Search NASA⌕ Search

SEARCH · Search NASA

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An analysis of physics limited dispatch of nuclear renewable integrated energy systems using deep reinforcement learning and dynamic modeling

Previous approaches to dispatching nuclear integrated energy systems (NIES) have focused on the profitability and flexibility of these systems to operate on energy grids with highly variable pricing. However, due to the complexity involved in modeling and designing these systems, there has been less emphasis on ensuring that these dispatch strategies are physically achievable. It is imperative to develop methods that allow the system to remain within the desired NIES operating conditions and perform this based on realistic limited forecasted information. This research employs next generation artificial intelligence, namely deep reinforcement learning (DRL), and a dynamic system model written in Modelica to find a safe and profitable dispatch strategy for a solar nuclear hybrid design. The DRL agent is shown to find a novel dispatch strategy that manages both power ramping and power levels while respecting operational limits. This DRL-based dispatch is compared to other dispatching strategies including an optimal design solution from mixed integer linear programming (MILP). It is found that incorporating the physics of such a tightly coupled NIES limits the profitability of the MILP-based dispatch strategy. As a result, the MILP solution overestimates the design’s generated revenue. In contrast, DRL significantly reduces the number of breaches of safe operational conditions during energy arbitrage while maintaining profitability. Furthermore, this work paves the way for a more detailed assessment of NIES profitability and could be used to aid operator decisions on future NIES projects.

14 - SOLAR ENERGY↗
DOE OSTI2020

Cost-optimal evaluation of centralized and distributed microgrid topologies considering voltage constraints

Optimal design of hybrid renewable mini-grids requires both economic and power quality considerations. Existing modeling approaches address these considerations via separate or loosely coupled models. Here, we extend REopt—a techno-economic optimization model developed at the National Renewable Energy Laboratory—to consider both within a single model. REopt formulates the design problem as a mixed-integer linear program that solves for a site's optimal technology mix, sizing, and operation to minimize life cycle cost. REopt has traditionally assumed a single node system. In the work presented here, we expand the REopt platform to consider multiple connected nodes with associated voltage constraints. In order to do this, we model power flow using a fixed-point linear approximation method. Additionally, we then use the model to explore design considerations of mini-grids in Sub-Saharan Africa. Specifically, we evaluate under what combinations of transmission line distance and capacity it is technically viable and economically preferable to build multiple isolated mini-grids versus an interconnected, centralized system.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2019

SimCCS: An open-source tool for optimizing CO 2 capture, transport, and storage infrastructure

Commercial-scale carbon capture and storage (CCS) technology will involve deploying infrastructure on a massive and costly scale. This effort will require careful and comprehensive planning to ensure that capture locations, storage sites, and the dedicated CO 2 distribution pipelines are selected in a robust and cost-effective manner. Presented in 2009, SimCCS is an optimization model for integrated system design that enables researchers, stakeholders, and policy makers to design CCS infrastructure networks. SimCCS 2.0 is a complete, ground-up redesign that is now a portable software package, useable and shareable by the CCS research, industrial, policy, and public communities. SimCCS 2.0 integrates multiple new capabilities including a refined optimization model, novel candidate network generation techniques, and optional integration with high-performance computing platforms. Accessing user-provided CO 2 source, sink, and transportation data, SimCCS 2.0 creates candidate transportation routes and formalizes an optimization problem that determines the most cost-effective CCS system design. This optimization problem is further solved either through a high-performance computing interface, or through third-party software on a local desktop computing platform. Finally, SimCCS 2.0 employs an open-access geographic information system framework to enable analysis and visualization capabilities. SimCCS 2.0 is written in Java and is publicly available via GitHub to encourage collaboration, modification, and community development.

