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At least 109 records · Page 6

All sources NASA NTRS DOE OSTI

DOE OSTI2020

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↗

NASA NTRS1990

Ascent guidance algorithm using lidar wind measurements

The formulation of a general nonlinear programming guidance algorithm that incorporates wind measurements in the computation of ascent guidance steering commands is discussed. A nonlinear programming (NLP) algorithm that is designed to solve a very general problem has the potential to address the diversity demanded by future launch systems. Using B-splines for the command functional form allows the NLP algorithm to adjust the shape of the command profile to achieve optimal performance. The algorithm flexibility is demonstrated by simulation of ascent with dynamic loading constraints through a set of random wind profiles with and without wind sensing capability.

Cramer, Evin J.↗

NASA NTRS1986

The expanded LaGrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrainted optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

NASA NTRS1988

The expanded Lagrangian system for constrained optimization problems

Smooth penalty functions can be combined with numerical continuation/bifurcation techniques to produce a class of robust and fast algorithms for constrained optimization problems. The key to the development of these algorithms is the Expanded Lagrangian System which is derived and analyzed in this work. This parameterized system of nonlinear equations contains the penalty path as a solution, provides a smooth homotopy into the first-order necessary conditions, and yields a global optimization technique. Furthermore, the inevitable ill-conditioning present in a sequential optimization algorithm is removed for three penalty methods: the quadratic penalty function for equality constraints, and the logarithmic barrier function (an interior method) and the quadratic loss function (an interior method) for inequality constraints. Although these techniques apply to optimization in general and to linear and nonlinear programming, calculus of variations, optimal control and parameter identification in particular, the development is primarily within the context of nonlinear programming.

Poore, A. B.↗

NASA NTRS1984

Applying optimization software libraries to engineering problems

Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.

Healy, M. J.↗

NASA NTRS1980

Preliminary demonstration of a robust controller design method

Alternative computational procedures for obtaining a feedback control law which yields a control signal based on measurable quantitites are evaluated. The three methods evaluated are: (1) the standard linear quadratic regulator design model; (2) minimization of the norm of the feedback matrix, k via nonlinear programming subject to the constraint that the closed loop eigenvalues be in a specified domain in the complex plane; and (3) maximize the angles between the closed loop eigenvectors in combination with minimizing the norm of K also via the constrained nonlinear programming. The third or robust design method was chosen to yield a closed loop system whose eigenvalues are insensitive to small changes in the A and B matrices. The relationship between orthogonality of closed loop eigenvectors and the sensitivity of closed loop eigenvalues is described. Computer programs are described.

Anderson, L. R.↗

DOE OSTI2021

Topology optimization of 3D photonic crystals with complete bandgaps

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1974

Computer-aided design of control systems to meet many requirements

A method is described for using nonlinear programing in the computer-aided design of airplane control systems. It is assumed that the quality of such systems depends on many criteria. These criteria are included in the constraints vector (instead of attempting to combine them into a single scalar criterion, as is usually done), and the design proceeds through a sequence of nonlinear programing solutions in which the designer varies the specification of sets of requirements levels. The method is applied to design of a lateral stability augmentation system (SAS) for a fighter airplane, in which the requirements vector is chosen from the official handling qualities specifications. Results are shown for several simple SAS configurations designed to obtain desirable handling qualities over all design flight conditions with minimum feedback gains. The choice of the final design for each case is not unique but depends on the designer's decision as to which achievable set of requirements levels represents the best for that system. Results indicate that it may be possible to design constant parameter SAS which can satisfy the most stringent handling qualities requirements for fighter airplanes in all flight conditions. The role of the designer as a decision maker, interacting with the computer program, is discussed. Advantages of this type of designer-computer interaction are emphasized. Desirable extensions of the method are indicated.

Schy, A. A.↗

NASA NTRS1995

Practical aspects of variable reduction formulations and reduced basis algorithms in multidisciplinary design optimization

This paper discusses certain connections between nonlinear programming algorithms and the formulation of optimization problems for systems governed by state constraints. The major points of this paper are the detailed calculation of the sensitivities associated with different formulations of optimization problems and the identification of some useful relationships between different formulations. These relationships have practical consequences; if one uses a reduced basis nonlinear programming algorithm, then the implementations for the different formulations need only differ in a single step.

Lewis, Robert Michael↗

NASA NTRS1982

Further developments in the controlled growth approach for optimal structural synthesis

It is pointed out that the use of nonlinear programming methods in conjunction with finite element and other discrete analysis techniques have provided a powerful tool in the domain of optimal structural synthesis. The present investigation is concerned with new strategies which comprise an extension to the controlled growth method considered by Hajela and Sobieski-Sobieszczanski (1981). This method proposed an approach wherein the standard nonlinear programming (NLP) methodology of working with a very large number of design variables was replaced by a sequence of smaller optimization cycles, each involving a single 'dominant' variable. The current investigation outlines some new features. Attention is given to a modified cumulative constraint representation which is defined in both the feasible and infeasible domain of the design space. Other new features are related to the evaluation of the 'effectiveness measure' on which the choice of the dominant variable and the linking strategy is based.

