Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Integer Optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Tightest Mixed-Integer Programming Formulations for Quadratic SCUC Optimization

In this project, we developed new, tighter Mixed-Integer Programming (MIP) formulations for the combined Alternating Current (AC) Security-Constrained Unit Commitment (SCUC) and Security-Constrained Optimal Power Flow (SCOPF). The work addresses a critical challenge in power system operations: efficiently determining which generation units to commit and how to optimally dispatch them while maintaining network reliability constraints for both normal and contingency scenarios. Our efforts: 1. Advance the Understanding of SCUC/SCOPF Modeling: By introducing tighter MIP formulations and leveraging cutting-edge optimization tools (Julia/JuMP, PowerModels.jl), this project has pushed forward the state of the art in efficient power systems scheduling. 2. Enhance Technical and Economic Feasibility: The methods developed provide more accurate and potentially faster solutions to large-scale, realistic scheduling and dispatch problems in electric power systems, which can translate into improved reliability and potentially lower costs for grid operations. 3. Benefit to the Public: Greater efficiency in power system operations leads to cost savings for utilities and end-users. Improved reliability and integration of advanced modeling approaches can facilitate the adoption of clean energy resources and better accommodate uncertainties in renewable generation. Because this technology could impact bulk power markets and reliability, these innovations have far-reaching public benefits in terms of cost savings, reliability, and sustainability.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Multilane Automated Driving With Optimal Control and Mixed-Integer Programming

Road vehicle lane changes often initiate traffic disturbances and can therefore impact road networks’ energy and time efficiency. Furthermore, unexpected changes in traffic conditions may also render lane changes counterproductive for the lane-changing vehicle. Vehicle-to-vehicle connectivity combined with anticipative control could address these challenges via improved lane change decisions by automated vehicles. In a move toward this objective, receding horizon control cast as a mixed-integer quadratic program is used to plan lane changing and acceleration in a coupled optimization. A long-term pacing module, based on Pontryagin’s minimum principle from optimal control theory, sets terminal and input references for receding horizon control to target a user’s expected travel time. To remove nonlinear vehicle dynamics from the receding horizon controller, lane change commands are passed to a pure pursuit steering module whose response is approximated by a second-order linear model. Here, comparison against a rule-based reactive algorithm in arterial and highway scenarios shows an 8.9%–13.7% reduction in energy consumption and a 5.2%–10.3% reduction in the travel time, along with navigational improvements.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS2008

Efficient G(sup 4)FET-Based Logic Circuits

A total of 81 optimal logic circuits based on four-gate field-effect transistors (G(sup 4)4FETs) have been designed to implement all Boolean functions of up to three variables. The purpose of this development was to lend credence to the expectation that logic circuits based on G(sup 4)FETs could be more efficient (in the sense that they could contain fewer transistors), relative to functionally equivalent logic circuits based on conventional transistors. A G(sup 4)FET a combination of a junction field-effect transistor (JFET) and a metal oxide/semiconductor field-effect transistor (MOSFET) superimposed in a single silicon island and can therefore be regarded as two transistors sharing the same body. A G(sup 4)FET can also be regarded as a single device having four gates: two side junction-based gates, a top MOS gate, and a back gate activated by biasing of a silicon-on-insulator substrate. Each of these gates can be used to control the conduction characteristics of the transistor; this possibility creates new options for designing analog, radio-frequency, mixed-signal, and digital circuitry. One such option is to design a G(sup 4)FET to function as a three-input NOT-majority gate, which has been shown to be a universal and programmable logic gate. Optimal NOT-majority-gate, G(sup 4)FET-based logic-circuit designs were obtained in a comparative study that also included formulation of functionally equivalent logic circuits based on NOR and NAND gates implemented by use of conventional transistors. In the study, the problem of finding the optimal design for each logic function and each transistor type was solved as an integer-programming optimization problem. Considering all 81 non-equivalent Boolean functions included in the study, it was found that in 63% of the cases, fewer logic gates (and, hence, fewer transistors) would be needed in the G(sup 4)FET-based implementations.

