Search NASA⌕ Search

SEARCH · Search NASA

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.

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

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Optimization-Driven Scenario Grouping

Scenario decomposition algorithms for stochastic programs compute bounds by dualizing all nonanticipativity constraints and solving individual scenario problems independently. Here, we develop an approach that improves on these bounds by reinforcing a carefully chosen subset of nonanticipativity constraints, effectively placing scenarios into groups. Specifically, we formulate an optimization problem for grouping scenarios that aims to improve the bound by optimizing a proxy metric based on information obtained from evaluating a subset of candidate feasible solutions. We show that the proposed grouping problem is NP-hard in general, identify a polynomially solvable case, and present two formulations for solving the problem: a matching formulation for a special case and a mixed-integer programming formulation for the general case. We use the proposed grouping scheme as a preprocessing step for a particular scenario decomposition algorithm and demonstrate its effectiveness in solving standard test instances of two-stage 0–1 stochastic programs. Using this approach, we are able to prove optimality for all previously unsolved instances of a standard test set. Additionally, we implement this scheme as a preprocessing step for PySP, a publicly available and widely used implementation of progressive hedging, and compare this grouping approach with standard grouping approaches on large-scale stochastic unit commitment instances. Finally, the idea is extended to propose a finitely convergent algorithm for two-stage stochastic programs with a finite feasible region.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A Parallel Computing Framework for Finding the Supported Solutions to a Biobjective Network Optimization Problem

Abstract Solving multi‐objective combinatorial optimization problems can quickly become computationally challenging when applied to large networks generated from big data. Present‐day first‐rate Mixed Integer Programming (MIP) solvers have parallelism built‐in to take advantage of multicore architectures; but specialized network optimization algorithms that can often solve graph problems more efficiently than a general MIP solver are typically programmed serially. Thus, these network algorithm implementations do not take full advantage of modern multicore computer capabilities. Many parallel computing languages include a fork/join framework into their concurrency packages that allow for simple conversion of recursive serial algorithms to operate in parallel without having to use complicated low‐level message‐passing interfaces. Fork/join is particularly well suited to divide and conquer algorithms such as Non‐Inferior Set Estimation (NISE) method for computing the supported Pareto front of a multi‐objective optimization problem. This work develops a simple general parallel NISE (pNISE) implementation using the Java 7 concurrency tools, and then offers results from a specific implementation of solving a bi‐objective shortest path problem. The results indicate that this method is capable of sizeable speed‐ups on both small‐scale personal computers as well as large‐scale shared memory supercomputers. Finally, other network problems suitable to this method are discussed, including multi‐objective variants of the minimum spanning tree problem, transportation problem, assignment problem, maximum flow problem, and the minimum‐cost flow problem. Copyright © 2015 John Wiley & Sons, Ltd.

Medrano, Fernando Antonio↗
DOE OSTI2018

Evolutionary computation algorithms to coordinating order acceptance and batch delivery for an integrated supply chain scheduling

This paper proposes a novel approach of coordinating decisions in an integrated supply chain (ISC): coordinating order acceptance (OA) and batch delivery (BD) due to round trip transportation (RTT) and using third-party logistics (3PL) vehicles. The paper aims at trading off among accepted orders revenue, delivery costs as well as any penalties incurred in the ISC to maximize the total benefit. A novel mixed-integer programming is proposed for the problem. In addition, the paper provides a heuristic to form batches and develops a hybrid evolutionary computation algorithms based on particle swarm optimization (PSO) and genetic algorithm (GA) to solve the problem. An information sharing mechanism is improved and applied. To explore and to locate the proposed PSO in a better neighborhood, a local search is proposed. Taguchi experimental design is utilized to set the appropriate values of the algorithms’ parameters and random instances are generated to evaluate the performance of the algorithms. The paper investigates the profitability sensitivity of the problem to parameters and analyzes the effect of the changes in the parameters on the performance of our proposed algorithms. The attained results show the appropriate performance of our algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Bi-objective approaches for home healthcare medical team planning and scheduling problem

In this paper, we study the medical team planning and scheduling in home healthcare within a weekly horizon, including the planning of nursing visits and the daily traveling route scheduling. Two objectives are considered: the first one is to minimize the total operation cost of the healthcare agency and the second one is to maximize the patient satisfaction. The problem is formulated as a mixed integer program, to seek for a trade-off between two objectives, with the characteristics of the patient requirements including nursing types, nursing frequency and service length considered. Medical team types, available service days and overwork penalty are also respected in the model. Then an ϵ-constraint method is adopted to obtain exact non-dominated solutions. To address large-scale problem instances, three heuristic approaches are developed to generate approximate Pareto fronts in a reasonable time. The set of non-dominated solutions are valuable for decision-making. Computational experiments are conducted and the results demonstrate the efficiency of the approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dispatch optimization of a concentrating solar power system under uncertain solar irradiance and energy prices

