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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 OSTI2023

A Mixed integer linear programming‐based distributed energy management for networked microgrids considering network operational objectives and constraints

Abstract Mixed integer linear programming (MILP)–based distributed energy management for networked microgrids embedded modern distribution systems is proposed. Considering the diverse ownership of microgrids, distributed energy resources (DERs) that interface directly with utilities and responsive loads, an alternating direction method of multipliers–based distributed framework was formulated for the scheduling of networked microgrids embedded modern distribution systems by adjusting nodal price signals iteratively. In addition, to make the formulated optimization problems resolvable through more accessible and popular MILP solvers, different linearisation techniques were employed to transform the nonlinear terms into linear or mixed integer linear formats. The proposed MILP‐based distributed method preserves all participants' autonomy (e.g., microgrids, DERs that interface directly with utilities and responsive loads), while incentivising them to actively participate in the distribution system operation with price signals. The proposed method is validated with results of numerical simulation using a modern distribution system consisting of multiple networked microgrids, DERs that interface directly with utilities, as well as responsive loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2022

Foraging with MUSHROOMS: A Mixed-integer Linear Programming Scheduler for Multimessenger Target of Opportunity Searches with the Zwicky Transient Facility

Electromagnetic follow-up of gravitational-wave detections is very resource intensive, taking up hours of limited observation time on dozens of telescopes. Creating more efficient schedules for follow-up will lead to a commensurate increase in counterpart location efficiency without using more telescope time. Widely used in operations research and telescope scheduling, mixed-integer linear programming is a strong candidate to produce these higher-efficiency schedules, as it can make use of powerful commercial solvers that find globally optimal solutions to provided problems. We detail a new target-of-opportunity scheduling algorithm designed with Zwicky Transient Facility in mind that uses mixed-integer linear programming. We compare its performance to gwemopt, the tuned heuristic scheduler used by the Zwicky Transient Facility and other facilities during the third LIGO–Virgo gravitational-wave observing run. This new algorithm uses variable-length observing blocks to enforce cadence requirements and to ensure field observability, along with having a secondary optimization step to minimize slew time. We show that by employing a hybrid method utilizing both this scheduler and gwemopt, the previous scheduler used, in concert, we can achieve an average improvement in detection efficiency of 3%–11% over gwemopt alone for a simulated binary neutron star merger data set consistent with LIGO–Virgo's third observing run, highlighting the potential of mixed-integer target of opportunity schedulers for future multimessenger follow-up surveys.

B Parazin↗
DOE OSTI2025

Alternative mixed integer linear programming optimization for joint job scheduling and data allocation in grid computing

This paper presents a novel approach to the joint optimization of job scheduling and data allocation in grid computing environments. We formulate this joint optimization problem as a mixed integer quadratically constrained program. To tackle the nonlinearity in the constraint, we alternatively fix a subset of decision variables and optimize the remaining ones via Mixed Integer Linear Programming (MILP). We solve the MILP problem at each iteration via an off-the-shelf MILP solver. Our experimental results show that our method significantly outperforms existing heuristic methods, employing either independent optimization or joint optimization strategies. We have also verified the generalization ability of our method over grid environments with various sizes and its high robustness to the algorithm setting.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Mixed Integer Linear Programming in Planning

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

Christina Erwin↗
DOE OSTI2024

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

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

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2010

A Mixed Integer Linear Program for Solving a Multiple Route Taxi Scheduling Problem

Aircraft movements on taxiways at busy airports often create bottlenecks. This paper introduces a mixed integer linear program to solve a Multiple Route Aircraft Taxi Scheduling Problem. The outputs of the model are in the form of optimal taxi schedules, which include routing decisions for taxiing aircraft. The model extends an existing single route formulation to include routing decisions. An efficient comparison framework compares the multi-route formulation and the single route formulation. The multi-route model is exercised for east side airport surface traffic at Dallas/Fort Worth International Airport to determine if any arrival taxi time savings can be achieved by allowing arrivals to have two taxi routes: a route that crosses an active departure runway and a perimeter route that avoids the crossing. Results indicate that the multi-route formulation yields reduced arrival taxi times over the single route formulation only when a perimeter taxiway is used. In conditions where the departure aircraft are given an optimal and fixed takeoff sequence, accumulative arrival taxi time savings in the multi-route formulation can be as high as 3.6 hours more than the single route formulation. If the departure sequence is not optimal, the multi-route formulation results in less taxi time savings made over the single route formulation, but the average arrival taxi time is significantly decreased.