42 ENGINEERING↗
DOE OSTI2022

Physics-based modeling and information-theoretic sensor and settings selection for tool wear detection in precision machining

Precision machining of metals is an energy intensive process with applications and impacts across the manufacturing industry. The energy efficiency, product yield, and maintenance of the precision machine require a digital twin that can assist with prognostics and health management. In this report a physics-based model is developed and validated against face milling data, and then used for the timely and precise inference of machining faults that cannot be measured directly. Computer numerical control (CNC) measurements of power and force are used through this physics-based machining model to predict deviations of the outputs of power consumption and cutting forces during normal operation. A model-based fault detection and isolation methodology is applied to determine the optimal (traditional and available) sensor suite and the test settings (admissible input values) that improve the inference of tool wear in face milling. The optimal sensor suite and input test settings are obtained by solving a mixed integer non-linear program that optimizes information-theoretic metrics relevant to the detection and isolation of tool wear from steady-state or transient machining measurements. Dynamic time warping and k—NN classification are then used to validate the robustness of the optimal design for fault detection test design, including the optimal sensor suite.

42 ENGINEERING↗
DOE OSTI2020

Impacts of Integrating Topology Reconfiguration and Vehicle-to-Grid Technologies on Distribution System Operation

Autonomous electric vehicles (AEVs) provide unique opportunities to cope with the uncertainties of distributed energy generation in distribution networks. But the effects are limited by both inherent radial topology and the behaviors of decentralized AEVs. As such, we investigate the potential benefits of dynamic distribution network reconfiguration (DDNR), taking into account AEVs' spatial-temporal availability and their charging demand. We propose a mixed integer programming model to optimally coordinate the charging/discharging of AEVs with DDNR, while satisfying AEVs' original travel plan. Numerical studies based on a test system overlaying the IEEE 33-node test feeder and Sioux Falls transportation network show that DDNR and AEV complement each other, which improves the operation of the distribution system. We also conduct sensitivity analyses on inputs including renewable fluctuation and AEVs penetration level.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2018

VULCON: A System for Vulnerability Prioritization, Mitigation, and Management

Vulnerability remediation is a critical task in operational software and network security management. In this paper, an effective vulnerability management strategy, called VULCON (VULnerability CONtrol), is developed and evaluated. The strategy is based on two fundamental performance metrics: i). Time-to-Vulnerability Remediation (TVR) and; ii). Total Vulnerability Exposure (TVE). VULCON takes as input real vulnerability scan reports, metadata about the discovered vulnerabilities, asset criticality, and personnel resources. VULCON uses a mixed integer multi-objective optimization algorithm to prioritize vulnerabilities for patching, such that the above performance metrics are optimized subject to the given resource constraints. VULCON has been tested on multiple months of real scan data from a Cyber-Security Operations Center (CSOC). Results indicate an overall Total Vulnerability Exposure reduction of 8.97\% when VULCON optimizes a realistic security analyst workforce's effort. Additionally, it is demonstrated that VULCON can determine monthly resources required to maintain a target TVE score. As such, VULCON provides valuable operational guidance for improving vulnerability response processes in CSOCs.

Farris, Katheryn A.↗
DOE OSTI2021

District EnErgy Planner (DEEP) v2

The District EnErgy Planner - DEEP is an Mixed Integer Linear Programming (MILP) optimization software tool to solve district energy system, technology configuration, operation strategies, and energy retail business schemes. DEEP takes user input energy demand on heating, cooling and electricity demand. Energy loss through pipeline is calculated for heating and cooling from central plants. The optimal system configuration to minimize the district energy system life cycle cost or minimize CO2 emission is calculated based on energy balance equations and various constraints. The recent update on DEEP include a feature of waste heat utilization energy balance based optimization to take into accounts of different temperature bands of heat into account to maximize system efficiency. Another feature is to optimize district energy retail by provide optimal pricing scheme for heating, cooling and electricity to end users to incorporate district to grid demand response.

