Search NASA⌕ Search

SEARCH · Search NASA

Results for “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.

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

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Data-Driven Energy Resilience Assessment and Enhancement in Urban Communities: A Case Study in Detroit

This paper presents a data-driven framework for assessing and enhancing energy resilience in urban communities. The resilience assessment is based on two datasets: 1) annual aggregated power outage data and 2) 15-minute interval outage data. High-impact, low-probability (HILP) events are identified within these datasets to evaluate community resilience under extreme conditions. To enhance resilience, an optimization framework utilizing mixed integer linear programming is developed to determine the optimal sizing and placement of solar photovoltaic (PV) systems and battery energy storage systems (BESS). This method offers a cost-effective and practical solution for improving energy resilience in vulnerable communities. Furthermore, a case study of the City of Detroit in Michigan demonstrates the effectiveness of the framework through simulation and validation.

Energy resilience assessment↗
DOE OSTI2016

Bidding strategy for microgrid in day-ahead market based on hybrid stochastic/robust optimization

In this paper, we propose an optimal bidding strategy in the day-ahead market of a microgrid consisting of intermittent distributed generation (DG), storage, dispatchable DG and price responsive loads. The microgrid coordinates the energy consumption or production of its components and trades electricity in both the day-ahead and real-time markets to minimize its operating cost as a single entity. The bidding problem is challenging due to a variety of uncertainties, including power output of intermittent DG, load variation, day-ahead and real-time market prices. A hybrid stochastic/robust optimization model is proposed to minimize the expected net cost, i.e., expected total cost of operation minus total benefit of demand. This formulation can be solved by mixed integer linear programming. The uncertain output of intermittent DG and day-ahead market price are modeled via scenarios based on forecast results, while a robust optimization is proposed to limit the unbalanced power in real-time market taking account of the uncertainty of real-time market price. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator, a battery and a responsive load show the advantage of stochastic optimization in addition to robust optimization.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Optimizing Vehicle Fleet and Assignment for Concentrating Solar Power Plant Heliostat Washing

Concentrating solar power central-receiver plants use thousands of sun-tracking mirrors, i.e., heliostats, to reflect sunlight to a central receiver, which collects and uses the heat to generate electricity. Over time, soiling reduces the reflectivity of the heliostats and, therefore, the efficiency of the system. Current industry practice sends vehicles to wash heliostats in an ad hoc fashion. We present a mixed-integer nonlinear program that determines wash vehicle fleet size, mix, and assignment of wash crews to heliostats to minimize the sum of (i) the revenues lost due to heliostat soiling, (ii) the costs of hiring wash crews and operating the vehicles, and (iii) the costs of purchasing wash vehicles. We establish conditions for convexity of the objective function, and then propose a decomposition method that enables near-optimal solutions to the wash vehicle fleet sizing and assignment problem on the order of a couple of minutes. Furthermore, these solutions yield hundreds of thousands of dollars in savings per year over current industry practices.

14 SOLAR ENERGY↗
DOE OSTI2021

Design and dispatch optimization of packaged ice storage systems within a connected community

The traditional implementation of cool thermal energy storage (CTES) must be reimagined within the context of a dynamic grid and smart buildings operating as connected communities. As most buildings do not operate central chillers or connect to district cooling loops, this necessitates a broader use of packaged CTES. Our objective is to begin answering the question of how such packaged CTES should be implemented within a connected community. We do so by presenting a simulation–optimization workflow employing building energy modeling software and a mixed-integer linear program to design and dispatch a packaged CTES technology to achieve minimum total annual cost. We demonstrate this methodology on a seven-building case study using current utility rates and find that total annual cooling energy costs can be reduced by 17.8% compared to baseline, after accounting for the cost of storage. We perform three parametric sensitivity studies to evaluate modeling assumptions and obtain the prioritization of storage procurement as a function of annualized life-cycle cost of storage. We find that a community optimization approach provides significantly different results than individual building optimizations and provides greater savings compared to baseline.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2019

A Non-Exhaustive Search Algorithm to Identify Distribution Grid Operational Topology