Montoya, Justin Vincent↗
DOE OSTI2026

Optimizing district energy systems by integrating Borehole Thermal Energy Storage Using a Mixed-Integer Linear Programming g-function framework with a Multi-Timescale Rolling Horizon method

Shallow geothermal has gained increasing attention in recent years; however, a reliable framework for its accurate incorporation into large-scale energy system optimization remains lacking. This study proposes a Mixed-Integer Linear Programming (MILP) framework combined with the g-function approach to integrate Borehole Thermal Energy Storage (BTES) technology into energy system optimization. Validation against a Modelica-based reservoir network simulation demonstrates that the proposed framework effectively captures the ground thermal response under varying energy loads and accurately estimates the borefield energy supply. To enhance scalability, a Rolling Horizon with Multi-Timescale (RH-MTS) method is further introduced, reducing computational time by 73 % for the 1-year optimization model with only minor loss of optimality. The framework is demonstrated through the case study of the UC Berkeley campus. Results indicate that BTES is a cost-effective and low-carbon solution: two borefields comprising 382 boreholes can meet 8.0 % and 6.6 % of the total campus heating and cooling demand, respectively, at an average energy rate of 0.70–0.77 USD/kWh and carbon intensity of 0.54 kg-CO2/kWh. Short-term analysis reveals a 35%–65% decline in BTES energy flow after 3–6 months of continuous heating/cooling operation, while long-term simulation shows that annual energy production of BTES can vary by up to 12.0 % after four years before stabilizing. Overall, this study develops a novel optimization framework that couples physics-based g-function method with MILP optimization framework, thereby advancing methodological development for shallow-geothermal integration and providing actionable guidance for BTES deployment in district-energy systems.

Yang, Jiahui↗
DOE OSTI2025

Mapping Spiking Neural Networks to Heterogeneous Crossbar Architectures using Integer Linear Programming

Advances in novel hardware devices and architectures allow Spiking Neural Network (SNN) evaluation using ultra-low power, mixed-signal, memristor crossbar arrays. As individual network sizes quickly scale beyond the dimensional capabilities of single crossbars, networks must be mapped onto multiple crossbars. Crossbar sizes within modern Memristor Crossbar Architectures (MCAs) are determined predominately not by device technology but by network topology; more, smaller crossbars consume less area thanks to the high structural sparsity found in larger, brain-inspired SNNs. Motivated by continuing increases in SNN sparsity due to improvements in training methods, we propose utilizing heterogeneous crossbar sizes to further reduce area consumption. This approach was previously unachievable as prior compiler studies only explored solutions targeting homogeneous MCAs. Our work improves on the state-of-the-art by providing Integer Linear Programming (ILP) formulations supporting arbitrarily heterogeneous architectures. By modeling axonal interactions between neurons, our methods produce better mappings while removing inhibitive a priori knowledge requirements. We first show a 16.7-27.6% reduction in area consumption for square-crossbar homogeneous architectures. Then, we demonstrate 66.9-72.7% further reduction when using a reasonable configuration of heterogeneous crossbar dimensions. Next, we present a new optimization formulation capable of minimizing the number of inter-crossbar routes. When applied to solutions already near-optimal in area, an 11.9-26.4% routing reduction is observed without impacting area consumption. Finally, we present a profile-guided optimization capable of minimizing the number of runtime spikes between crossbars. Compared to the best-area-then-route optimized solutions, we observe a further 0.5-14.8% inter-crossbar spike reduction while requiring 1–3 orders of magnitude less solver time.