Vatan, Farrokh↗
DOE OSTI2021

Optimizing design and dispatch of a renewable energy system

Renewable energy technologies are becoming increasingly important due to their cost-competitiveness, and because of enhanced climate concerns. We demonstrate the capabilities of an integer-programming optimization model that minimizes capital (investment) and operational costs, and utility charges, while adhering to system sizing constraints, demand requirements, and interoperability characteristics of the systems chosen. Furthermore, the model recommends an optimally sized mix of renewable energy, conventional generation, and energy storage technologies, while simultaneously optimizing the corresponding dispatch strategy. Our case studies explore several venues, i.e., a small campus and a local hospital, with complex utility rate tariffs, multi-technology integration opportunities, and incentives for renewable power production. Using an optimization model, versus applying rules of thumb, can produce millions of dollars in savings over a 25-year time horizon and result in thousands of kilowatts of installed renewable energy.

25 ENERGY STORAGE↗
DOE OSTI2021

Optimal decision trees for categorical data via integer programming

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

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Protection settings optimizer

SAND2023-06672O The Protection Settings Optimizer (PSO) uses system and fault data as inputs to formulate the problem of calculating relay settings as a mixed integer, nonlinear optimization problem (MINLP). The MINLP is solved using a genetic algorithm-based optimizer that attempts to find settings to reduce the relay operating times. The PSO protects the power system by using the steady-state fault voltages and currents, which then calculates the optimal device setting to protect the power system. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Patel, Trupal↗
DOE OSTI2020

The potential of quantum annealing for rapid solution structure identification

Abstract The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations of unquestionable performance gains leveraging novel hardware platforms have faced significant obstacles. One key challenge is understanding the algorithmic properties that distinguish such devices from established optimization approaches. Through the careful design of contrived optimization tasks, this work provides new insights into the computation properties of quantum annealing and suggests that this model has the potential to quickly identify the structure of high-quality solutions. A meticulous comparison to a variety of algorithms spanning both complete and local search suggests that quantum annealing’s performance on the proposed optimization tasks is distinct. This result provides new insights into the time scales and types of optimization problems where quantum annealing has the potential to provide notable performance gains over established optimization algorithms and suggests the development of hybrid algorithms that combine the best features of quantum annealing and state-of-the-art classical approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A Lagrangian dual method for two-stage robust optimization with binary uncertainties

This report presents a new exact method to calculate worst-case parameter realizations in two-stage robust optimization problems with categorical or binary-valued uncertain data. Traditional exact algorithms for these problems, notably Benders decomposition and column-and-constraint generation, compute worst-case parameter realizations by solving mixed-integer bilinear optimization subproblems. However, their numerical solution can be computationally expensive not only due to their resulting large size after reformulating the bilinear terms, but also because decision-independent bounds on their variables are typically unknown. We propose an alternative Lagrangian dual method that circumvents these difficulties and is readily integrated in either algorithm. We specialize the method to problems where the binary parameters switch on or off constraints as these are commonly encountered in applications, and discuss extensions to problems that lack relatively complete recourse and to those with integer recourse. Numerical experiments provide evidence of significant computational improvements over existing methods.

42 ENGINEERING↗
DOE OSTI2023

Optimization of Energy Storage System Economics and Controls by Incorporating Battery Degradation Costs in REopt

