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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

We develop an adaptive, multivariate partitioning algorithm for solving nonconvex, Mixed-Integer Nonlinear Programs (MINLPs) with polynomial functions to global optimality. In particular, we present an iterative algorithm that exploits piecewise, convex relaxation approaches via disjunctive formulations to solve MINLPs that is different than conventional spatial branch-and-bound approaches. The algorithm partitions the domains of variables in an adaptive and non-uniform manner at every iteration to focus on productive areas of the search space. Furthermore, domain reduction techniques based on sequential, optimization-based bound-tightening and piecewise relaxation techniques, as a part of a presolve step, are integrated into the main algorithm. Finally, we demonstrate the effectiveness of the algorithm on well-known benchmark problems (including Pooling and Blending instances) from MINLPLib and compare our algorithm with state-of-the-art global optimization solvers. With our novel approach, we solve several large-scale instances, some of which are not solvable by state-of-the-art solvers. We also succeed in reducing the best known optimality gap for a hard, generalized pooling problem instance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimal operations of a nuclear-based integrated energy system: A mixed integer program approach

A nuclear-based integrated energy system (IES), consisting of multiple carbon-free energy generation and conversion technologies to meet heterogeneous end-use demands, offers a promising approach to decarbonizing the U.S. economy. Operating such an IES is challenging due to its complexity and the diverse end-use demands, such as heating and electricity. This paper aims to address the optimal operation of an IES composed of a small modular reactor (SMR), a steam manifold, a balance of plant (BOP), a high-temperature steam electrolysis (HTSE) system, a district heating (DH) network, and electrical grids. We formulate the system’s operation as a mixed integer linear programming (MILP) problem to maximize net revenues from sales of electricity and hydrogen. To evaluate the efficacy of the proposed model, we conduct a 24-hour simulation considering day-ahead (DA) electricity prices from CAISO and a varying DH demand profile with hourly resolution. The simulation results show that our model effectively optimizes the operation by selling electricity during on-peak periods and purchasing electricity for hydrogen production during off-peak periods, while satisfying operating constraints within the IES.

08 HYDROGEN↗
DOE OSTI2024

Flexible dynamic boundary microgrid operation considering network and load unbalances

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Further, negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Machine Learning with Gradient-Based Optimization of Nuclear Waste Vitrification with Uncertainties and Constraints

Gekko is an optimization suite in Python that solves optimization problems involving mixed-integer, nonlinear, and differential equations. The purpose of this study is to integrate common Machine Learning (ML) algorithms such as Gaussian Process Regression (GPR), support vector regression (SVR), and artificial neural network (ANN) models into Gekko to solve data based optimization problems. Uncertainty quantification (UQ) is used alongside ML for better decision making. These methods include ensemble methods, model-specific methods, conformal predictions, and the delta method. An optimization problem involving nuclear waste vitrification is presented to demonstrate the benefit of ML in this field. ML models are compared against the current partial quadratic mixture (PQM) model in an optimization problem in Gekko. GPR with conformal uncertainty was chosen as the best substitute model as it had a lower mean squared error of 0.0025 compared to 0.018 and more confidently predicted a higher waste loading of 37.5 wt% compared to 34 wt%. The example problem shows that these tools can be used in similar industry settings where easier use and better performance is needed over classical approaches. Future works with these tools include expanding them with other regression models and UQ methods, and exploration into other optimization problems or dynamic control.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Environmental and economic optima of solar home systems design: A combined LCA and LCC approach

Here, we compare the economic and environmental optimal design of Solar Home Systems (SHSs) and explore the role of economic incentives (such as tariffs and technology costs) in approximating the two optima. To achieve that, we present a methodology for the environmental and economic evaluation of grid-connected SHSs: user-scale electric systems involving a photovoltaic (PV) power system and a battery energy storage system. The proposed methodology is based on a mixed integer linear programming (MILP) optimization, life cycle assessment and life cycle costing. This methodological framework is applied to a case study involving a typical SHS installation in Italy. The results of the environmental optimal design brought to the evaluation of a 3.25 kW PV assisted by 8.66 kWh of nickel cobalt manganese batteries, whereas the costs of the SHS are minimized by a small PV system (less than 1 kW). Results underline that the environmental optimal configurations rely on battery technologies, which entails a significant cost compared to the grid connection. In contrast, the economic optimal design solutions is less impactful than the grid mix both from an environmental and economic points of view. Thanks to a reduction of batteries and PV costs, the environmental impact of the economic optimal design is expected to decrease in the future.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2024

A Convexification-Based Outer-Approximation Method for Convex and Nonconvex MINLP

The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the Outer-Approximation method. We propose a refined convexification-based Outer-Approximation method alongside a Branch-and-Bound method for both convex and nonconvex Mixed-Integer Nonlinear Programming problems. These methods have been developed and incorporated into the open-source Mixed-Integer Nonlinear Decomposition Toolbox for Pyomo-MindtPy. Comprehensive benchmark tests were conducted, validating the effectiveness and reliability of our proposed algorithms. These tests highlight the improvements achieved by incorporating convexification and domain reduction techniques into the Outer-Approximation and Branch-and-Bound methods.