Distribution grid, in general, is constructionally loopy but a radially operated network. Opening and closing of suitable tie-switches allow transition from one topology to another. Identifying the operational topology of a distribution system is essential for accurate control actions. This paper proposes a non-exhaustive search approach to detect the operational topology of the distribution feeder by estimating the switch statuses. In this work, a mixed-integer linear programming approach is proposed that finds the correct operational topology by identifying the system load demand and power flow variables that are closest to the corresponding measured values. The problem is constrained by distribution power flow and radial structure of the feeder. This formulation allows the inclusion of errors in power/line flow measurements making it more suitable for a practical distribution system. The proposed approach finds the correct operational topology without exhaustively searching for all possible topologies. We thoroughly validate the accuracy and effectiveness of the proposed approach in identifying correct operational topology using IEEE 123-node feeder with the help of numerous simulations studies. It is observed that the approach performs well even at very high percentages of load and flow measurement errors.

Missed detection ratio (MDR), Mixed-integer linear↗
DOE OSTI2016

Resilient Distribution System by Microgrids Formation After Natural Disasters

Microgrids with distributed generation provide a resilient solution in the case of major faults in a distribution system due to natural disasters. This paper proposes a novel distribution system operational approach by forming multiple microgrids energized by distributed generation from the radial distribution system in real-time operations, to restore critical loads from the power outage. Specifically, a mixed-integer linear program (MILP) is formulated to maximize the critical loads to be picked up while satisfying the self-adequacy and operation constraints for the microgrids formation problem, by controlling the ON/OFF status of the remotely controlled switch devices and distributed generation. A distributed multi-agent coordination scheme is designed via local communications for the global information discovery as inputs of the optimization, which is suitable for autonomous communication requirements after the disastrous event. The formed microgrids can be further utilized for power quality control and can be connected to a larger microgrid before the restoration of the main grids is complete. Numerical results based on modified IEEE distribution test systems validate the effectiveness of our proposed scheme.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Exploiting Identical Generators in Unit Commitment

Here, we present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down-time, and cost curves) into a single unit reduces redundancy in the search space induced by both exact symmetry (permutations of generator schedules) and certain classes of mutually non-dominated solutions. We study the impact of aggregation on two large-scale UC instances, one from the academic literature and another based on real-world operator data. Our computational tests demonstrate that when present, identical generators can negatively affect the performance of modern MILP solvers on UC formulations. Further, we show that our reformation of the UC MILP through aggregation is an effective method for mitigating this source of computational difficulty.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2018

Coordinated platooning with multiple speeds

In a platoon, vehicles travel one after another with small intervehicle distances; trailing vehicles in a platoon save fuel because they experience less aerodynamic drag. This work presents a coordinated platooning model with multiple speed options that integrates scheduling, routing, speed selection, and platoon formation/dissolution in a mixed-integer linear program that minimizes the total fuel consumed by a set of vehicles while traveling between their respective origins and destinations. The performance of this model is numerically tested on a grid network and the Chicago-area highway network. We find that the fuel-savings factor of a multivehicle system significantly depends on the time each vehicle is allowed to stay in the network; this time affects vehicles’ available speed choices, possible routes, and the amount of time for coordinating platoon formation. For problem instances with a large number of vehicles, we propose and test a heuristic decomposed approach that applies a clustering algorithm to partition the set of vehicles and then routes each group separately. When the set of vehicles is large and the available computational time is small, the decomposed approach finds significantly better solutions than does the full model.

33 ADVANCED PROPULSION SYSTEMS↗
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↗
DOE OSTI2023

Model-based predictive control of multi-stage air-source heat pumps integrated with phase change material-embedded ceilings

This paper presents a model-based predictive control strategy to optimize the operations of phase change material (PCM) ceiling panels coupled with a multi-stage air-source heat pump. A three-stage prototype heat pump unit has been built and tested in the laboratory, with the low and medium stages designed for space heating/cooling and the high compression stage dedicated to charging of the PCM energy storage. To facilitate optimal control of the integrated heat pump system, a mixed-integer linear programming formulation is derived through linearization of the heat pump model and a mixed-integer reformulation of the PCM dynamic governing equations. A predictive control strategy is synthesized based on the resultant control formulation and implemented in a receding horizon scheme that optimizes the PCM charging and the zone temperature schedules simultaneously to leverage both the passive (associated with building construction materials) and active (PCM) storage capacities of a building. The control strategy has been tested along with three benchmarking control scenarios using a co-simulation platform for a prototypical detached house in Atlanta, GA. In this study, test results showed that application of the proposed control strategy to the PCM-integrated heat pump could provide 27.1% electricity cost savings while a fine tuned rule-based control strategy could achieve cost savings of 20.4%, compared to a baseline case without PCM storage, under a time-of-use rate tariff.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2019