The use of stationary electrochemical energy storage systems utilizing lithium-ion batteries has increased rapidly as the production scale and price for lithium-ion batteries has decreased. These energy storage systems are crucial for maintaining grid resiliency, especially for grids operating with high penetration of renewable energy generation assets or for with a variety of distributed energy generation and storage systems. One challenging factor for the development of battery energy storage systems is estimating the proper sizing, in terms of both power and energy, that minimizes total costs over the lifetime of the systems; this calculation is difficult in simple cases, where a battery is costed independently, but is extremely challenging when building loads and electrical generation by photovoltaic resources are also considered. REopt is a techoeconomic optimization tool developed by NREL to address these challenges. Previously, battery degradation has been priced by simply assuming a 10-year replacement schedule for battery systems. However, this does not account for varying degradation trends observed across real-world batteries, or allow for batteries to be operated in a degradation-aware manner that optimizes battery dispatch based on operating costs. This work incorporates a battery life model into REopt. This battery life model is simple, so that it may be solvable within the constrains of a mixed-integer linear optimization problem, but is fit to accelerated aging data recorded in the lab. To achieve the best possible accuracy for lifetime estimates given these constraints, parameters for the battery life model in REopt are estimated by fitting 20-year simulations of battery life after identifying state-space battery degradation model from accelerated aging data. Comparisons of battery life predicted in REopt and from the state-space battery degradation model to ensure validity of lifetime estimates made by REopt. Battery life and cost is optimized by controlling three decision to minimize system life cost: battery sizing, daily state-of-charge, and daily energy-throughput. The cost of battery degradation as a function of these control variables is then estimated assuming two possible maintenance strategies: replacement, where the entire battery system is replaced if cell reach an end-of-life capacity threshold; and augmentation, which establishes a fund to pay for continual purchase of new batteries to maintain the initial energy capacity of the system. These two strategies offer conservative (for replacement) and optimistic (for augmentation) bounds for total system cost. The degradation cost incurred by these strategies is then used to control battery dispatch decisions, operating the battery in a degradation-aware manner that maximizes battery lifetime while also providing energy when favorable. Because the mixed-integer linear program has perfect foresight of future energy needs, batteries with degradation costs are always operated using 'just-in-time' charging, which is unrealistic, as no energy is left in the storage system to perform other energy services or to serve as emergency back-up power. To combat this, an inequality constraint on the average annual state-of-charge is imposed, and the sensitivity of system cost to average stored energy, e.g., the cost of system resiliency, can be quantified. Analysis of results has several conclusions, for instance, oversizing of battery storage systems is not a cost burden when battery storage is an optimal solution, as any additional battery capacity can simply be utilized to avoid costs of purchasing energy from a utility.

battery↗
NASA NTRS1989

Optimal selection of space transportation fleet to meet multi-mission space program needs

A space program that spans several decades will be comprised of a collection of missions such as low earth orbital space station, a polar platform, geosynchronous space station, lunar base, Mars astronaut mission, and Mars base. The optimal selection of a fleet of several recoverable and expendable launch vehicles, upper stages, and interplanetary spacecraft necessary to logistically establish and support these space missions can be examined by means of a linear integer programming optimization model. Such a selection must be made because the economies of scale which comes from producing large quantities of a few standard vehicle types, rather than many, will be needed to provide learning curve effects to reduce the overall cost of space transportation if these future missions are to be affordable. Optimization model inputs come from data and from vehicle designs. Each launch vehicle currently in existence has a launch history, giving rise to statistical estimates of launch reliability. For future, not-yet-developed launch vehicles, theoretical reliabilities corresponding to the maturity of the launch vehicles' technology and the degree of design redundancy must be estimated. Also, each such launch vehicle has a certain historical or estimated development cost, tooling cost, and a variable cost. The cost of a launch used in this paper includes the variable cost plus an amortized portion of the fixed and development costs. The integer linear programming model will have several constraint equations based on assumptions of mission mass requirements, volume requirements, and number of astronauts needed. The model will minimize launch vehicle logistic support cost and will select the most desirable launch vehicle fleet.

Morgenthaler, George W.↗
NASA NTRS1975

Optimal source codes for geometrically distributed integer alphabets

An approach is shown for using the Huffman algorithm indirectly to prove the optimality of a code for an infinite alphabet if an estimate concerning the nature of the code can be made. Attention is given to nonnegative integers with a geometric probability assignment. The particular distribution considered arises in run-length coding and in encoding protocol information in data networks. Questions of redundancy of the optimal code are also investigated.