The integration of thermal energy storage into a concentrating solar power system allows for mitigating some of the risk associated with uncertain solar irradiance and uncertain energy prices. We solve a 48 h dispatch optimization model with continually updated conditional point forecasts of both direct normal irradiance (DNI) and electricity prices with a rolling-horizon scheme at hourly resolution over the course of a year. Joint, conditional forecasts for DNI and prices are formed using an autoregressive moving-average time series model with exogenous weather predictors. We guide dispatch using a mixed-integer programming model, but in order to evaluate performance we use the System Advisor Model (SAM) of the National Renewable Energy Laboratory. SAM is a techno-economic simulation model that accounts for plant thermodynamics with higher fidelity. Our conditional DNI forecasts improve annual revenue by 4%–12% over using historical forecasts based on data from previous years. Conditional price forecasts improve annual revenue by 6%–19% in the real-time market over analogous historical forecasts. Updating these forecasts every six hours, rather than every 24 h, further improves annual revenue by 5%–6%. Here, we also investigate a method that values terminal inventory in our dispatch optimization model, again when used in a rolling-horizon scheme.

14 SOLAR ENERGY↗
DOE OSTI2017

Sustainable network design for multi-purpose pellet processing depots under biomass supply uncertainty

This work develops a two-stage stochastic mixed-integer programming model to manage multi- purpose pellet processing depots under feedstock supply uncertainty. The proposed optimization model would help to minimize cost and to mitigate emissions from the supply chain network. We consider three alternative Biomass Processing and Densi cation Depot (BPDD) technologies; namely, conventional pellet processing, high moisture pellet processing, and ammonia ber expansion. These three technologies pre-process/pre-treat and densify different types of biomass into more highly densi ed intermediate products for different markets in order to improve movability and overall supply network performance in terms of costs and emissions. A hybrid decomposition algorithm was developed that combines sample average approximation with an enhanced Progressive Hedging (PH) algorithm to solve this challenging NP -hard problem. Some heuristics such as Rolling Horizon (RH) heuristic, variable xing technique were later applied to further enhance the PH algorithm. Mississippi and Alabama were selected as a testing ground and ArcGIS was employed to visualize and validate the modeling results. The results of the analysis reveal promising insights that could lead to recommendations to help decision makers achieve a more cost-effective environmentally-friendly supply chain network.

09 BIOMASS FUELS↗
DOE OSTI2020

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that effectively leverage the complementary strengths of deterministic algorithms and QC techniques to overcome combinatorial complexity for solving large-scale mixed-integer programming problems. Four applications, namely the molecular conformation problem, job-shop scheduling problem, manufacturing cell formation problem, and the vehicle routing problem, are specifically addressed. Large-scale instances of these application problems across multiple scales ranging from molecular design to logistics optimization are computationally challenging for deterministic optimization algorithms on classical computers. To address the computational challenges, hybrid QC-based algorithms are proposed and extensive computational experimental results are presented to demonstrate their applicability and efficiency. The proposed QC-based solution strategies enjoy high computational efficiency in terms of solution quality and computation time, by utilizing the unique features of both classical and quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Co-optimizing Generation and Transmission Expansion with Wind Power in Large-Scale Power Grids Implementation in the US Eastern Interconnection

This paper studies the generation and transmission expansion co-optimization problem with a high wind power penetration rate in the US Eastern Interconnection (EI) power grid. In this paper, the generation and transmission expansion problem for the EI system is modeled as a mixed-integer programming (MIP) problem. Our paper also analyzed a time series generation method to capture the variation and correlation of both load and wind power across regions. The obtained series can be easily introduced into the expansion planning problem and then solved through existing MIP solvers. Simulation results show that the proposed planning model and series generation method can improve the expansion result significantly through modeling more detailed information of wind and load variation among regions in the US EI system. Moreover, the improved expansion plan that combines generation and transmission will aid system planners and policy makers to maximize the social welfare in large-scale power grids.

