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 163 records · Page 9

Optimal assignment for the single-household shared autonomous vehicle problem

Autonomous vehicles have the potential to transform the way people are transported. While driverless technology may mean fewer vehicles are required to transport people to and from their daily activities, such changes may result in increased congestion or total miles traveled. In this study, we solve the single-household shared autonomous vehicle problem to identify cost-optimal routings of vehicles throughout the day. Such a tool will be useful for consumers seeking to minimize cost and for regulators seeking to understand and predict how people may behave in different scenarios. Here, we provide a thorough literature review and construct a mixed-integer linear program to minimize the daily travel cost of a household attending a given set of activities. Since solution time is a determinant for applicability of such a model, we present the model in a component-wise fashion. This approach allows us to understand which features most affect the problem complexity and solution time. We note that modeling carpooling is the feature that most increases time to find an optimal solution, and we therefore propose a novel modeling technique for carpooling two people. We illustrate the performance of our model by comparing it with other models from the literature and note that our model can solve significantly larger problem instances and in a time that is short enough to facilitate real-time scheduling. We also highlight the utility of our model for regulators, who can use it to analyze quickly produced optimal routes under different cost/tax scenarios.

33 ADVANCED PROPULSION SYSTEMS↗

McCormick envelopes in mixed-integer PDE-constrained optimization

McCormick envelopes are a standard tool for deriving convex relaxations of optimization problems that involve polynomial terms. Such McCormick relaxations provide lower bounds, for example, in branch-and-bound procedures for mixed-integer nonlinear programs but have not gained much attention in PDE-constrained optimization so far. This lack of attention may be due to the distributed nature of such problems, which on the one hand leads to infinitely many linear constraints (generally state constraints that may be difficult to handle) in addition to the state equation for a pointwise formulation of the McCormick envelopes and renders bound-tightening procedures that successively improve the resulting convex relaxations computationally intractable. We analyze McCormick envelopes for a model problem class that is governed by a semilinear PDE involving a bilinearity and integrality constraints. We approximate the nonlinearity and in turn the McCormick envelopes by averaging the involved terms over the cells of a partition of the computational domain on which the PDE is defined. This yields convex relaxations that underestimate the original problem up to an a priori error estimate that depends on the mesh size of the discretization. These approximate McCormick relaxations can be improved by means of an optimization-based bound-tightening procedure. We show that their minimizers converge to minimizers to a limit problem with a pointwise formulation of the McCormick envelopes when driving the mesh size to zero. We provide a computational example, for which we certify all of our imposed assumptions. The results point to both the potential of the methodology and the gaps in the research that need to be closed. Our methodology provides a framework first for obtaining pointwise underestimators for nonconvexities and second for approximating them with finitely many linear inequalities in an infinite-dimensional setting.

Approximations and Expansions↗

Disjunctive optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems

This paper proposes a new optimization model and algorithm for long-term capacity expansion planning of reliable power generation systems. The model optimizes both investment decisions (e.g., size, location, and time to install, retire and decommission facilities) and operation decisions (e.g., on/off status, operating capacity, and expected power output). It is also able to optimize reserve systems (or backup systems), as well as the main systems, to improve power systems reliability. An impact of operational strategies of generators (i.e., participating in electricity production vs. remaining as idle units during operation) on power systems reliability is considered. Probability of equipment failures and capacity failure states are used to rigorously estimate the power systems reliability depending on design and operation strategies. The optimization model is formulated with Generalized Disjunctive Programming (GDP), which is reformulated as a mixed-integer linear programming (MILP) model using the Hull relaxation. Two reliability-related penalties, such as downtime penalty and unmet demand penalty, are included in the objective function to maximize reliability while minimizing the total net present cost. Furthermore, a bilevel decomposition with tailored cuts is developed to reduce computational times of the multi-scale optimization model. The effectiveness of the proposed model is shown by comparing the results with the results obtained from the expansion planning models that do not explicitly consider reliability. In conclusion, we also show that the proposed bilevel decomposition is computationally efficient for solving large scale problems through 5-years and 10-years planning case studies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

ALPS: A Linear Program Solver

ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.

Ferencz, Donald C.↗

Qualitative trend analysis based on a mixed-integer representation

Shape constrained spline fitting is a useful method to impose prior knowledge onto flexible semi-parametric models during parameter estimation. Most typically, the function shape is imposed through order restrictions on the regression coefficients. The intended shape is considered known or selected based on heuristic rules. In this study, we present a method to estimate the optimal set of order restrictions to segment a univariate data series into episodes with distinct shapes. This is also known as the qualitative trend analysis (QTA) problem. The obtained solution uses a trade-off between lack-of-fit and model complexity. Further, our practical implementation takes inspiration from the generalized order restricted information criterion (GORIC) for inequality-constrained model selection. From this, one learns (a) that QTA can be formulated as a mixed-integer quadratic program (MIQP) and (b) that the newly proposed mixed order restricted information criterion (MORIC) enables optimal segmentation. This is illustrated through didactic case studies.