Pohl, Devin [ORNL] (ORCID:0009000040149027)↗
NASA NTRS2009

A Mixed Integer Linear Program for Airport Departure Scheduling

Aircraft departing from an airport are subject to numerous constraints while scheduling departure times. These constraints include wake-separation constraints for successive departures, miles-in-trail separation for aircraft bound for the same departure fixes, and time-window or prioritization constraints for individual flights. Besides these, emissions as well as increased fuel consumption due to inefficient scheduling need to be included. Addressing all the above constraints in a single framework while allowing for resequencing of the aircraft using runway queues is critical to the implementation of the Next Generation Air Transport System (NextGen) concepts. Prior work on airport departure scheduling has addressed some of the above. However, existing methods use pre-determined runway queues, and schedule aircraft from these departure queues. The source of such pre-determined queues is not explicit, and could potentially be a subjective controller input. Determining runway queues and scheduling within the same framework would potentially result in better scheduling. This paper presents a mixed integer linear program (MILP) for the departure-scheduling problem. The program takes as input the incoming sequence of aircraft for departure from a runway, along with their earliest departure times and an optional prioritization scheme based on time-window of departure for each aircraft. The program then assigns these aircraft to the available departure queues and schedules departure times, explicitly considering wake separation and departure fix restrictions to minimize total delay for all aircraft. The approach is generalized and can be used in a variety of situations, and allows for aircraft prioritization based on operational as well as environmental considerations. We present the MILP in the paper, along with benefits over the first-come-first-serve (FCFS) scheme for numerous randomized problems based on real-world settings. The MILP results in substantially reduced delays as compared to FCFS, and the magnitude of the savings depends on the queue and departure fix structure. The MILP assumes deterministic aircraft arrival times at the runway queues. However, due to taxi time uncertainty, aircraft might arrive either earlier or later than these deterministic times. Thus, to incorporate this uncertainty, we present a method for using the MILP with "overlap discounted rolling planning horizon". The approach is based on valuing near-term decision results more than future ones. We develop a model of taxitime uncertainty based on real-world data, and then compare the baseline FCFS delays with delays using the above MILP in a simple rolling-horizon method and in the overlap discounted scheme.

Gupta, Gautam↗
NASA NTRS1975

Planning air transport network in Appalachia

Main issues to be considered in designing an air transport system are discussed, and a model for the selection of an optimal air network for a region is presented. It was desired to have the ability to consider a dense network of nodes and air routes and variations in schedules on routes, which in combination would represent virtually all conceivable alternatives. Linear and integer programming were chosen as the most promising analysis methodologies. Integer programming was found to be intractable, while linear programming provided efficient solutions. The model was applied to studying the feasibility of a STOL network in West Virginia. Based on allowable paths, an examination of intercity demands, and established growth points, desired levels of service expressed as minimum flights were determined for certain city pairs.

Carter, E. C.↗
NASA NTRS1987

A method for nonlinear optimization with discrete design variables

A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.

Olsen, Gregory R.↗
DOE OSTI2021

Disjunctive linear separation conditions and mixed-integer formulations for aircraft conflict resolution

In this paper, we address the aircraft conflict resolution problem in air traffic control. We introduce new mixed-integer programming formulations for aircraft conflict resolution with speed, heading and altitude control which are based on disjunctive linear separation conditions. We first examine the two-dimensional aircraft conflict resolution problem with speed and heading control represented as continuous decision variables. We show that the proposed disjunctive linear separation conditions are equivalent to the classical nonlinear conditions for aircraft separation. Further, we characterise conflict-free trajectories based on aircraft velocity bounds and propose a simple pre-processing algorithm to identify aircraft pairs which are either always conflict-free, or which cannot be separated using speed and heading control only. We then incorporate altitude control and propose a lexicographic optimisation formulation that aims to minimise the number of flight level changes before resolving outstanding conflicts via two-dimensional velocity control. The proposed mixed-integer programming formulations are nonconvex, and we propose convex relaxations, decomposition methods and constraint generation algorithms to solve the two-dimensional and lexicographic optimisation formulations to guaranteed optimality. Numerical experiments on four types of conflict resolution benchmarking instances are conducted to test the performance of the proposed mixed-integer formulations. Further, the proposed method is compared against two benchmarks based on state-of-the-art approaches for the aircraft conflict resolution problem. Our numerical results show that the proposed method largely outperforms both benchmarks in terms of runtime and is able to solve significantly more instances to global optimality.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