17 WIND ENERGY↗
DOE OSTI2027

From zonal to nodal capacity expansion planning: Spatial aggregation impacts on a realistic test-case

Solving power system capacity expansion planning (CEP) problems at realistic spatial resolutions is computationally challenging. Thus, a common practice is to solve CEP over zonal models with low spatial resolution rather than over full-scale nodal power networks. Due to improvements in solving large-scale stochastic mixed integer programs, these computational limitations are becoming less relevant, and the assumption that zonal models are realistic and useful approximations of nodal CEP is worth revisiting. Here, this work is the first to conduct a systematic computational study on the assumption that spatial aggregation can reasonably be used for ISO-scale CEP. By considering a realistic, large-scale test network based on the state of California with over 8000 buses, we find that well-designed small spatial aggregations can yield good approximations but that coarser zonal models may result in large distortions of investment decisions, e.g., capacity under-investment of up to 41% for the lowest resolution model considered.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Feasible region-based heuristics for optimal transmission switching

In this paper, we develop a optimal transmission switching (OTS) heuristic based on DC optimal power flow (OPF) and assess the efficacy of the approach when implemented within AC OPF. Traditional formulations of the OTS problem can result in hundreds or thousands of binary variables for large networks, making the OTS problem challenging to solve on fast timescales even for relatively small networks. Here, we identify which constraints and therefore which variables are constraining the DC OPF feasible region, and rank them based on their impact on the cost function. We develop a heuristic algorithm which iteratively removes these constraints and solves a series of standard DC OPF problems. The heuristic is tested on a variety of PGlib networks and the results show that the algorithm can provide substantial cost decreases without having to solve any mixed integer programs. Additionally, we provide insights about the OTS problem, including identifying scenarios outside congestion where OTS can prove useful. Lastly, the performance of the DC-based heuristic is shown when the line switching decisions are implemented within AC OPF.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2015

Optimization of municipal solid waste collection and transportation routes

Graphical abstract: Display Omitted - Highlights: • Profitable integrated solid waste management system. • Optimal municipal waste collection scheme between the sources and waste collection centres. • Optimal path calculation between waste collection centres and transfer stations. • Optimal waste routing between the transfer stations and processing plants. - Abstract: Optimization of municipal solid waste (MSW) collection and transportation through source separation becomes one of the major concerns in the MSW management system design, due to the fact that the existing MSW management systems suffer by the high collection and transportation cost. Generally, in a city different waste sources scatter throughout the city in heterogeneous way that increase waste collection and transportation cost in the waste management system. Therefore, a shortest waste collection and transportation strategy can effectively reduce waste collection and transportation cost. In this paper, we propose an optimal MSW collection and transportation scheme that focus on the problem of minimizing the length of each waste collection and transportation route. We first formulize the MSW collection and transportation problem into a mixed integer program. Moreover, we propose a heuristic solution for the waste collection and transportation problem that can provide an optimal way for waste collection and transportation. Extensive simulations and real testbed results show that the proposed solution can significantly improve the MSW performance. Results show that the proposed scheme is able to reduce more than 30% of the total waste collection path length.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2013

Uncertainty Quantification in CO 2 Sequestration Using Surrogate Models from Polynomial Chaos Expansion

In this paper, surrogate models are iteratively built using polynomial chaos expansion (PCE) and detailed numerical simulations of a carbon sequestration system. Output variables from a numerical simulator are approximated as polynomial functions of uncertain parameters. Once generated, PCE representations can be used in place of the numerical simulator and often decrease simulation times by several orders of magnitude. However, PCE models are expensive to derive unless the number of terms in the expansion is moderate, which requires a relatively small number of uncertain variables and a low degree of expansion. To cope with this limitation, instead of using a classical full expansion at each step of an iterative PCE construction method, we introduce a mixed-integer programming (MIP) formulation to identify the best subset of basis terms in the expansion. This approach makes it possible to keep the number of terms small in the expansion. Monte Carlo (MC) simulation is then performed by substituting the values of the uncertain parameters into the closed-form polynomial functions. Based on the results of MC simulation, the uncertainties of injecting CO{sub 2} underground are quantified for a saline aquifer. Moreover, based on the PCE model, we formulate an optimization problem to determine the optimal CO{sub 2} injection rate so as to maximize the gas saturation (residual trapping) during injection, and thereby minimize the chance of leakage.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Real-Time Corrective Switching in Response to Simultaneous Contingencies

The standard optimal power flow (OPF) problem is an economic dispatch (ED) problem combined with transmission constraints, which are based on a static topology. Prior research has demonstrated that cooptimization of generation dispatch and transmission topology results in cost savings. However, the computational complexity associated with topology control (TC) has been a major deterrent to its implementation. The proposed work investigates the application of a heuristic, a greedy algorithm, to improve the computational time for the TC problem while still maintaining the ability to find quality solutions. An expression is derived, which indicates the impact on the objective for a marginal change in the state of a transmission line. This expression is used to generate a priority list with potential candidate lines for switching, which may provide huge improvements to the system. The advantage of this method is that it is a fast heuristic as compared to using mixed integer programming (MIP) to find a solution. The heuristic is tested on real-time applications such as N-1 events, N - m events (m simultaneous contingencies), and cascading events. The proposed algorithm specifically targets cases that lead to load shedding in the system and provides a quick and efficient method to restore the loads by improving the deliverability of reserves via TC. Simulation results on the IEEE 73 bus test system and the IEEE 118 bus test system suggest a significant improvement in the amount of load served to the system with TC as opposed to without TC with minimal time and computation.

