use of global optimization techniques, with many algorithms not able to guarantee feasibility. To overcome the challenges in solving this class of problems we propose the use of a multi-parametric based algorithm for the solution of bi-level mixed-integer linear and quadratic programming problems, capable of providing the exact and global solution. The main idea of this approach is to treat the lower scheduling problem as a multi-parametric programming problem in which the design decisions are considered as parameters. Here, the resulting parametric solutions can then be substituted into the upper level design problem, which can be solved as a set of single-level deterministic programming problems. Through the developed formulation and algorithm we are able to supply the decision makers with the exact solution of the integrated design and scheduling problem.

42 ENGINEERING↗
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↗
NASA NTRS1987

Mathematical programming formulations for satellite synthesis

The problem of satellite synthesis can be described as optimally allotting locations and sometimes frequencies and polarizations, to communication satellites so that interference from unwanted satellite signals does not exceed a specified threshold. In this report, mathematical programming models and optimization methods are used to solve satellite synthesis problems. A nonlinear programming formulation which is solved using Zoutendijk's method and a gradient search method is described. Nine mixed integer programming models are considered. Results of computer runs with these nine models and five geographically compatible scenarios are presented and evaluated. A heuristic solution procedure is also used to solve two of the models studied. Heuristic solutions to three large synthesis problems are presented. The results of our analysis show that the heuristic performs very well, both in terms of solution quality and solution time, on the two models to which it was applied. It is concluded that the heuristic procedure is the best of the methods considered for solving satellite synthesis problems.

Bhasin, Puneet↗
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.↗
NASA NTRS1986

Parallel scheduling of recursively defined arrays

A new method of automatic generation of concurrent programs which constructs arrays defined by sets of recursive equations is described. It is assumed that the time of computation of an array element is a linear combination of its indices, and integer programming is used to seek a succession of hyperplanes along which array elements can be computed concurrently. The method can be used to schedule equations involving variable length dependency vectors and mutually recursive arrays. Portions of the work reported here have been implemented in the PS automatic program generation system.

Myers, T. J.↗
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↗
NASA NTRS1992

Stacking sequence optimization of simply supported laminates with stability and strain constraints

An integer programming formulation for the design of symmetric and balanced rectangular composite laminates with simply supported boundary conditions subject to buckling and strain constraints is presented. The design variables that define the stacking sequence of the laminate are ply-identity zero-one integers. The buckling constraint is linear in terms of the ply-identity design variables, but strains are nonlinear functions of these variables. A linear approximation is developed for the strain constraints so that the problem can be solved by sequential linearization using the branch and bound algorithm. Examples of graphite-epoxy plates under biaxial compression are presented. Optimum stacking sequences obtained using the linear approximation are compared with global optimum designs obtained using a genetic search procedure.

Nagendra, S.↗
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↗