Hajela, P.↗

NASA NTRS1991

A parallel trajectory optimization tool for aerospace plane guidance

A parallel trajectory optimization algorithm is being developed. One possible mission is to provide real-time, on-line guidance for the National Aerospace Plane. The algorithm solves a discrete-time problem via the augmented Lagrangian nonlinear programming algorithm. The algorithm exploits the dynamic programming structure of the problem to achieve parallelism in calculating cost functions, gradients, constraints, Jacobians, Hessian approximations, search directions, and merit functions. Special additions to the augmented Lagrangian algorithm achieve robust convergence, achieve (almost) superlinear local convergence, and deal with constraint curvature efficiency. The algorithm can handle control and state inequality constraints such as angle-of-attack and dynamic pressure constraints. Portions of the algorithm have been tested. The nonlinear programming core algorithm performs well on a variety of static test problems and on an orbit transfer problem. The parallel search direction algorithm can reduce wall clock time by a factor of 10 for this part of the computation task.

Psiaki, Mark L.↗

NASA NTRS1997

Preliminary Design of Low-Thrust Interplanetary Missions

For interplanetary missions, highly efficient electric propulsion systems can be used to increase the mass delivered to the destination and/or reduce the trip time over typical chemical propulsion systems. This technology is being demonstrated on the Deep Space 1 mission - part of NASA's New Millennium Program validating technologies which can lower the cost and risk and enhance the performance of future missions. With the successful demonstration on Deep Space 1, future missions can consider electric propulsion as a viable propulsion option. Electric propulsion systems, while highly efficient, produce only a small amount of thrust. As a result, the engines operate during a significant fraction of the trajectory. This characteristic makes it much more difficult to find optimal trajectories. The methods for optimizing low-thrust trajectories are typically categorized as either indirect, or direct. Indirect methods are based on calculus of variations, resulting in a two-point boundary value problem that is solved by satisfying terminal constraints and targeting conditions. These methods are subject to extreme sensitivity to the initial guess of the variables - some of which are not physically intuitive. Adding a gravity assist to the trajectory compounds the sensitivity. Direct methods parameterize the problem and use nonlinear programming techniques to optimize an objective function by adjusting a set of variables. A variety of methods of this type have been examined with varying results. These methods are subject to the limitations of the nonlinear programming techniques. In this paper we present a direct method intended to be used primarily for preliminary design of low-thrust interplanetary trajectories, including those with multiple gravity assists. Preliminary design implies a willingness to accept limited accuracy to achieve an efficient algorithm that executes quickly.

Sims, Jon A.↗

NASA NTRS1990

Constrained optimization using design of experiment surfaces

An algorithm for solving constrained optimization problems is presented. First, design of experiment techniques are used to survey the design space. After evaluating the objective and constraint functions, as specified by Taguchi orthogonal arrays, analytical models of these functions are generated using a least-squares regression analysis. Next, a nonlinear programming package is used to optimize the analytical model. Based on the optimization information, the design space is reduced so as to close in around the minimum, and the entire procedure is repeated until convergence. An important feature of the algorithm is that function gradients are not required; therefore, for problems in which gradients would have to be estimated using finite-differences the number of function evaluations required for the optimization is significantly reduced, when compared with traditional nonlinear programming techniques. In addition, there is no requirement that the gradients must be smooth and continuous.

Bolt, Marvin Vance↗

DOE OSTI2026

Data for KETCHUP: Parameterizing of Large-Scale Kinetic Models Using Multiple Datasets with Different Reference States

Repository for Kinetic Estimation Tool Capturing Heterogeneous Datasets Using Pyomo (KETCHUP), a flexible parameter estimation tool that leverages a primal-dual interior-point algorithm to solve a nonlinear programming (NLP) problem that identifies a set of parameters capable of recapitulating the steady-state fluxes and concentrations in wild-type and perturbed metabolic networks. KETCHUP can use K-FIT [2] input files. Example K-FIT input files are located in the K-FIT repository at https://github.com/maranasgroup/K-FIT.

Metabolomics↗

DOE OSTI2016

Thermal energy storage to minimize cost and improve efficiency of a polygeneration district energy system in a real-time electricity market

District energy systems can produce low-cost utilities for large energy networks, but can also be a resource for the electric grid by their ability to ramp production or to store thermal energy by responding to real-time market signals. In this work, dynamic optimization exploits the flexibility of thermal energy storage by determining optimal times to store and extract excess energy. This concept is applied to a polygeneration distributed energy system with combined heat and power, district heating, district cooling, and chilled water thermal energy storage. The system is a university campus responsible for meeting the energy needs of tens of thousands of people. The objective for the dynamic optimization problem is to minimize cost over a 24-h period while meeting multiple loads in real time. The paper presents a novel algorithm to solve this dynamic optimization problem with energy storage by decomposing the problem into multiple static mixed-integer nonlinear programming (MINLP) problems. Another innovative feature of this work is the study of a large, complex energy network which includes the interrelations of a wide variety of energy technologies. Results indicate that a cost savings of 16.5% is realized when the system can participate in the wholesale electricity market.

