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Results for “Mixed-integer programming”

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
DOE OSTI2024

Paired Hydro-Battery Hybrid System Operations Using MIQP Based Multi-Objective Optimization

Hybridizing a hydropower plant with a battery energy storage system is often a very expensive decision. So to make the case for feasibility of hybridization the cost benefit analysis must be comprehensive. Most literature found on this subject only uses one out of many different available value streams to carry out a feasibility analysis. To that end, in this study we propose a multi-objective optimization formulation and a mixed-integer quadratic programming optimization engine that considers multiple different value streams and optimizes hydro-battery hybrid system paired operations to maximize revenue generated from energy arbitrage while simultaneously minimizing the total hydro turbine mileage thus reducing turbine starts and stops and improving turbines life all while following all environmental constraints and not violating any limitations either regulatory or preferential (i.e., to support recreational activities like white water rafting, etc.). In this study we also implemented the developed optimization methodology to a real-world case study of Bagnell dam hydropower facility (8 units totaling 240 MW rated power capacity) which is owned and operated by our industry partner Ameren Energy Inc. The case study outcomes shows that by hybridizing the Bagnell dam hydropower facility with a 60 MW x 2-hr battery energy storage system, the annual benefits can be increased over \$6 million while reducing the annual mileage averaged per turbine and number of start/stops by over 98\% and 85\% respectively.

Chalishazar, Vishvas H.↗
DOE OSTI2024

Assessing the Reliability Benefits of Energy Storage as a Transmission Asset

Utilizing energy storage solutions to reduce the need for traditional transmission investments has been recognized by system planners and supported by federal policies in recent years. This work demonstrates the need for detailed reliability assessment for quantitative comparison of the reliability benefits of energy storage and traditional transmission investments. First, a mixed-integer linear programming expansion planning model considering candidate transmission lines and storage technologies is solved to find the least-cost investment decisions. Next, operations under the resulting system configuration are simulated in a probabilistic reliability assessment which accounts for weather-dependent forced outages. The outcome of this work, when applied to TPPs, is to further equalize the consideration of energy storage compared to traditional transmission assets by capturing the value of storage for system reliability.

co-optimization↗
DOE OSTI2024

Distributionally Robust Bilevel Optimization Model for Distribution Network With Demand Response Under Uncertain Renewables Using Wasserstein Metrics

Here, we consider a distribution network integrating demand response (DR) participants in the presence of uncertain renewable suppliers and outdoor temperatures. A bilevel optimization model is proposed to capture the intricate dynamics between price-incentivized DR participants and distribution system operations, including energy procurement and active/reactive power flows. The model is formulated as a distributional robust bilevel optimization using Wasserstein metrics. We show favorable data-driven properties including out-of-sample guarantee and asymptotic consistency. Furthermore, we present a tractable mixed-integer linear programming reformulation and characterize the worst-case distribution. Computational experiments are conducted on a modified 33-bus system. Our findings underscore the efficacy of the pricing strategies derived from the proposed bilevel optimization model. These strategies not only effectively manage DR participants' behavior but also bring equity considerations among households with various characteristics to light. The results contribute to a deeper understanding of the interplay between distribution system operators and DR participants.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

