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

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2024

A Convexification-Based Outer-Approximation Method for Convex and Nonconvex MINLP

The advancement of domain reduction techniques has significantly enhanced the performance of solvers in mathematical programming. This paper delves into the impact of integrating convexification and domain reduction techniques within the Outer-Approximation method. We propose a refined convexification-based Outer-Approximation method alongside a Branch-and-Bound method for both convex and nonconvex Mixed-Integer Nonlinear Programming problems. These methods have been developed and incorporated into the open-source Mixed-Integer Nonlinear Decomposition Toolbox for Pyomo-MindtPy. Comprehensive benchmark tests were conducted, validating the effectiveness and reliability of our proposed algorithms. These tests highlight the improvements achieved by incorporating convexification and domain reduction techniques into the Outer-Approximation and Branch-and-Bound methods.

Optimization↗
NASA NTRS2022

Alternative regularizations for Outer-Approximation algorithms for convex MINLP

In this work, we extend the regularization framework from Kronqvist et al. (Math Program 180(1):285–310, 2020) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance metrics and Lagrangean approximations, used in the projection problem for finding new integer combinations to be used within the Outer-Approximation (OA) method. The new approach, called Regularized Outer-Approximation (ROA), has been implemented as part of the open-source Mixed-integer nonlinear decomposition toolbox for Pyomo—MindtPy. We compare the OA method with seven regularization function alternatives for ROA. Moreover, we extend the LP/NLP Branch and Bound method proposed by Quesada and Grossmann (Comput Chem Eng 16(10–11):937–947, 1992) to include regularization in an algorithm denoted RLP/NLP. We provide convergence guarantees for both ROA and RLP/NLP. Finally, we perform an extensive computational experiment considering all convex MINLP problems in the benchmark library MINLPLib. The computational results show clear advantages of using regularization combined with the OA method.

Convex Mixed-integer nonlinear programming↗
DOE OSTI2018

Derivative-free robust optimization by outer approximations

We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We demonstrate the practical benefits of the algorithm on a new class of test problems.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

A multitree approach for global solution of ACOPF problems using piecewise outer approximations

Electricity markets rely on the rapid solution of the optimal power flow (OPF) problem to determine generator power levels and set nodal prices. Traditionally, the OPF problem has been formulated using linearized, approximate models, ignoring nonlinear alternating current (AC) physics. These approaches do not guarantee global optimality or even feasibility in the real ACOPF problem. We introduce an outer-approximation approach to solve the ACOPF problem to global optimality based on alternating solution of upper- and lower-bounding problems. The lower-bounding problem is a piecewise relaxation based on strong second-order cone relaxations of the ACOPF, and these piecewise relaxations are selectively refined at each major iteration through increased variable domain partitioning. Our approach is able to efficiently solve all but one of the test cases considered to an optimality gap below 0.1%. This approach opens the door for global solution of MINLP problems with AC power flow equations.

42 ENGINEERING↗
DOE OSTI2017

Polyhedral approximation in mixed-integer convex optimization

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. Here, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based on constructing polyhedral outer approximations of the convex constraints, resulting in a global solution by solving a finite number of mixed-integer linear and continuous convex subproblems. The key advance we present is to strengthen the polyhedral approximations by constructing them in a higher-dimensional space. In order to automate this extended formulation we rely on the algebraic modeling technique of disciplined convex programming (DCP), and for generality and ease of implementation we use conic representations of the convex constraints. Although our framework requires a manual translation of existing models into DCP form, after performing this transformation on the MINLPLIB2 benchmark library we were able to solve a number of unsolved instances and on many other instances achieve superior performance compared with state-of-the-art solvers like Bonmin, SCIP, and Artelys Knitro.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Optimal Network Topology for Node-Breaker Representations With AC Power Flow Constraints

It has been demonstrated that network topology optimization (NTO) may change the topology of power system networks, and consequently, provide additional flexibility to reduce network congestion and violations. Most NTO problems are formulated based on the bus-branch model in which it is challenging to represent a realistic picture of all substation configurations. In this paper, we explore advantages of substation reconfiguration modeling based on node-breaker representations for NTO problem with full nonlinear alternating current power flow. It also proposes a tailored solution algorithm to solve this nonconvex mixed-integer nonlinear programming through the outer approximation method. The proposed solution approach iterates between a mixed-integer linear programming and a nonlinear subproblem. Additional enhancements to further accelerate the iteration process are illustrated. Numerical case studies demonstrate the relative economic and operational impact of optimal network topology with node-breaker representations.