Gallager, R. G.↗
DOE OSTI2023

Encoding trade-offs and design toolkits in quantum algorithms for discrete optimization: coloring, routing, scheduling, and other problems

Challenging combinatorial optimization problems are ubiquitous in science and engineering. Several quantum methods for optimization have recently been developed, in different settings including both exact and approximate solvers. Addressing this field of research, this manuscript has three distinct purposes. First, we present an intuitive method for synthesizing and analyzing discrete (i.e., integer-based) optimization problems, wherein the problem and corresponding algorithmic primitives are expressed using a discrete quantum intermediate representation (DQIR) that is encoding-independent. This compact representation often allows for more efficient problem compilation, automated analyses of different encoding choices, easier interpretability, more complex runtime procedures, and richer programmability, as compared to previous approaches, which we demonstrate with a number of examples. Second, we perform numerical studies comparing several qubit encodings; the results exhibit a number of preliminary trends that help guide the choice of encoding for a particular set of hardware and a particular problem and algorithm. Our study includes problems related to graph coloring, the traveling salesperson problem, factory/machine scheduling, financial portfolio rebalancing, and integer linear programming. Third, we design low-depth graph-derived partial mixers (GDPMs) up to 16-level quantum variables, demonstrating that compact (binary) encodings are more amenable to QAOA than previously understood. We expect this toolkit of programming abstractions and low-level building blocks to aid in designing quantum algorithms for discrete combinatorial problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Alternating Direction Decomposition with Strong Bounding and Convexification (ADDSBC) for Solving Security Constrained AC Unit Commitment Problems

This project aims to develop efficient and robust computational methods for solving the security-constrained unit commitment and alternating current optimal power flow problem (SC-UC-ACOPF). The SC-UC-ACOPF problem is at the center of the short-term operation of the U.S. Power Grid. It is solved every week, every day, and every 10 minutes to plan for the optimal action of electricity generation and consumption by minimizing the generation cost and maintaining power system reliability against potential disruptions of equipment failures. In mathematical terms, SC-UC-ACOPF is a challenging large-scale mixed-integer nonlinear optimization model. This means that the decisions involve both discrete variables, e.g. the turning on and off of generators and switching of transmission lines and transformers, and continuous decisions, e.g. the amount of energy generated by each generator and the power flows in the power grid. The physics of the power flow is described by nonlinear equations involving real and reactive power and bus voltages. Another key feature is the large number of contingencies, i.e. the system needs to stay reliable in face of failure of any one equipment, such as transmission lines and generators. The U.S. power grids are extremely complicated and large scale with more than 5,000 generators, 50,000 buses, and 100,000 high-voltage transmission lines, making the SC-UC-ACOPF a very large-scale computation challenge. The research developed in this project aims to solve the SC-UC-ACOPF problems in the three timescales, i.e. weekly, daily, and every 10-min. The proposed computational methods are built on a principled algorithmic approach of decomposition and penalization. More specifically, the algorithm develops spatial and temporal decomposition by exploiting the strong temporal coupling and weak spatial coupling of the UC problem and the complementary feature, i.e. weak temporal coupling and strong spatial coupling of the ACOPF problem. The algorithm also leverages recent progresses in strong convex relaxation of ACOPF. A unique feature of the proposed approach is that it generates a valid, global upper bound on the optimal maximum profit. In this way, a global optimality gap is available to measure the quality of the solution. To further speed up computation, the research team has developed a plethora of effective heuristics to strengthen the iterative penalty-based decomposition framework. For instance, a heuristic is developed to construct inner approximations of the time coupling constraints within the time decoupled problems. Contingencies are pre-screened and low-rank matrix computation is exploited to find the almost unique solution to each contingency. A novel heuristic for line switching is proposed and tested with positive impacts on instances where line switching is beneficial. Taking a systematic approach and carefully handling every detail of the problem pays off. The TIM-GO’s performance throughout the trials and the final event was stellar. TIM-GO garnered the second highest total prize money and is ranked in the top three positions across all categories of comparison.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

New approaches for efficient solution of hitting set problem

A new method for solving the hitting set problem is proposed. This method is based on the mapping of the problem onto an integer programming optimization problem. this new approach provides an algorithm with much better performance compare to the algorithms for the hitting set problem that currently are used for solving the diagnosis problem.

integer programming↗
DOE OSTI2025

Energy efficiency in industrial drying: A hybrid ultrasonic system with a novel dynamic optimization framework