42 ENGINEERING↗

Optimal Scheduling of an Isolated Microgrid With Battery Storage Considering Load and Renewable Generation Uncertainties

By modeling the uncertainty of spinning reserves provided by energy storage with probabilistic constraints, a new optimal scheduling mode is proposed in this paper for minimizing the operating costs of an isolated microgrid (MG) by using chance-constrained programming. The model is transformed into a readily solvable mixed integer linear programming formulation in general algebraic modeling system (GAMS) via a proposed discretized step transformation approach and finally solved by applying the CPLEX solver. By properly setting the confidence levels of the spinning reserve probability constraints, the MG operation can achieve a tradeoff between reliability and economy. The test results on the modified Oak Ridge National Laboratory Distributed Energy Control and Communication lab MG test system reveal that the proposal significantly exceeds the commonly used hybrid intelligent algorithm with much better and more stable optimization results and significantly reduced calculation times.

Li, Yang↗

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↗

Cost-optimal evaluation of centralized and distributed microgrid topologies considering voltage constraints

Optimal design of hybrid renewable mini-grids requires both economic and power quality considerations. Existing modeling approaches address these considerations via separate or loosely coupled models. Here, we extend REopt—a techno-economic optimization model developed at the National Renewable Energy Laboratory—to consider both within a single model. REopt formulates the design problem as a mixed-integer linear program that solves for a site's optimal technology mix, sizing, and operation to minimize life cycle cost. REopt has traditionally assumed a single node system. In the work presented here, we expand the REopt platform to consider multiple connected nodes with associated voltage constraints. In order to do this, we model power flow using a fixed-point linear approximation method. Additionally, we then use the model to explore design considerations of mini-grids in Sub-Saharan Africa. Specifically, we evaluate under what combinations of transmission line distance and capacity it is technically viable and economically preferable to build multiple isolated mini-grids versus an interconnected, centralized system.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Design Considerations of a Coordinative Demand Charge Mitigation Strategy

This paper presents a coordinative demand charge mitigation (DCM) strategy for reducing electricity consumption during system peak periods. Available DCM resources include batteries, diesel generators, controllable loads, and conservation voltage reduction. All resources are directly controlled by load serving entities. A mixed integer linear programming based energy management algorithm is developed to optimally coordinate of DCM resources considering the load payback effect. To better capture system peak periods, two different kinds of load forecast are used: the day-ahead load forecast and the peak-hour probability forecast. Five DCM strategies are compared for reconciling the discrepancy between the two forecasting results. The DCM strategies are tested using actual utility data. Simulation results show that the proposed algorithm can effectively mitigate the demand charge while preventing the system peak from being shifted to the payback hours. We also identify the diminishing return effect, which can help load serving entities optimize the size of their DCM resources.

Hu, Rongxing↗

Toward a MILP Modeling Framework for Distribution System Restoration

Large-scale blackouts and extreme weather events in recent decades raise the concern for improving the resilience of electric power infrastructures. Distribution service restoration (DSR), a fundamental application in outage management systems, allows restoration solutions for system operators when power outages happen. As distribution generators (DGs) and remotely controllable devices are increasingly installed in distribution systems, an advanced DSR framework is critical to perform optimally coordinated restoration that can achieve maximal restoration performance. This work introduces a DSR modeling framework, which can generate optimal switching sequences and estimated time of restoration in the presence of remotely controllable switches, manually operated switches, and dispatchable DGs. Two mathematical models, a variable time step model and a fixed time step model, are presented and compared. The proposed models are formulated as a mixed-integer linear programming model, and their effectiveness is evaluated via the IEEE 123 node test feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗

An Approach to Reasoning Service Migration in Data and Reasoning Fabric (DRF) Implementation

In this paper we consider service migration problem for Data and Reasoning Fabric (DRF) enabled airspace operations assuming a fixed cloud/edge infrastructure with allocated computing, storage and power resources, where cloud/edge servers, and communication stations are in a wired connected network, while vehicles use a wireless network for communication. The objective is to automatically select the best location for the requested service execution, which achieves minimum cost while satisfying the user quality of service (QoS) and available resources constraints. To this end, estimates of the response time, consumed energy and total cost are defined for each potential compute location. A mixed-integer linear program is then formulated and solved to identify optimal compute locations given QoS constraints, network infrastructure limitations, with worst-case vehicle positioning. The approach is applied to trajectory re-planning use case to avoid a collision with an emergency vehicle in real time.