42 ENGINEERING↗
DOE OSTI2021

Practical algorithms for multivariate rational approximation

We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process to efficiently and robustly compute the coefficients of the rational approximation. Our second approach is based on an optimization formulation that allows us to include structural constraints on the rational approximation (in particular, constraints demanding the absence of singularities), resulting in a semi-infinite optimization problem that we solve using an outer approximation approach. We present results for synthetic and real-life HEP data, and we compare the approximation quality of our approaches with that of traditional polynomial approximations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2005

Deep Interior Mission: Imaging the Interior of Near-Earth Asteroids Using Radio Reflection Tomography

Near-Earth asteroids are important exploration targets since they provide clues to the evolution of the solar system. They are also of interest since they present a clear danger to Earth. Our mission objective is to image the internal structure of two NEOs using radio reflection tomography (RRT) in order to explore the record of asteroid origin and impact evolution, and to test the fundamental hypothesis that some NEOs are rubble piles rather than consolidated bodies. Our mission s RRT technique is analogous to doing a CAT scan of the asteroid from orbit. Closely sampled radar echoes are processed to yield volumetric maps of mechanical and compositional boundaries, and to measure interior material dielectric properties. The RRT instrument is a radar that operates at 5 and 15 MHz with two 30-m (tip-to-tip) dipole antennas that are used in a cross-dipole configuration. The radar transmitter and receiver electronics have heritage from JPL's MARSIS contribution to Mars Express, and the antenna is similar to systems used in IMAGE and LACE missions. The 5-MHz channel is designed to penetrate greater than 1 km of basaltic rock, and 15-MHz penetrates a few hundred meters or more. In addition to RRT volumetric imaging, we use redundant color cameras to explore the surface expressions of unit boundaries, in order to relate interior radar imaging to what is observable from spacecraft imaging and from Earth. The camera also yields stereo color imaging for geology and RRT-related compositional analysis. Gravity and high fidelity geodesy are used to explore how interior structure is expressed in shape, density, mass distribution and spin. Ion thruster propulsion is utilized by Deep Interior to enable tomographic radar mapping of multiple asteroids. Within the Discovery AO scheduling parameters we identify two targets, S-type 1999 ND43 (approximately 500 m diameter) and V-type 3908 Nyx (approximately 1 km), asteroids whose compositions bracket the diversity of solar system materials that we are likely to encounter, from undifferentiated to highly evolved. The 5-15 MHz radar is capable of probing more primitive bodies (e.g. comets or C-types) that may be available given other launch schedules. 5 MHz radar easily penetrates, with the required SNR , greater than 1 km of basalt (a good analog for Nyx). Basalt has a greater loss tangent than expected for most asteroids, although iron-rich M-types are probably not appropriate targets. 15 MHz radar penetrates the outer approximately 100 m of rocky 1 km asteroids and the deep interiors of comets. Laboratory studies of the most common NE0 materials expected (S-, C- and V-type meteorite analogs) will commence in 2005.

Safaeinili, A.↗
DOE OSTI2023

Reducing Conservativeness of Polytopic Linear-Parameter-Varying Robust Vehicle Sideslip Angle Observer Through Minimum-Area Convex Quadrilateral Design

The polytopic linear-parameter-varying (LPV) method has become increasingly popular for designing intelligent control and estimation systems for ground vehicles, particularly for the vehicle sideslip angle observer. In vehicle lateral dynamics, the vehicle longitudinal velocity-induced nonlinearities are conventionally outer-approximated with polytopes such as rectangles or triangles to obtain a polytopic LPV system. Yet, such polytopic approximations tend to be conservative and may lead to inadequate observer performance. To address this issue, a minimum-area convex quadrilateral construction is proposed in this paper to reduce design conservatism. The suggested design is demonstrated through the synthesis of an LPV H ∞ robust vehicle sideslip angle observer. Furthermore, a dSPACE-ASM simulation study is conducted to demonstrate the effectiveness and the advantage of the proposed polytopic construction over a baseline approach.