Optimization↗
DOE OSTI2023

Incorporation of market signals for the optimal design of post combustion carbon capture systems

Recent studies have shown that fossil generators equipped with post-combustion carbon capture (PCC) systems are needed to reduce the cost of deep decarbonization. Such generators need to be flexible and responsive to grid conditions, particularly in a high variable renewable energy (VRE) environment. In this work, we evaluate the net present value (NPV) of retrofitting an existing natural gas combined cycle (NGCC) unit with a flexible PCC system while incorporating market signals from a high VRE grid. We use our industrial partner’s NGCC configuration as representative of existing NGCC units and Svante’s rapid-temperature swing adsorption (TSA) for PCC. Because of its ability to rapidly startup/shutdown and ramp-up/ramp-down, the chosen capture technology is very attractive for load-following operations. For a given set of market signals, we formulate a two-stage stochastic multi-period optimization problem, under the price-taker assumption, to simultaneously optimize the design of the capture system and operation of the entire plant. Rigorous models for the NGCC unit, PCC system, and compression system are developed using commercial process simulators and validated with either plant or vendor data. For computational tractability, we develop surrogate/reduced-order models for use in the optimization problem. The surrogate model for the NGCC plant is constructed by linearizing the rigorous dynamic model at 75% load, while data-driven nonlinear surrogate models for the capture and compression systems are constructed using simulation data from the rigorous models. The optimization problem, formulated as a mixed integer bilinear program, is implemented in the IDAES® integrated platform and solved to global optimality using Gurobi 9.5. Using this formulation, we determine the profitability of retrofitting an existing NGCC unit with the chosen capture system for multiple regions in the U.S. under two scenarios with different carbon prices. Importantly, the results show that the optimal decision strongly depends on the region and on the carbon price, thereby demonstrating the importance of the inclusion of market signals in the design process.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS1985

An optimal spacecraft scheduling model for the NASA deep space network

A computer model is described which uses mixed-integer linear programming to provide optimal DSN spacecraft schedules given a mission set and specified scheduling requirements. A solution technique is proposed which uses Bender's method and a heuristic starting algorithm.

Webb, W. A.↗
DOE OSTI2025

Optimal Mitigation Planning For Adversarial Scenarios

We propose a generalized framework which performs an optimal partitioning of a limited budget into various organizational sectors in order to improve the cybersecurity of a smart device or component in the Cyber Physical Energy System (CPS). The framework identifies the adversarial threats and possible attack sequences which can be performed to exploit cyber vulnerabilities of the component. Thereafter, we formulate an Mixed Integer Linear Programming (MILP) optimization problem which aims to evaluate the optimal budget partitions in order to minimize the number of highly likely attack sequences. Though we provide results for using the framework in CPES, the proposed methodology can be extended for multiple domains with a set of known adversarial and mitigation actions.

Purohit, Sumit [Pacific Northwest National Laborat↗
DOE OSTI2022

Integrating Concentrating Solar Power Technologies into the Hybrid Optimization and Performance Platform (HOPP)

As the world increases renewable energy deployment, there is an increasing interest in hybridizing various generation and storage technologies to maximize net benefit to the developer and/or off-taker. A particularly interesting combination of renewable technologies is concentrating solar power (CSP) with thermal energy storage (TES), photovoltaics (PV), and electrochemical battery energy storage (BESS). Due to the system complexity of CSP technology, it is difficult to evaluate the technological and financial performance of a CSP-PV hybrid system without detailed modeling of annual operations. To address this challenge, we have developed a modeling framework for evaluating the performance and financial viability of CSP systems hybridized with PV and battery technologies. This modeling effort incorporates CSP tower and trough systems into an existing modeling tool recently developed by NREL referred to as the Hybrid Optimization and Performance Platform (HOPP). This report outlines the modeling methodology as well as preliminary results from example case studies conducted using the model. The methodology describes: (i) the integration of CSP tower and troughs into HOPP using python interfaces to access System Advisor Model (SAM) underlining technology models, (ii) the mathematical formulation of the mixed integer linear program dispatch optimization model which optimizes operations of storage asset to either maximize system revenue or minimize operating cost while load following, (iii) the design analysis methods implemented within HOPP, and (iv) simulation clustering for the purposes of reducing computational expense. We exercise the model using a case study of a future scenario where we assume (i) CSP and PV technologies achieve the 2030 cost targets provided by the Solar Energy Technologies Office (SETO), (ii) battery costs reduce to the 2030 mid cost projection presented by NREL. Lastly, (iii) electricity prices for southern California in 2030 are provided by NREL's Cambium database, and (iv) a capacity payment of $150/kW-yr based on the system capacity factor during the to 100 net-load hours.