Electric power systems↗
DOE OSTI2023

Co-design optimization of combined heat and power-based microgrids

With the emergent need for clean and reliable energy resources, hybrid energy systems, such as the microgrid, are widely adopted in the United States. A microgrid can consist of various distributed energy resources, for instance, combined heat and power (CHP) systems. Here, the CHP module is a distributed cogeneration technology that produces electricity and recaptures heat generated as a by-product. It is an energy-efficient technology converting heat that would otherwise be wasted to valuable thermal energy. For an optimal system configuration, this study develops a novel co-design optimization framework for CHP-based cogeneration microgrids. The framework provides the stakeholder with a method to optimize investments and attain resilient operations. The proposed co-design framework has a mixed integer programming (MIP) model that outputs decisions for both plant designs and operating controls. The microgrid considered in this study contains six components: the CHP, boiler, heat recovery unit, thermal storage system, power storage system, and photovoltaic plant. After solving the MIP model, the optimal design parameters of each component can be found to minimize the total installation cost of all components in the microgrid. Furthermore, the online costs from energy production, operation, maintenance, machine startup, and disruption-induced unsatisfied loads are minimized by solving the optimal control decisions for operations. Case studies based on designing a CHP-based microgrid with empirical data are conducted. Moreover, we consider both nominal and disruptive operational scenarios to validate the performance of the proposed co-design framework in terms of a cost-effective, resilient system.

42 ENGINEERING↗
DOE OSTI2020

An Optimization-Based Planning Tool for On-Demand Mobility Service Operations

Regions worldwide are adopting and exploring low-speed automated electric shuttle (AES) service as an on-demand shared mobility service in dense geofenced urban areas. Building on this concept, the National Renewable Energy Laboratory (NREL) recently developed the Automated Mobility District (AMD) toolkit. The AMD toolkit—comprising of a travel micro-simulation model and an energy estimation model—estimates the mobility and energy impacts of a given shuttle configuration within an AMD. Early-stage AMD deployments need to find optimal operational configurations that include: (a) passenger capacity of an AES, (b) time-dependent routes, and (c) fleet size (AES units) to satisfy the demand for the region. This research extends the AMD toolkit functionality by developing an optimization-based planning module that will assist in the operations of AES units. We developed a constrained mixed-integer program accounting for passenger waiting time, battery range, and passenger capacity of AES units. For scalability, we demonstrated the Tabu search-based solution technique for a real-world network—a proposed AMD deployment in Greenville, South Carolina, USA. Compared to rule-based operations, our developed solution yields higher travel time and energy savings for the network at different demand levels. The sensitivity analyses for waiting time thresholds indicate nonlinearity in the system performance, underscoring the need to meet shared-use mobility user-level expectations. The developed optimization framework can be adapted and extended to accommodate different categories of shared-use on-demand mobility services.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗
DOE OSTI2025

Strategic Placement and Sizing of Distributed Generation for Resilience Enhancement of Distribution Grids With Microgrid Formation

The rise in frequency and severity of extreme weather events highlights the need for resilient power distribution networks. Microgrids can help improve the resilience of distribution grids by providing continuous power supply using local distribution generation (DG) when the distribution grid fails. In this paper, we propose an approach for optimal placement and sizing of DG to form multiple microgrids throughout the distribution network by restoration actions such as switching operations in case of distribution grid outages caused by extreme weather events. Considering the randomness of damaged distribution lines, the DG placement and sizing problem is formulated as a two-stage stochastic mixed-integer program, with the first stage determining the placement and size of DG, and the second stage focusing on minimizing the amount of load shedding through network restoration and microgrid formations for each scenario. Due to the large number of scenarios, the sample average approximation (SAA) method is employed to solve the problem. The results of case studies on a modified IEEE 33 bus distribution grid demonstrate the effectiveness of the proposed DG placement and sizing strategy in improving the resilience of distribution grids by allowing the formation of multiple microgrids. In addition, the robustness and accuracy of the SAA method are validated through various case studies.

Distributed generation planning↗
DOE OSTI2016

Solving Open MIP Instances with ParaSCIP on Supercomputers Using up to 80,000 Cores

This paper describes how we solved 12 previously unsolved mixed-integer programming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper we describe the basic parallelization mechanism of ParaSCIP, improvements of the dynamic load balancing and novel techniques to exploit the power of parallelization for MIP solving. We give a detailed overview of computing times and statistics for solving open MIPLIB instances.

97 MATHEMATICS AND COMPUTING↗