Air mobility↗

Delivery drone route planning over a battery swapping network

Many enterprises invest on drone delivery research and development to drop off packages at consumers’ doorsteps in a matter of minutes. We study delivery drone route planning over a battery swapping network allowing farther reach by penetrating current battery capacity constraints. A mixed-integer nonlinear programming model is created to plan efficient drone routing over the swapping machines by minimizing the delivery lead time. We develop an exact solution method, evaluate its performance, and compare it with a straightforward nonlinear solver application. A case study highlights the applicability of the model. Data and source code to the solver are publicly shared.

drone battery swapping↗

An MILP-Based Distributed Energy Management for Coordination of Networked Microgrids

An MILP-based distributed energy management for the coordination of networked microgrids is proposed in this paper. Multiple microgrids and the utility grid are coordinated through iteratively adjusted price signals. Based on the price signals received, the microgrid controllers (MCs) and distribution management system (DMS) update their schedules separately. Then, the price signals are updated according to the generation–load mismatch and distributed to MCs and DMS for the next iteration. The iteration continues until the generation–load mismatch is small enough, i.e., the generation and load are balanced under agreed price signals. Through the proposed distributed energy management, various microgrids and the utility grid with different economic, resilient, emission and socio-economic objectives are coordinated with generation–load balance guaranteed and the microgrid customers’ privacy preserved. In particular, a piecewise linearization technique is employed to approximate the augmented Lagrange term in the alternating direction method of multipliers (ADMM) algorithm. Thus, the subproblems are transformed into mixed integer linear programming (MILP) problems and efficiently solved by open-source MILP solvers, which would accelerate the adoption and deployment of microgrids and promote clean energy. The proposed MILP-based distributed energy management is demonstrated through various case studies on a networked microgrids test system with three microgrids.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Optimal Sizing and Dispatch of Solar Power with Storage

Designers of utility-scale solar plants with storage, seeking to maximize some aspect of plant performance, face multiple challenges. In many geographic locations, there is significant penetration of photovoltaic generation, which depresses energy prices during the hours of solar availability. An energy storage system affords the opportunity to dispatch during higher-priced time periods, but complicates plant design and dispatch decisions. Solar resource variability compounds these challenges, because determining optimal system sizes requires simultaneously considering how the plant will be operated under the imposed market and weather conditions. We develop an approach to analyze the economic performance of hybrid and single-technology solar power plants, which incorporates optimal dispatch, and considers the expected electricity market and weather conditions. We utilize the System Advisor Model software package to simulate the operation of multiple renewable generation and energy storage technologies, in conjunction with hourly-fidelity generation decisions determined by a revenue-maximizing, mixed-integer linear program. We show that, under our assumed market and weather conditions, the lifetime benefit-to-cost ratio can be improved by 6 to 19 percent, relative to a baseline design without optimizing, and that a concentrating solar power with thermal energy storage design produces significantly more energy per year, but is less profitable under our cost assumptions.

black-box optimization↗

Designing a drone delivery network with automated battery swapping machines

Drones are projected to alter last-mile delivery, but their short travel range is a concern. In this study, we propose a drone delivery network design using automated battery swapping machines (ABSMs) to extend ranges. The design minimizes the long-term delivery costs, including ABSM investment, drone ownership, and cost of the delivery time, and locates ABSMs to serve a set of customers. We build a mixed-integer nonlinear program that captures the nonlinear waiting time of drones at ABSMs. To solve the problem, we create an exact solution algorithm that finds the globally optimal solution using a derivative-supported cutting-plane method. To validate the applicability of our program, we conduct a case study on the Chicago Metropolitan area using cost data from leading ABSM manufacturer and geographical data from the planning and operations language for agent-based regional integrated simulation (more commonly known as POLARIS). A sensitivity analysis identifies that ABSM service times and costs are the key parameters impacting the long-term adoption of drone delivery.

25 ENERGY STORAGE↗

Robust trajectory-constrained frequency control for microgrids considering model linearization error

Grid supportive modes integrated within inverter-based resources can improve the frequency response of renewable-rich microgrids. The synthesis of grid supportive modes to guarantee frequency trajectory constraints under a predefined disturbance set is challenging but essential. To tackle this challenge, a numerical optimal control (NOC)-based control synthesis methodology is proposed. Without loss of generality, a wind-diesel fed microgrid is studied, where we aim to design grid supportive functions in the wind turbine. In the control design, linearized models are used, and the linearization-induced errors are quantitatively analyzed by reachability and interval arithmetics and represented in the form of interval uncertainties. Then, the NOC problem can be formulated into a robust mixed-integer linear program. The control structure is strategically configured into two levels to realize online deployment. The proposed control is verified on the modified 33-node microgrid with a full-order three-phase nonlinear model in Simulink. In conclusion, the simulation results show the effectiveness of the proposed control paradigm and the necessity of considering linearization-induced uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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↗