25 ENERGY STORAGE↗

DOE OSTI2020

Connected Vehicle-Based Traffic Signal Coordination

This study presents a connected vehicles (CVs)-based traffic signal optimization framework for a coordinated arterial corridor. The signal optimization and coordination problem are first formulated in a centralized scheme as a mixed-integer nonlinear program (MINLP). The optimal phase durations and offsets are solved together by minimizing fuel consumption and travel time considering an individual vehicle’s trajectories. Due to the complexity of the model, we decompose the problem into two levels: an intersection level to optimize phase durations using dynamic programming (DP), and a corridor level to optimize the offsets of all intersections. In order to solve the two-level model, a prediction-based solution technique is developed. The proposed models are tested using traffic simulation under various scenarios. Compared with the traditional actuated signal timing and coordination plan, the signal timing plans generated by solving the MINLP and the two-level model can reasonably improve the signal control performance. When considering varies vehicle types under high demand levels, the proposed two-level model reduced the total system cost by 3.8% comparing to baseline actuated plan. MINLP reduced the system cost by 5.9%. It also suggested that coordination scheme was beneficial to corridors with relatively high demand levels. For intersections with major and minor street, coordination conducted for major street had little impacts on the vehicles at the minor street.

42 ENGINEERING↗

DOE OSTI2012

Magnetostatic focal spot correction for x-ray tubes operating in strong magnetic fields using iterative optimization

Purpose: Combining x-ray fluoroscopy and MR imaging systems for guidance of interventional procedures has become more commonplace. By designing an x-ray tube that is immune to the magnetic fields outside of the MR bore, the two systems can be placed in close proximity to each other. A major obstacle to robust x-ray tube design is correcting for the effects of the magnetic fields on the x-ray tube focal spot. A potential solution is to design active shielding that locally cancels the magnetic fields near the focal spot. Methods: An iterative optimization algorithm is implemented to design resistive active shielding coils that will be placed outside the x-ray tube insert. The optimization procedure attempts to minimize the power consumption of the shielding coils while satisfying magnetic field homogeneity constraints. The algorithm is composed of a linear programming step and a nonlinear programming step that are interleaved with each other. The coil results are verified using a finite element space charge simulation of the electron beam inside the x-ray tube. To alleviate heating concerns an optimized coil solution is derived that includes a neodymium permanent magnet. Any demagnetization of the permanent magnet is calculated prior to solving for the optimized coils. The temperature dynamics of the coil solutions are calculated using a lumped parameter model, which is used to estimate operation times of the coils before temperature failure. Results: For a magnetic field strength of 88 mT, the algorithm solves for coils that consume 588 A/cm{sup 2}. This specific coil geometry can operate for 15 min continuously before reaching temperature failure. By including a neodymium magnet in the design the current density drops to 337 A/cm{sup 2}, which increases the operation time to 59 min. Space charge simulations verify that the coil designs are effective, but for oblique x-ray tube geometries there is still distortion of the focal spot shape along with deflections of approximately 3 mm in the radial and circumferential directions on the anode. Conclusions: Active shielding is an attractive solution for correcting the effects of magnetic fields on the x-ray focal spot. If extremely long fluoroscopic exposure times are required, longer operation times can be achieved by including a permanent magnet with the active shielding design.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2019

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

We develop an adaptive, multivariate partitioning algorithm for solving nonconvex, Mixed-Integer Nonlinear Programs (MINLPs) with polynomial functions to global optimality. In particular, we present an iterative algorithm that exploits piecewise, convex relaxation approaches via disjunctive formulations to solve MINLPs that is different than conventional spatial branch-and-bound approaches. The algorithm partitions the domains of variables in an adaptive and non-uniform manner at every iteration to focus on productive areas of the search space. Furthermore, domain reduction techniques based on sequential, optimization-based bound-tightening and piecewise relaxation techniques, as a part of a presolve step, are integrated into the main algorithm. Finally, we demonstrate the effectiveness of the algorithm on well-known benchmark problems (including Pooling and Blending instances) from MINLPLib and compare our algorithm with state-of-the-art global optimization solvers. With our novel approach, we solve several large-scale instances, some of which are not solvable by state-of-the-art solvers. We also succeed in reducing the best known optimality gap for a hard, generalized pooling problem instance.

97 MATHEMATICS AND COMPUTING↗