Drying processes are among the most energy-consuming operations in industrial and manufacturing settings, demanding strategic selection, design, and control for enhanced efficiency. Advancing drying technologies is critical for improving sustainability, lowering energy use, reducing carbon emissions, and minimizing waste. This study explores two innovative strategies aimed at transforming drying processes into sustainable, low-carbon systems by reducing energy consumption, minimizing waste, and maintaining a strong emphasis on preserving product quality. The first strategy showcases a sub-pilot scale hybrid ultrasonic-convective dryer for agrifood products. This technology, powered by electricity (process electrification), integrates non-thermal ultrasonic dehydration with convective heating and is presented as a sustainable and energy-efficient solution that enhances eco-friendly practices. The second strategy involves introducing and implementing a novel, multiobjective, mixed integer dynamic optimization technique to determine the optimal time-dependent process parameter values for the drying operation. This optimization technique yields operating conditions that are piecewise constant in time aiming to maximize the energy efficiency of the hybrid ultrasonic-convective dryer while ensuring strict adherence to product quality constraints. By adopting the hybrid ultrasonic-convective dryer, a notable 35% improvement in energy efficiency was achieved compared to conventional hot-air drying systems for drying apple slices. The proposed optimization framework further enhanced energy efficiency by nearly 14% over the most efficient process on the identical testbed, under static operating conditions. The reported enhancements have been experimentally validated. Regarding drying time (thereby improving production yield), the developed hybrid ultrasonic-convective dryer demonstrates as much as a 41% reduction in total processing time, which is further optimized by an additional 10% using our proposed optimization framework. The research outcomes have profound implications for the design and operation of drying systems, encompassing crucial aspects such as process electrification, cost-effectiveness, energy savings, time efficiency, product yield, product quality, and process automation.

Dynamic optimization↗
DOE OSTI2021

Optimal Design of Sustainable Ammonia-Based Food–Energy–Water Systems with Nitrogen Management

As the basis for virtually any form of nitrogen fertilizers, ammonia plays a vital role in agriculture; in addition, there has been an increased interest in its use as a carbon-free energy carrier. However, ammonia is also associated with two major environmental concerns: CO 2 emissions from the conventional production process and nitrogen pollution from the excessive use of ammonia-based fertilizers. To mitigate these environmental impacts, we develop an optimization framework for the design of a sustainable ammonia-based agricultural system that synergistically integrates the production of ammonia from renewable resources and effective measures for nitrogen management. The proposed model captures the effect of intermittency by incorporating both design and detailed operational decisions. Here, by applying a multiscale time representation that reduces the problem size and a tailored surrogate model that accurately approximates model nonlinearity, we are able to achieve optimal solutions within reasonable computation times. A computational case study is conducted using real-world data from a local farm in Morris, Minnesota, and the results indicate the trade-off between cost and nitrogen loss. Importantly, we show that practicing effective nitrogen management can significantly reduce the nitrogen loss with only a small increase in net present cost.

10 SYNTHETIC FUELS↗
DOE OSTI2025

Networked Microgrid Topology Reconfiguration to Promote Fairness in Proactive Load Shedding

Increasing occurrences of natural disasters and grid emergency events consistently challenge the safe and reliable operations of power systems. During such emergency situations, system operators may proactively shed load to mitigate risks. However, uncoordinated implementation of load shedding may disrupt electricity supply and even lead to cascading failures. Meanwhile, it is crucial to address potential biases affecting different customers when executing load shedding. This paper addresses the dynamic topology reconfiguration problem for networked microgrids with distributed energy resources under emergency conditions. Specifically, we propose a novel rolling-horizon optimization model that integrates fairness-aware constraints into the networked microgrid topology reconfiguration. Unlike existing approaches that focus solely on efficiency or apply fairness considerations in static settings, our method explicitly incorporates temporal fairness constraints to restrict repeated or excessive load curtailment for load blocks. Moreover, the fairness-aware constraints are specifically developed for the context of dynamic networked microgrid topology reconfiguration, and are designed to be convex or amenable to linear reformulations, which offers a more tractable alternative to traditional models with non-convex formulations. Numerical studies on a modified IEEE 13-bus system and a larger-sized SMART-DS networked microgrid system demonstrate the performance of the proposed algorithm towards more fairness-aware networked microgrid topology reconfiguration decision-making.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

97 MATHEMATICS AND COMPUTING↗