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Results for “Mixed-integer optimization”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A decomposition-based design optimization method with applications

A two-level design optimization metholology is described. A progress report of its application to Printed Wiring Board (PWB) assembly examples is given. The design of PWB assemblies is a complex task which is generally conducted as a sequential process. Individual PWBs are usually designed first, followed by the composition of the PWBs into an assembly. As a result, optimizing design considerations such as assembly reliability cannot be accomplished. This study showed that a two-level decomposition method can be employed to optimize for reliability at both the PWB- and the assembly-level in a coupled manner. The two-level decomposition method also resolved the mixed-integer nonlinear programming nature of the problem rather easily.

Azarm, Shapour↗
NASA NTRSDate not supplied

Mixed Integer Linear Programming in Planning

This project, Activity Planning with Resources for the Exploration of Space (APRES), uses a mixed-integer linear program (MILP) to solve planning problems. This work enables APRES to interpret a model file and output a solution with improved human readability. A plan model is optimized using a MILP solver and the best solution is taken. Once a plan is generated, it is parsed allowing it to retain only desired information and modified for swift human readability.

Christina Erwin↗
DOE OSTI2026

Optimal Operation of Residential High Performance Water Heater for Reduction of Electricity Cost and Peak Demand Through Field Validation

Water heating accounts for about 18% of a typical US home’s energy use. Modern water heaters have enabled control options through APIs, offering customers the opportunity to reduce their energy cost and peak demand by dynamically adjusting settings. A water heater’s capacity to store energy using its storage tank makes it an asset for peak demand reduction and energy cost savings. For this reason, a mixed-integer linear programming model is proposed to minimize the energy cost of a high-performance water heater while also reducing the peak demand of the residential household under a time-of-use utility rate by dynamically changing the water heater’s running mode. Specifically, a multi-objective optimization model is formulated to determine the mode settings of the water heater considering hot water use, time-of-use rate, and peak demand limit of the residential household. The mode settings are associated with different dead bands of water temperature for triggering on/off action of the heat pump and heating element. A 66-gal hybrid electric high performance water heater was used for numerical simulation and practical experiments. The simulation results were well aligned with measurements of practical experiments, validating the soundness of the thermodynamic model. In addition, reductions of energy cost, enabling affordability, and reducing peak demand are demonstrated. The research team also developed a software framework with dashboards to automatically and continuously monitor and manage devices.

Liu, Guodong [ORNL] (ORCID:0000000213498608)↗
DOE OSTI2025

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗
DOE OSTI2025

A New Hybrid Quantum-Classical Algorithm for Solving the Unit Commitment Problem

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.

Aboumrad, Willie [IonQ, Inc]↗
DOE OSTI2026

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↗
DOE OSTI2025

Optimization of a Mixed Fleet of Aerial Drones for Medical Supplies: A Case Study of Blood Delivery Logistics

Aerial drones have emerged as an innovative solution for faster transportation of time-sensitive items (e.g., emergency medical supplies), potentially reducing the transmission of contagious diseases and enhancing healthcare availability through contactless autonomous delivery. We study fleet sizing and efficient scheduling of a mixed fleet of drones for delivering time-sensitive medical items having distinct release and due times to minimize the required fleet size and fleet composition, the required number of additional batteries, and the total energy consumption. We continuously track the remaining battery energy of drones to determine the optimal timing for battery replacement, rather than replacing the battery at each node. Using actual drone flight test data, we employed a machine learning (ML) method to estimate the energy consumption of different drone types during flight segments for different operating parameters. We present a novel mixed-integer programming model to efficiently formulate the problem that integrates the estimated energy consumption functions from ML. We propose a new greedy heuristic (GH) algorithm and a customized genetic algorithm (GA) for solving large-scale instances of this problem faster. Results demonstrate that the GH algorithm is substantially faster than the accelerated CPLEX and the GA, while sacrificing the solution quality by a small amount. Results based on an actual blood sample delivery case study from Pendleton, Oregon, United States, show that using a mixed fleet of drones reduces the total cost and total energy consumption up to 18.18% and 28.7%, respectively, compared to using a homogeneous fleet.

29 - ENERGY PLANNING, POLICY AND ECONOMY↗
DOE OSTI2025

Strategic Placement and Sizing of Distributed Generation for Resilience Enhancement of Distribution Grids With Microgrid Formation

The rise in frequency and severity of extreme weather events highlights the need for resilient power distribution networks. Microgrids can help improve the resilience of distribution grids by providing continuous power supply using local distribution generation (DG) when the distribution grid fails. In this paper, we propose an approach for optimal placement and sizing of DG to form multiple microgrids throughout the distribution network by restoration actions such as switching operations in case of distribution grid outages caused by extreme weather events. Considering the randomness of damaged distribution lines, the DG placement and sizing problem is formulated as a two-stage stochastic mixed-integer program, with the first stage determining the placement and size of DG, and the second stage focusing on minimizing the amount of load shedding through network restoration and microgrid formations for each scenario. Due to the large number of scenarios, the sample average approximation (SAA) method is employed to solve the problem. The results of case studies on a modified IEEE 33 bus distribution grid demonstrate the effectiveness of the proposed DG placement and sizing strategy in improving the resilience of distribution grids by allowing the formation of multiple microgrids. In addition, the robustness and accuracy of the SAA method are validated through various case studies.