14 SOLAR ENERGY↗
DOE OSTI2025

A Fast Dynamic Internal Predictive Power Scheduling Approach for Power Management in Microgrids: Preprint

This paper presents a Dynamic Internal Predictive Power Scheduling (DIPPS) approach for optimizing power management in microgrids, particularly focusing on external power exchanges among diverse prosumers. DIPPS utilizes a dynamic objective function with a time-varying binary parameter to control the timing of power transfers to the external grid, facilitated by efficient usage of energy storage for surplus renewable power. The microgrid power scheduling problem is modeled as a mixed-integer nonlinear programming (MINLP-PS) and subsequently transformed into a mixed-integer linear programming (MILPPS) optimization through McCormick's relaxation to reduce computational complexity. A predictive window window with 6 data points is solved at an average of 0.92s, a 97.6% improvement over the 38.27s required for the MINLP-PS formulation, implying the numerical feasibility of the DIPPS approach for real-time implementation. Finally, the approach is validated against a static objective using real-world load data across three case studies with different time-varying parameters, demonstrating the ability of DIPPS to optimize power exchanges and efficiently utilize distributed resources while shifting the external power transfers to specified time durations.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Optimization for Bioenergy Systems

The Sustainable Aviation Fuel (SAF) Grand Challenge (Langholtz, 2024 ) seeks to generate 35 billion gallons of SAF each year by 2050, with corn stover, an agricultural byproduct, playing a key role as a feedstock. This study develops an optimization framework to enhance the quality and quantity of corn stover while ensuring economic and environmental viability. Using the Decision Support System for Agrotechnology Transfer (DSSAT) crop model, we simulate the effects of cover crops on rotation yield, soil moisture balance, and nitrogen cycling across diverse climates and soils. The model outputs, including yield data and soil quality changes, inform a Mixed-Integer Linear Programming (MILP) optimization model. This model aims to maximize economic and environmental returns by incorporating production costs, direct and indirect income, and environmental incentives. The optimization model evaluates 280 agriculture management plans composed of various crop management strategies, including corn stover removal rates, cover crop adoption, and fertilization practices. It seeks to identify the optimal combination of crop and tillage decisions for each subfield, maximizing profits while enhancing soil carbon sequestration and reducing greenhouse gas emissions. Outputs include detailed subfield locations, optimal management plans, and profits per hectare and per acre, allowing for comparison with literature values on farm profits. This study provides a robust optimization framework supporting the SAF Grand Challenge by proposing economically viable and environmentally sustainable strategies for corn stover utilization. The findings highlight corn stover's potential as a sustainable feedstock for SAF production, offering practical solutions to enhance its quality and quantity while maintaining soil health. Idaho is used as a case study to demonstrate the framework's applicability and effectiveness in real-world scenarios. Langholtz, M. H., Davis, M., Hellwinckel, C., De La Torre Ugarte, D., Efroymson, R., Jacobson, R., Milbrandt, A., Coleman, A., Davis, R., Kline, K. L., Badgett, A., Curran, S., Schmidt, E., Theiss, T., Fried, J., English, B., Lambert, L., Cook, H., Field, J., ... Walker, L. (2024). 2023 Billion-Ton Report: An Assessment of U.S. Renewable Carbon Resources. https://doi.org/10.2172/2441098 DSSAT Foundation. (2025). Decision Support System for Agrotechnology Transfer (DSSAT). Retrieved from https://dssat.net/

09 - BIOMASS FUELS↗
DOE OSTI2018

Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints

Here, we propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current (AC) model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage second-order cone relaxations, piecewise outer approximations, and optimization-based bounds tightening to guarantee a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Virtual-Voltage Partition-Based Approach to Optimal Transmission Switching

This article deals with optimal transmission switching (OTS) problems involving binary decisions about network topology and nonconvex power flow constraints. We adopt a semidefinite programming formulation for the optimal power flow (OPF) problem that, however, remains nonconvex due to the presence of discrete variables and bilinear products between the decision variables. To tackle the latter, we introduce a physically inspired, virtual-voltage approximation that leads to provable lower and upper bounds on the solution of the original problem. To deal with the exponential complexity caused by the discrete variables, we introduce a graph partition-based algorithm that breaks the problem into several parallel mixed-integer subproblems of smaller size. Simulations on the IEEE bus test cases demonstrate the high degree of accuracy and affordable computational requirements of our approach.