PDPTW-DB: MILP-Based Offline Route Planning for PDPTW with Driver Breaks

The Pickup and Delivery Problem with Time Windows (PDPTW) involves optimizing routes for vehicles to meet pickup and delivery requests within specific time constraints, a challenge commonly faced in logistics and transportation. Microtransit, a flexible and demand-responsive service using smaller vehicles within defined zones, can be effectively modeled as a PDPTW. Yet, the need for driver breaks—a key human constraint—is frequently overlooked in PDPTW solutions, despite being necessary for regulatory compliance. This study presents a novel mixed-integer linear programming formulation for the Pickup and Delivery Problem with Time Windows and Driver Breaks (PDPTW-DB). To the best of our knowledge this formulation is the first to consider mandatory periodic driver breaks within optimized Microtransit routes. The proposed model incorporates regulatory compliant break scheduling directly within the vehicle routing optimization framework. By considering driver break requirements as an integral component of the optimization process, rather than as a post-processing step, the model enables the generation of routes that respect hours of service regulations while minimizing operational costs. This integrated approach facilitates the generation of schedules that are operationally efficient and prioritize driver welfare through driver breaks. We work with a public transit agency from the southern USA, and highlight the specific nuances of driver break optimization, and present a Pickup and Delivery Problem with Time Windows formulation for optimizing Microtransit operations and scheduling driver breaks. We validate our approach using real-world data from the transit agency. Our results validate our formulation in producing cost-effective, and regulation-compliant solutions.

Applied Computing, Transportation↗
DOE OSTI2024

DEPLOYING FAST CHARGING INFRASTRUCTURE FOR ELECTRIC VEHICLES IN URBAN NETWORKS: AN ACTIVITY-BASED APPROACH

This paper explores an important problem under the domain of network modeling, the optimal configuration of charging infrastructure for electric vehicles (EVs) in urban networks considering EV users' daily activities and charging behavior. This study proposes a charging behavior simulation model considering different initial state of charge (SOC), travel distance, availability of home chargers, and the daily schedule of trips for each traveler. The proposed charging behavior simulation model examines the complete chain of trips for EV users as well as the interdependency of trips traveled by each driver. The problem of finding the optimum charging configuration is then formulated as a mixed-integer nonlinear programming problem that considers the dynamics of travel time and travel distance, the interdependency of trips made by each driver, limited range of EVs, remaining battery capacity for recharging, waiting time in queue, and detour to access a charging station. This problem is solved using a metaheuristic approach for a large-scale case network. A series of examples are presented to demonstrate the model efficacy and explore the impact of energy consumption on the final SOC and the optimum charging infrastructure.

Chain of Trips↗
DOE OSTI2024

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.

bound tightening↗
DOE OSTI2025

New Results on Communication- and Memory-Aware Load Balancing Model and Algorithms

While load balancing in distributed-memory computing has been well-studied, we present an innovative approach to this problem: a unified, reduced-order model that combines three key components to describe “work” in a distributed system: computation, communication, and memory. Our model enables an optimizer to explore complex tradeoffs in task placement, such as augmented parallelism, at the expense of data replication increasing memory usage. We propose a fully distributed, heuristic-based load balancing optimization algorithm, and demonstrate that it quickly finds close-to-optimal solutions. We formalize the complex optimization problem as a mixed-integer linear program, and compare it to our strategy. Finally, we show that when applied to an electromagnetics code, our approach obtains up to 2.3x speedups for the imbalanced execution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimal Design of Food Packaging Considering Waste Management Technologies to Achieve Circular Economy

Plastic packaging plays a fundamental role in the food industry, avoiding food waste and facilitating food access. The increasing plastic production and the lack of appropriate plastic waste management technologies represent a threat to the environmental and human welfare. Therefore, there is an urgent need to identify sustainable packaging solutions. Circular economy (CE) promotes reducing waste and increasing recycling practices to achieve sustainability. In this work, we propose a CE framework based on multi-objective optimization, considering both economic and environmental impacts, to identify optimal packaging designs and waste management technologies. Using mixed-integer linear programming (MILP), techno-economic analysis (TEA), and life cycle assessment (LCA), this work aims to build the first steps in packaging design, informing about the best packaging alternatives and the optimal technology or technologies to process packaging waste. For the economic analysis, we consider the minimum increase in price (MIP) when adding recycling to the cost of each packaging solution, while for the environmental analysis, the greenhouse gas emissions impact was considered. A case study on ground coffee packaging is used to illustrate the proposed framework. The results demonstrate that the multilayer bag option is the most convenient when considering both the chosen economic and environmental impacts.