Distributed generation planning↗
NASA NTRS2011

A Simulation Based Approach to Optimize Berth Throughput Under Uncertainty at Marine Container Terminals

Berth scheduling is a critical function at marine container terminals and determining the best berth schedule depends on several factors including the type and function of the port, size of the port, location, nearby competition, and type of contractual agreement between the terminal and the carriers. In this paper we formulate the berth scheduling problem as a bi-objective mixed-integer problem with the objective to maximize customer satisfaction and reliability of the berth schedule under the assumption that vessel handling times are stochastic parameters following a discrete and known probability distribution. A combination of an exact algorithm, a Genetic Algorithms based heuristic and a simulation post-Pareto analysis is proposed as the solution approach to the resulting problem. Based on a number of experiments it is concluded that the proposed berth scheduling policy outperforms the berth scheduling policy where reliability is not considered.

Golias, Mihalis M.↗
DOE OSTI2024

Multi-parametric analysis for mixed integer linear programming: An application to transmission upgrade and congestion management

Upgrading the capacity of existing transmission lines is essential for meeting the growing energy demands, facilitating the integration of renewable energy, and ensuring the security of the transmission system. This study focuses on the selection of lines whose capacities and by how much should be expanded from the perspective of the Independent System Operators (ISOs) to minimize the total system cost. We employ advanced multi-parametric programming and an enhanced branch-and-bound algorithm to address complex mixed-integer linear programming (MILP) problems, considering multi-period time constraints and physical limitations of generators and transmission lines. To characterize the various decisions in transmission expansion, we model the increased capacity of existing lines as parameters within a specified range. This study first relaxes the binary variables to continuous variables and applies the Lagrange method and Karush-Kuhn-Tucker (KKT) conditions to obtain optimal solutions and identify critical regions associated with active and inactive constraints. Moreover, we extend the traditional branch-and-bound (B&B) method by determining the problem’s upper and lower bounds at each node of the B&B decision tree, helping to manage computational challenges in large-scale MILP problems. Here, we compare the difference between the upper and lower bounds to obtain an approximate optimal solution within the decision-makers’ tolerable error range. In addition, the first derivative of the objective function on the parameters of each line is used to inform the selection of lines for easing congestion and maximizing social welfare. Finally, the capacity upgrades are selected by weighing the reductions in system costs against the expense of upgrading line capacities. The findings are supported by numerical simulations and provide transmission-line planners with decision-making guidance.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1987

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↗
DOE OSTI2025

IM3 Projected U.S. Western Interconnection Grid Stress Dataset

This dataset provides projected grid stress and reliability results (including all model inputs and outputs from GO WEST and TEP) for Integrated Multisector, Multiscale Modeling (IM3) Phase 2 simulations across eight different scenarios for the U.S. Western Interconnection through 2055. The scenarios include combinations of two Shared Socioeconomic Pathways (SSP3 and SSP5) with four high-resolution climate projections specific to the United States from a set of Thermodynamic Global Warming (TGW) simulations. These climate projections include "hotter" and "cooler" variants for two Representative Concentration Pathways (RCP4.5 and RCP8.5). The resulting eight simulations are: rcp45cooler_ssp3 rcp45cooler_ssp5 rcp45hotter_ssp3 rcp45hotter_ssp5 rcp85cooler_ssp3 rcp85cooler_ssp5 rcp85hotter_ssp3 rcp85hotter_ssp5 GO WEST is an open-source power grid modeling framework for the U.S. Western Interconnection, which allows users to tailor the model depending on their research study and science questions. It covers 28 balancing authorities (BAs) and 12 states in U.S. Western Interconnection. GO WEST allows users to select different number of nodes and come up with a simplified network by utilizing 10,000 nodal topology of the U.S. Western Interconnection (ACTIVSg10k). Users can select different number of nodes, mathematical formulations (linear programming vs. mixed-integer linear programming), transmission line limit scaling factors, and hurdle rate scaling factors. GO WEST offers a unit commitment and economic dispatch (UC/ED) module to simulate grid operations on an hourly scale. In this sense, users can calibrate and validate their model versions by comparing model outputs to historical datasets. TEP is an open-source transmission capacity expansion model, built on the GO WEST framework. It utilizes linear programming to optimize transmission capacity addition investment on existing lines within the GO WEST framework. The TEP model only increases the thermal capacity of existing transmission lines and does not add new lines to the system, which leaves the topology preserved. In order to use TEP model, users need to create scenarios with the GO WEST framework. Please refer to README file for a detailed description of the dataset including individual files and references.