Feng, Wei↗
DOE OSTI2025

Planning Amidst Uncertainty: Identifying Core CCS Infrastructure Robust to Storage Uncertainty

Carbon Capture and Storage (CCS) is a critical technology for reducing anthropogenic CO2 emissions, but its large-scale deployment is complicated by uncertainties in geological storage performance. These uncertainties pose significant financial and operational risks, as underperforming storage sites can lead to costly infrastructure modifications, inefficient pipeline routing, and economic shortfalls. To address this challenge, we propose a novel optimization workflow that is based on mixed-integer linear programming and explicitly integrates probabilistic modeling of storage uncertainty into CCS infrastructure design. This workflow generates multiple infrastructure scenarios by sampling storage capacity distributions, optimally solving each scenario using a mixed-integer linear programming model, and aggregating results into a heatmap to identify core infrastructure components that have a low likelihood of underperforming. A risk index parameter is introduced to balance trade-offs between cost, CO2 processing capacity, and risk of underperformance, allowing stakeholders to quantify and mitigate uncertainty in CCS planning. Applying this workflow to a CCS dataset from the US Department of Energy’s Carbon Utilization and Storage Partnership project reveals key insights into infrastructure resilience. Reducing the risk index from 15% to 0% is observed to lead to an 83.7% reduction in CO2 processing capacity and a 77.1% decrease in project profit, quantifying the trade-off between risk tolerance and project performance. Furthermore, our results highlight critical breakpoints, where small adjustments in the risk index produce disproportionate shifts in infrastructure performance, providing actionable guidance for decision-makers. Unlike prior approaches that aimed to cheaply repair underperforming infrastructure, our workflow constructs robust CCS networks from the ground up, ensuring cost-effective infrastructure under storage uncertainty. These findings demonstrate the practical relevance of incorporating uncertainty-aware optimization into CCS planning, equipping decision-makers with a tool to make informed project planning decisions.

Olson, Daniel↗
DOE OSTI2021

Solar Field Layout and Aimpoint Strategy Optimization

The existing methods that determine heliostat aiming strategies for concentrating solar power (CSP) central receiver plants typically use heuristics and/or are computationally expensive, and they lack flexibility for different desired flux profiles and receiver geometries. Because of the interaction between layout and aimpoint strategy, considering the former without accounting for the latter may yield solutions with superfluous heliostats that cannot be used efficiently without compromising receiver flux constraints. To that end, we develop a software decision tool that uses innovative optimization methods to both optimize aimpoint strategies and improve candidate layouts for the solar collection field of a CSP central receiver plant. A CSP plant’s effectiveness relies on the optical efficiency of the solar field, which may be limited by losses due to (i) the cosine effect, (ii) atmospheric attenuation, (iii) interference (i.e., shading and blocking) between heliostats, (iv) spillage as a result of heliostat positioning and geometry, and (iv) some heliostats’ inability to direct irradiance to the receiver without damage due to excessive thermal flux. The goal of this work is to obtain optimized aiming strategies and improved solar field layouts that reduce capital cost and increase field optical efficiency and utilization, while meeting the power requirements of a given CSP receiver design. We formulate the aimpoint optimization problem as a mixed-integer linear programming model, which we then decompose into submodels that we solve in parallel. The decomposition subdivides the solar field into sections, and aimpoint strategies for each section are obtained independently of the others. To improve existing layouts, we develop a utilization-weighted efficiency metric that we use to relocate heliostats to sections of the solar field with similar efficiency and higher utilization. Finally, to connect our software to high-fidelity flux models, we develop a Python application programming interface for SolarPILOT, a mature software package that characterizes solar field performance and generates the heliostat layouts and flux maps that serve as input to our models.