Life Cycle Analysis↗
DOE OSTI2024

Research Highlight - Dispatch Optimization, System Design and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage

We highlight our work from our previous publication titled "Dispatch Optimization, System Design, and Cost Benefit Analysis of a Nuclear Reactor with Molten Salt Thermal Storage" published in MDPI Energies 2022 (doi.org/10.3390/en15103599). Variable renewable energy availability has increased the volatility in energy prices in most markets. Nuclear power plants, with a large ratio of capital to variable costs, have historically operated as base load energy suppliers but the need for more flexible operation is increasing. We simulate the techno-economic performance of a 950 MWt nuclear power plant, based on the Westinghouse lead-cooled fast reactor, coupled with molten salt thermal storage as a method for flexible energy dispatch. We use the System Advisor Model to model the nuclear reactor thermal power input and power cycle operating modes. We combine this robust engineering model with a mixed-integer linear program model for optimized dispatch scheduling. We then simulate the coupled nuclear and thermal storage system under different market scenarios with varying price volatility. We find that the coupled plant outperforms the base plant under markets where energy price peaks fluctuate by a factor of two or more about the mean price. We show that a calculated power purchase agreement price for the plant improves by up to 10% when operating under California energy market conditions. Sensitivity analysis on the thermal storage cost shows that the optimal design remains unchanged even when doubling costs.

97 MATHEMATICS AND COMPUTING↗
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 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 OSTI2024

Near-Optimal Solutions for Day-Ahead Unit Commitment

Given the difficulty and the time pressure of solving unit commitment problems, near -optimal solutions (those with 0.1 or 0.001% optimality gaps) are often used in practice. The choice in which of the near -optimal solutions is used, however, is random. We investigate the impact of solution choice on the revenues obtained by generator owners across a variety of pricing schemes and problem instances.

market-clearing↗
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 OSTI2025

Physics-Informed Graph Neural Networks for Collaborative Dynamic Reconfiguration and Voltage Regulation in Unbalanced Distribution Systems

Network reconfiguration has long been employed as a strategic approach to minimize power distribution system losses and effectively regulate voltage levels. Tap-changing voltage regulators are also critical for controlling bus voltages, especially in accommodating the increasing integration of distributed energy resources (DERs) with intermittent outputs. This paper introduces novel methodologies to address the challenges of dynamic reconfiguration and optimal tap setting in unbalanced three-phase distribution systems. We propose an approximated mixed-integer quadratically constrained program (MIQCP) to model dynamic reconfiguration, along with a pioneering formulation for voltage regulator (VR) tap-setting based on Special Ordered Set type 1 (SOS1). To mitigate computational complexity, we propose a physics-informed spatial-temporal graph convolutional network (STGCN) with an integrated link classifier. The proposed approach enables efficient solution generation by fixing specific variables in the MIQCP instance and solving the simplified sub-MIP using an MIP solver. Numerical studies demonstrate the superior prediction accuracy of our STGCN model compared to baseline neural network models, resulting in reduced DER curtailment and voltage deviation with shorter computation time.

dynamic reconfiguration↗
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↗
DOE OSTI2024

Enhancing power grid resilience to winter storms via generator winterization with equity considerations

Here we develop two-stage stochastic programming models for generator winterization that enhance power grid resilience while incorporating social equity. The first stage in our models captures the investment decisions for generator winterization, and the second stage captures the operation of a degraded power grid, with the objective of minimizing load shed and social inequity. To incorporate equity into our models, we propose a concept called adverse effect probability that captures the disproportionate effects of power outages on communities with varying vulnerability levels. Grid operations are modeled using DC power flow, and equity is captured through mean or maximum adverse effects experienced by communities. We apply our models to a synthetic Texas power grid, using winter storm scenarios created from the generator outage data from the 2021 Texas winter storm. Our extensive numerical experiments show that more equitable outcomes, in the sense of reducing adverse effects experienced by vulnerable communities during power outages, are achievable with no impact on total load shed through investing in winterization of generators in different locations and capacities.

24 POWER TRANSMISSION AND DISTRIBUTION↗
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↗