The role of service areas in the optimization of FSS orbital and frequency assignments

An implicit relationship is derived which relates the topocentric separation of two satellites required for a given level of single-entry protection to the separation and orientation of their service areas. The results are presented explicitly for circular beams and topocentric angles. A computational approach is given for elliptical beams and for use with longitude and latitude variables. It is found that the geocentric separation depends primarily on the service area separation, secondarily on a parameter which characterizes the electrical design, and only slightly on the mean orbital position of the satellites. Both linear programming and mixed integer programming algorithms are implemented. Possible objective function choices are discussed, and explicit formulations are presented for the choice of the sum of the absolute deviations of the orbital locations from some prescribed 'ideal' location set. A test problem involving six service areas is examined with results that are encouraging with respect to applying the linear programming procedure to larger scenarios.

Levis, C. A.↗
DOE OSTI2021

Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation

In this work, we consider the problem of designing a cloak for waves described by the Helmholtz equation from an integer programming point of view. The problem can be modeled as a PDE-constrained optimization problem with integer-valued control inputs that are distributed in the computational domain. A first-discretize-then-optimize approach results in a large-scale mixed-integer nonlinear program that is in general intractable because of the large number of integer variables that arise from the discretization of the domain. Instead, we propose an efficient algorithm that is able to approximate the local infima of the underlying nonconvex infinite-dimensional problem arbitrarily close without the need to solve the discretized finite-dimensional integer programs to optimality. We optimize only the continuous relaxations of the approximations for local minima and then apply the sum-up rounding methodology to obtain integer-valued controls. If the solutions of the discretized continuous relaxations converge to a local minimizer of the continuous relaxation, then the resulting discrete-valued control sequence converges weakly \(^*\) in \(L^\infty\) to the same local minimizer. These approximation properties follow under suitable refinements of the involved discretization grids. Our results use familiar concepts arising from the analytical properties of the underlying PDE and complement previous results, derived from a topology optimization point of view.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimal Electrification Using Renewable Energies: Microgrid Installation Model with Combined Mixture k-Means Clustering Algorithm, Mixed Integer Linear Programming, and Onsset Method

Optimal planning and design of microgrids are priorities in the electrification of off-grid areas. Indeed, in one of the Sustainable Development Goals (SDG 7), the UN recommends universal access to electricity for all at the lowest cost. Several optimization methods with different strategies have been proposed in the literature as ways to achieve this goal. This paper proposes a microgrid installation and planning model based on a combination of several techniques. The programming language Python 3.10 was used in conjunction with machine learning techniques such as unsupervised learning based on K-means clustering and deterministic optimization methods based on mixed linear programming. These methods were complemented by the open-source spatial method for optimal electrification planning: onsset. Four levels of study were carried out. The first level consisted of simulating the model obtained with a cluster, which is considered based on the elbow and k-means clustering method as a case study. The second level involved sizing the microgrid with a capacity of 40 kW and optimizing all the resources available on site. The example of the different resources in the Togo case was considered. At the third level, the work consisted of proposing an optimal connection model for the microgrid based on voltage stability constraints and considering, above all, the capacity limit of the source substation. Finally, the fourth level involved a planning study of electrification strategies based mainly on microgrids according to the study scenario. The results of the first level of study enabled us to obtain an optimal location for the centroid of the cluster under consideration, according to the different load positions of this cluster. Then, the results of the second level of study were used to highlight the optimal resources obtained and proposed by the optimization model formulated based on the various technology costs, such as investment, maintenance, and operating costs, which were based on the technical limits of the various technologies. In these results, solar systems account for 80% of the maximum load considered, compared to 7.5% for wind systems and 12.5% for battery systems. Next, an optimal microgrid connection model was proposed based on the constraints of a voltage stability limit estimated to be 10% of the maximum voltage drop. The results obtained for the third level of study enabled us to present selective results for load nodes in relation to the source station node. Finally, the last results made it possible to plan electrification using different network technologies and systems in the short and long term. The case study of Togo was taken into account. The various results obtained from the different techniques provide the necessary leads for a feasibility study for optimal electrification of off-grid areas using microgrid systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Optimal, centralized dynamic curbside parking space zoning