14 SOLAR ENERGY↗
DOE OSTI2021

Optimal decision trees for categorical data via integer programming

Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. Our approach can also handle numerical features via thresholding. Here we show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

A Model Predictive Control Based Generator Start-Up Optimization Strategy for Restoration With Microgrids as Black-Start Resources

Microgrids (MGs) can operate in an islanded mode and serve as black-start resources for power system restoration (PSR). Here, a model predictive control (MPC) based generator start-up optimization strategy for PSR is proposed utilizing MGs as black-start resources. First, the generator start-up sequence (GSUS) optimization is formulated as a mixed integer linear programming. Then, the uncertainties of MG black-start resources (MBSRs) are modeled by discretizing the probability distribution of the forecast errors, and representative scenarios for MBSRs extracted by formulating the probability mass transportation problem. Third, the generator start-up optimization strategy considering MBSRs is proposed utilizing the MPC technique, in which the optimization objective is to maximize the energy capability of the power systems and minimize the load curtailment of the MGs in each looking-ahead interval. Simulations on the IEEE 118 bus system with MGs and Zhejiang provincial power system in China verify that the introduced strategy for PSR can successfully restore the power system and effectively determine the optimal GSUS.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Optimal Membrane Cascade Design for Critical Mineral Recovery Through Logic-based Superstructure Optimization

Critical minerals and rare earth elements play an important role in our climate change initiatives, particularly in applications related with energy storage. Here, we use discrete optimization approaches to design a process for the recovery of Lithium and Cobalt from battery recycling, through membrane separation. Our contribution involves proposing a Generalized Disjunctive Programming (GDP) model for the optimal design of a multistage diafiltration cascade for Li-Co separation. By solving the resulting nonconvex mixed-integer nonlinear program model to global optimality, we investigated scalability and solution quality variations with changes in the number of stages and elements per stage. Results demonstrate the computational tractability of the nonlinear GDP formulation for design of membrane separation processes while opening the door for decom-position strategies for multicomponent separation cascades. Future work aims to extend the GDP formulation to account for stage installation and explore various decomposition techniques to enhance solution efficiency.

Ovalle, Daniel↗
DOE OSTI2019

Joint Fleet Sizing and Charging System Planning for Autonomous Electric Vehicles

This paper studies the joint fleet sizing and charging system planning problem for a company operating a fleet of autonomous electric vehicles (AEVs) for passenger and goods transportation. Most of the relevant published papers focus on intracity scenarios and adopt heuristic approaches, e.g., agent based simulation, which do not guarantee optimality. In contrast, we propose a mixed integer linear programming model for intercity scenarios. This model incorporates comprehensive considerations of 1) limited AEV driving range; 2) optimal AEV routing and relocating operations; 3) time-varying origin-destination transport demands; and 4) differentiated operation cost structure of passenger and goods transportation. The proposed model can be computational expensive when the scale of the transportation network is large. We then exploit the structure of this program to expedite its solution. Numerical experiments are conducted to validate the proposed method. Our experimental results show that AEVs in passenger and goods transportation have remarkable planning and operation differences. We also demonstrate that intelligent routing and relocating operations, charging system and vehicle parameters, e.g., charging power, battery capacity, driving speed etc., can significantly affect the economic efficiency and the planning results of an AEV fleet.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS2018

A Markov Decision Process Framework for Optimal Airport Reconfiguration

The airport runway configuration is defined as a combination set of runways for arrivals and departures used at a point during operation of the airport. An optimal configuration of these runways depends on a number of factors, including traffic demand, wind magnitude and direction, other adverse weather conditions, and noise restrictions, among others. Based on the current state of these factors and predictions of traffic demand and weather conditions, runway configuration changes are made and coordinated between tower controller, other air traffic control facilities, pilots, and ground personnel. Reconfigurations can be quite disruptive to airport operations; minimizing their frequency and scheduling them well in advance is essential for mitigating some of the added workload for controllers and pilots. Unfortunately, deciding on an appropriate time to change is challenging for human decision makers. Not only do multiple factors need to be evaluated, but the uncertainty in their forecasts must also be considered. Previous optimization methods, such as mixed linear integer programming, have been proposed. Although these methods can reason over a large set of variables, they do not systematically handle the uncertainty associated with weather movement, traffic demands, and other variables. In this work, we introduce a Markov Decision Process (MDP)-based decision making framework which can reason effectively over the inherent uncertainties and make optimal decisions on if/when to change the airport configuration. In a prototype implementation, we present a single runway with three aircraft and utilize knowledge of the forecasted wind speed and direction to determine whether to keep or change the current runway configuration. Our aim through this work is to present a framework for airport reconfiguration which can be scalable to additional aircraft, multiple runways, and various input parameters. This technique will optimize the airport reconfiguration procedure by providing a proactive approach, optimizing not just at the next optimal opportunity for a reconfiguration based on varying atmospheric and traffic conditions in the terminal airspace, but also anticipating future necessary reconfigurations. This will eliminate the inefficiencies of frequent changes currently associated with runway reconfiguration procedures.