Capacity Expansion Model↗
DOE OSTI2025

Optimal Economic Dispatch and Load-Following Strategies for Nuclear Integrated Energy Systems

The need for distributed and adaptable energy resources that can handle the growing unpredictability in both supply and demand is rising as the power system continues to modernize. In order to satisfy those needs and maintain grid resilience, nuclear power plants can dynamically control their output, despite typically being used as baseload generators. By incorporating energy storage and renewable energy sources, nuclear integrated energy systems are designed to satisfy the electrical and thermal demands of different end-user applications while ensuring flexible power operation. These systems generate revenue by participating in both wholesale and ancillary services electricity markets, as well as commodity markets for various byproducts generated from coupled industrial processes. This study addresses the economic dispatch efficiency of a tightly coupled nuclear integrated energy system comprising a gigawatt-scale light water reactor, commercialized in the U.S., a high-temperature steam electrolysis unit, a district heating network, and specified electrical loads. To demonstrate the nuclear power plant’s flexibility within the day-ahead unit commitment and economic dispatch framework, while maintaining equilibrium even during periods of refueling outages, this paper develops a mixed-integer linear programming framework that models the subsystems and components of its nuclear steam supply system. A systematic comparative analysis of flexible versus baseload nuclear power plant operation under varying levels of renewable energy integration indicates that flexible operation enhances system profitability by more than 18% while also increasing energy storage utilization, improving reactor responsiveness to load fluctuations, and allowing for greater participation across numerous electricity markets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS2017

Efficient Trajectory Options Allocation for the Collaborative Trajectory Options Program

The Collaborative Trajectory Options Program (CTOP) is a Traffic Management Initiative (TMI) intended to control the air traffic flow rates at multiple specified Flow Constrained Areas (FCAs), where demand exceeds capacity. CTOP allows flight operators to submit the desired Trajectory Options Set (TOS) for each affected flight with associated Relative Trajectory Cost (RTC) for each option. CTOP then creates a feasible schedule that complies with capacity constraints by assigning affected flights with routes and departure delays in such a way as to minimize the total cost while maintaining equity across flight operators. The current version of CTOP implements a Ration-by-Schedule (RBS) scheme, which assigns the best available options to flights based on a First-Scheduled-First-Served heuristic. In the present study, an alternative flight scheduling approach is developed based on linear optimization. Results suggest that such an approach can significantly reduce flight delays, in the deterministic case, while maintaining equity as defined using a Max-Min fairness scheme.

Traffic Management Initiative (TMI)↗
NASA NTRS2012

Efficient Computation of Separation-Compliant Speed Advisories for Air Traffic Arriving in Terminal Airspace

A class of problems in air traffic management asks for a scheduling algorithm that supplies the air traffic services authority not only with a schedule of arrivals and departures, but also with speed advisories. Since advisories must be finite, a scheduling algorithm must ultimately produce a finite data set, hence must either start with a purely discrete model or involve a discretization of a continuous one. The former choice, often preferred for intuitive clarity, naturally leads to mixed-integer programs, hindering proofs of correctness and computational cost bounds (crucial for real-time operations). In this paper, a hybrid control system is used to model air traffic scheduling, capturing both the discrete and continuous aspects. This framework is applied to a class of problems, called the Fully Routed Nominal Problem. We prove a number of geometric results on feasible schedules and use these results to formulate an algorithm that attempts to compute a collective speed advisory, effectively finite, and has computational cost polynomial in the number of aircraft. This work is a first step toward optimization and models refined with more realistic detail.

Sadovsky, Alexander V.↗
NASA NTRS1981

An optimization model for energy generation and distribution in a dynamic facility

An analytical model is described using linear programming for the optimum generation and distribution of energy demands among competing energy resources and different economic criteria. The model, which will be used as a general engineering tool in the analysis of the Deep Space Network ground facility, considers several essential decisions for better design and operation. The decisions sought for the particular energy application include: the optimum time to build an assembly of elements, inclusion of a storage medium of some type, and the size or capacity of the elements that will minimize the total life-cycle cost over a given number of years. The model, which is structured in multiple time divisions, employ the decomposition principle for large-size matrices, the branch-and-bound method in mixed-integer programming, and the revised simplex technique for efficient and economic computer use.

Lansing, F. L.↗
DOE OSTI2026

A Decomposition-Based Learn-To-Optimize Approach with Feasibility Layer Assistance for Sub-Hourly Unit Commitment

Sub-hourly unit commitment (UC) with 15-min intervals is gaining significant attention as a way to respond rapidly to the fluctuations in electricity supply and demand introduced by renewable resources. However, the increased temporal resolution and complex inter-temporal dependencies pose substantial computational challenges for traditional optimization methods. To this end, this paper explores a decomposition-based learn-to-optimize approach. Building on recent advances in machine learning, our method revisits the long- overlooked Lagrangian relaxation framework, which is a classical decomposition technique that enables tractable subproblem solving. These smaller subproblems are inherently well-suited for machine learning, as their reduced dimensionality and structural regularity allow predictive models to efficiently learn and generalize solution patterns. We thus propose a generic predictive model, which embeds Gated Recurrent Units (GRUs) and Attention in the encoder-decoder structure, and integrate a rule-based feasibility layer to capture temporal dependencies, reduce training effort, and improve feasibility w.r.t. unit-level constraints. Our method has been validated on the IEEE 118-bus system, demonstrating promising performance in solving sub-hourly UC problems efficiently and feasibly.

97 MATHEMATICS AND COMPUTING↗