In this paper we formulate a dynamic mixed integer program for optimally zoning curbside parking spaces subject to transportation policy-inspired constraints and regularization terms. First, we illustrate how given some objective of curb zoning valuation as a function of zone type (paid parking, bus stop, etc.), dynamically rezoning involves unrolling this optimization program over a fixed time horizon. Second, we implement two different solution methods given an example curb zoning valuation. In the first method, we solve long horizon dynamic zoning problems via approximate dynamic programming. In the second method, we employ Dantzig-Wolfe decomposition to break-up the mixed-integer program into a master problem and several sub-problems that can be solved in parallel. This speeds up the computational solve-time of the MIP considerably. We present simulation results and comparisons of the different employed techniques on vehicle arrival-rate data obtained for a neighborhood in downtown Seattle, Washington, USA.

Nazir, Mohammad Nawaf↗
NASA NTRS2005

Two Methods for Efficient Solution of the Hitting-Set Problem

A paper addresses much of the same subject matter as that of Fast Algorithms for Model-Based Diagnosis (NPO-30582), which appears elsewhere in this issue of NASA Tech Briefs. However, in the paper, the emphasis is more on the hitting-set problem (also known as the transversal problem), which is well known among experts in combinatorics. The authors primary interest in the hitting-set problem lies in its connection to the diagnosis problem: it is a theorem of model-based diagnosis that in the set-theory representation of the components of a system, the minimal diagnoses of a system are the minimal hitting sets of the system. In the paper, the hitting-set problem (and, hence, the diagnosis problem) is translated from a combinatorial to a computational problem by mapping it onto the Boolean satisfiability and integer- programming problems. The paper goes on to describe developments nearly identical to those summarized in the cited companion NASA Tech Briefs article, including the utilization of Boolean-satisfiability and integer- programming techniques to reduce the computation time and/or memory needed to solve the hitting-set problem.

Vatan, Farrokh↗
NASA NTRS1997

Dynamic Flow Management Problems in Air Transportation

In 1995, over six hundred thousand licensed pilots flew nearly thirty-five million flights into over eighteen thousand U.S. airports, logging more than 519 billion passenger miles. Since demand for air travel has increased by more than 50% in the last decade while capacity has stagnated, congestion is a problem of undeniable practical significance. In this thesis, we will develop optimization techniques that reduce the impact of congestion on the national airspace. We start by determining the optimal release times for flights into the airspace and the optimal speed adjustment while airborne taking into account the capacitated airspace. This is called the Air Traffic Flow Management Problem (TFMP). We address the complexity, showing that it is NP-hard. We build an integer programming formulation that is quite strong as some of the proposed inequalities are facet defining for the convex hull of solutions. For practical problems, the solutions of the LP relaxation of the TFMP are very often integral. In essence, we reduce the problem to efficiently solving large scale linear programming problems. Thus, the computation times are reasonably small for large scale, practical problems involving thousands of flights. Next, we address the problem of determining how to reroute aircraft in the airspace system when faced with dynamically changing weather conditions. This is called the Air Traffic Flow Management Rerouting Problem (TFMRP) We present an integrated mathematical programming approach for the TFMRP, which utilizes several methodologies, in order to minimize delay costs. In order to address the high dimensionality, we present an aggregate model, in which we formulate the TFMRP as a multicommodity, integer, dynamic network flow problem with certain side constraints. Using Lagrangian relaxation, we generate aggregate flows that are decomposed into a collection of flight paths using a randomized rounding heuristic. This collection of paths is used in a packing integer programming formulation, the solution of which generates feasible and near-optimal routes for individual flights. The algorithm, termed the Lagrangian Generation Algorithm, is used to solve practical problems in the southwestern portion of United States in which the solutions are within 1% of the corresponding lower bounds.

Patterson, Sarah Stock↗