runway reconfiguration↗
DOE OSTI2020

Optimization of harvest and logistics for multiple lignocellulosic biomass feedstocks in the northeastern United States

A mixed-integer linear programming model was developed to optimize the multiple biomass feedstock supply chains, including feedstock establishment, harvest, storage, transportation, and preprocessing. The model was applied for analyses of multiple biomass feedstocks at county level for 13 states in the northeastern United States. In the base case with a demand of 180,000 dry Mg/year of biomass, the delivered costs ranged from $\$67.90$ to $\$86.97$ per dry Mg with an average of $\$79.58$ /dry Mg. The biomass delivered costs by county were from $\$67.90$ to 150.81 per dry Mg across the northeastern U.S. Considered the entire study area, the delivered cost averaged $\$85.30$ /dry Mg for forest residues, $\$84.47$ /dry Mg for hybrid willow, $\$99.68$ for switchgrass and $\$97.87$ per dry Mg for Miscanthus. Seventy seven out of 387 counties could be able to deliver biomass at $84 per dry Mg or less a target set by US DOE by 2022. A sensitivity analysis was also conducted to evaluate the effects of feedstock availability, feedstock price, moisture content, procurement radius, and facility demand on the delivered cost. Lastly, our results showed that procurement radius, facility capacity, and forest residue availability were the most sensitive factors affecting the biomass delivered costs.

09 BIOMASS FUELS↗
DOE OSTI2024

A multi-objective optimization model for cropland design considering profit, biodiversity, and ecosystem services

More sustainable agricultural methods are needed to alleviate the decreases in biodiversity and ecosystem services that have occurred because of industrial agriculture. One such method is the inclusion of alternative crops into croplands that can support biodiversity, reduce erosion and chemical runoff, and sequester carbon in the soil. However, the question of where such crops should be planted to balance competing economic and environmental objectives remains open. To this end, we develop a mixed-integer quadratically constrained program to optimize the layout of a cropland considering economic, biodiversity, greenhouse gas emissions, and water quality objectives. We include spatially varying fertilization as a decision variable in addition to crop establishment location. We further include the effect of core area and edges between different crops on biodiversity. To demonstrate the applicability of the model, we apply it to an example field, showing how the optimal cropland design changes as a decision-maker prioritizes different objectives and as edges have different impacts on biodiversity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Microgrid Assisted Design for Remote Areas

In this work, we present a three-stage multiobjective mixed-integer linear programming (MILP) for the optimal expansion planning and operation of isolated multienergy microgrids in remote areas. By selecting the optimal distributed generators (DGs) and energy storage systems (ESSs) mix selection, siting, sizing, and scheduling in the remote microgrid, the proposed model is targeted to minimize the annualized total cost of microgrids while enhancing the performance of the system, i.e., minimizing the voltage deviations and line power loss. To represent the electricity and heat flow between generation resources and various electrical, heating, and cooling loads in the isolated microgrid, linearized power flow, and heat flow constraints are employed in the proposed optimization model. The available capacity of DGs and ESSs are modeled as discrete constants instead of continuous variables for practical purpose. Numerical simulation results on a remote microgrid consisting of DGs, ESSs, and various loads validate the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