Distributed biomass supply chain cost optimization to evaluate multiple feedstocks for a biorefinery

Conventional practices of siting all biomass preprocessing operations at the biorefinery is widely believed to be the most cost-effective solution for feedstock supply because of economies of scale. Yet, biomass preprocessing operations could be decentralized by moving the preprocessing operations to distributed biomass preprocessing centers, also known as “depots” located near biomass sources. We present a comparative case study with multiple biomass resources to analyze biorefinery feedstock supply logistics designs having distributed depots and a primary depot co-located with the biorefinery. A mixed-integer linear programming model was developed to simultaneously optimize feedstock sourcing decisions, and optimal preprocessing depot locations and size, utilizing biomass resources from agricultural residue, energy and municipal solid waste to meet carbohydrate specifications and feedstock demand for a biochemical conversion process. Findings from a case study in the US showed that a biorefinery could increase its feedstock supply draw area and supply volume by 57.3%, 177.4% respectively without increasing the feedstock delivered cost by adopting distributed depot-in the feedstock supply chain design. A distributed-depot-based supply chain can be more economical by selecting optimal mix of biomass resource, optimal siting and depot scales during feedstock supply chain design. The results from this study indicate that a biorefinery can utilize dynamic blending to meet the feedstock quality specifications as well as larger supply radius in the distributed depot-based supply chain design to access more available biomass to handle potential feedstock supply uncertainty.

09 BIOMASS FUELS↗
DOE OSTI2018

Optimal blending management of biomass resources used for biochemical conversion

This research develops an optimization model to describe the tradeoff among blend components in the least-cost biomass blend, based on resource availability, quality requirements, and logistics cost for a biochemical conversion. A mixed-integer linear programming model is developed to determine the least-cost blend from a set of candidate feedstocks. A case study – based on a biorefinery located in western Kansas that uses three-pass corn stover, two-pass corn stover, switchgrass, miscanthus, and municipal solid waste fractions to meet biochemical conversion specifications and feedstock demand – shows that the delivered cost of an optimal blend that meets carbohydrate and ash specifications is 12.12% higher than the delivered cost of optimal blend that meets a carbohydrate specification only. The results indicate that a least-cost blend that meets both carbohydrate and ash specifications consists of miscanthus (48.2%) and switchgrass (29.4%) whereas the least-cost blend meeting carbohydrate specification only comprises three-pass corn stover (55.4%) and two-pass corn stover (20.4%). Here an optimal blend uses a low-cost municipal solid waste fraction in all cases, implying that blending could be a potential strategy to reduce delivered feedstock cost.

09 BIOMASS FUELS↗
DOE OSTI2021

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Cooperative Routing for an Air–Ground Vehicle Team—Exact Algorithm, Transformation Method, and Heuristics

This paper considers a cooperative vehicle routing problem for an intelligence, surveillance, and reconnaissance mission in the presence of communication constraints between the vehicles. The proposed framework uses a ground vehicle and an unmanned aerial vehicle (UAV) that travel cooperatively and visit a set of targets while satisfying the communication constraints. The problem is formulated as a mixed-integer linear program, and a branch-and-cut algorithm is developed to solve the problem to optimality. Furthermore, a transformation method and a heuristic are also developed for the problem. The effectiveness of all the algorithms is corroborated through extensive computational experiments on several randomly generated instances. Furthermore, this paper is motivated by an intelligence, surveillance, and reconnaissance mission involving a single unmanned aerial vehicle (UAV) and a ground vehicle, where the vehicles must coordinate their activity in the presence of communication constraints. The combination of a small UAV and a ground vehicle is an ideal platform for such missions, since small UAVs can fly at low altitudes and can avoid obstacles or threats that would be problematic for the ground vehicle alone. This paper addresses the coordinated routing problem involving these two vehicles and presents an algorithm to obtain an optimal solution for this problem, fast heuristics to obtain good feasible solutions, and also a transformation method to transform any instance of this cooperative vehicle routing problem to an instance of the one-in-a-set traveling salesman problem.

33 ADVANCED PROPULSION SYSTEMS↗