42 ENGINEERING↗
DOE OSTI2020

Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions and presents a strengthened version of the convex quadratic relaxation of the optimal transmission switching problem. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. Next, we introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent convex relaxations introduced for the optimal transmission switching problem in power systems. Using the proposed improvements, along with bound propagation, on 23 medium-sized test cases in the PGLib benchmark library with a relaxation gap of more than 1%, we reduce the gap to less than 1% on five instances. The tightened model has promising computational results when compared with state-of-the-art formulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A spatial superstructure approach to the optimal design of modular processes and supply chains

Modularity is a design principle that aims to provide flexibility for spatio-temporal assembly/disassembly and reconfiguration of systems. This design principle can be applied to multiscale (hierarchical) manufacturing systems that connect units, processes, facilities, and entire supply chains. Designing modular systems is challenging because of the need to capture spatial interdependencies that arise between system components due to product exchange/transport between components and due to product transformation in such components. In this work, we propose an optimization framework to facilitate the design of modular manufacturing systems. Central to our approach is the concept of a spatial superstructure, which is a graph that captures all possible system configurations and interdependencies between components. The spatial superstructure is a generalization of the notion of a superstructure and of a p-graph used in process design, in that it encodes spatial (geographical) context of the system components. Here, we show that this generalization facilitates the simultaneous design and analysis of processes, facilities, and of supply chains. Our framework aims to select the system topology from the spatial superstructure that minimizes design cost and that maximizes design modularity. We show that this design problem can be cast as a mixed-integer, multi-objective optimization formulation. We demonstrate these capabilities using a case study arising in the design of a plastic waste upcycling supply chain.

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

Recent advances and challenges in optimization models for expansion planning of power systems and reliability optimization

Optimization models for expansion planning of power systems aim to determine capacities, investment timing, and location of power systems to satisfy the power demands while minimizing the total cost. The models have become complex in recent years to reflect both regulations on conventional energy sources and the increasing penetration of renewable energy sources (RES). This paper reviews the basic concepts and optimization models for expansion planning of power systems. We first explain the definition and features of generation expansion planning (GEP), transmission expansion planning (TEP), and generation and transmission expansion planning (GTEP). To address the computational challenges of large-scale expansion planning problems, we review several simplifications including temporal and spatial aggregation, and decomposition methods. This paper also addresses power system reliability defined as the probability of satisfying the load demand while withstanding failures of components. Finally, the goal of this paper is to provide a research overview, discuss trends in expansion planning of power systems, and suggest directions for future research.

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

Extreme-scale EV charging infrastructure planning for last-mile delivery using high-performance parallel computing

Here, this paper addresses stochastic charger location and allocation problems under queue congestion for last-mile delivery using electric vehicles (EVs). The objective is to decide where to open charging stations and how many chargers of each type to install, subject to budgetary and waiting-time constraints. We formulate the problem as a mixed-integer non-linear program, where each station-charger pair is modeled as a multiserver queue with stochastic arrivals and service times to capture the notion of waiting in fleet operations. The model is extremely large, with billions of variables and constraints for a typical metropolitan area; even loading the model in solver memory is difficult, let alone solving it. To address this challenge, we develop a Lagrangian-based dual decomposition framework that decomposes the problem by station and leverages parallelization on high-performance computing systems, where the subproblems are solved by using a cutting plane method and their solutions are collected at the master level. We also develop a three-step rounding heuristic to transform the fractional subproblem solutions into feasible integral solutions. Computational experiments on data from the Chicago metropolitan area with hundreds of thousands of households and thousands of candidate stations show that our approach produces high-quality solutions in cases where existing exact methods cannot even load the model in memory. We also analyze various policy scenarios, demonstrating that combining existing depots with newly built stations under multiagency collaboration substantially reduces costs and congestion. These findings offer a scalable and efficient framework for developing sustainable large-scale EV charging networks.

Capacity allocation↗