Zhou, Xingyu↗
DOE OSTI2018

Global Solution Strategies for the Network-Constrained Unit Commitment Problem with AC Transmission Constraints

Here, we propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current (AC) model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. We exploit the mathematical structure of the unit commitment problem with AC power flow constraints (UC-AC) and leverage second-order cone relaxations, piecewise outer approximations, and optimization-based bounds tightening to guarantee a globally optimal solution at convergence. Numerical results on four benchmark problems illustrate the effectiveness of our algorithm, both in terms of convergence rate and solution quality.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Mixed Integer Nonlinear Programming Approaches to Enhance Resiliency and Response Strategies in Critical Infrastructure

Motivation. Critical infrastructures are large, complex engineered systems that must be operated robustly under abnormal conditions resulting from natural hazards or intentional acts. For example, electric power systems must be robust to line faults, water utilities must rapidly mitigate contamination incidents, and computing networks must adapt to adversarial intrusions to protect critical information. Problem. It is difficult for decision-makers within resiliency analysis in critical infrastructure to optimize designs and develop effective response strategies that can account for uncertainties. Facing incomplete information and the sheer scope that a natural hazard or attack vector may incorporate, response can be ineffective without reliable, scalable decision support tools. These problems are intrinsically nonlinear and involve discrete decisions, and unfortunately, existing off-the-shelf mathematical programming methods cannot support optimization-based decision-making of these nonlinear at scale. Method/Approach and Results. This project emphasized development of fundamental optimization strategies that supported real- time mitigation and response for critical infrastructures. In particular, the project developed multi- tree approaches based on piecewise outer-approximations for solution of mixed-integer nonlinear programming (MINLP) problems. These techniques alternate between an MILP or MISOCP relaxation to obtain a lower bound and candidate discrete solutions and an NLP subproblem to obtain upper bounds. Using tailored relaxations based on problem structure, these methods were used to solve several key applications in resilience and response of critical infrastructure. This work resulted in two open-source, copyrighted software packages: CORAMIN (https://github.com/Coramin/Coramin) -- an object-oriented mathematical programming framework that supports tailored multi-tree algorithms for solution of large- scale mixed-integer nonlinear programming; and EGRET (Electrical Grid Research and Engineering Toolkit) (https://github.com/grid- parity-exchange/Egret) -- a declarative mathematical programming framework built upon CORAMIN and Pyomo for formulation and solution of resilience and operations problems in power grid systems. Furthermore, these tools resulted in several important published results, including the following: The first known global optimization approach that could solve the unit-commitment problem with nonlinear power flow constraints on medium-sized test problems; Improved parallel optimization-based bounds tightening and strengthening of relaxations of AC power flow constraints; and, Optimization-based approaches for improved grid resilience and use of demand response to improve grid resilience with reduction in capital requirements. Result Implications. This project developed first-of-a-kind algorithms for decision-making in critical infrastructure resilience operations and planning, as well as a next-generation toolkit for MINLP researchers. These approaches leveraged high-performance computing architectures to solve some of the largest, most challenging nonlinear discrete optimization problems to global optimality, and these successes were captured in open-source software to enable optimization-based decision-making, and efficient solution of MINLP formulations for electric power transmission grids.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1996

Application of Hybrid Optimization-Expert System for Optimal Power Management on Board Space Power Station

The space power system has two sources of energy: photo-voltaic blankets and batteries. The optimal power management problem on-board has two broad operations: off-line power scheduling to determine the load allocation schedule of the next several hours based on the forecast of load and solar power availability. The nature of this study puts less emphasis on speed requirement for computation and more importance on the optimality of the solution. The second category problem, on-line power rescheduling, is needed in the event of occurrence of a contingency to optimally reschedule the loads to minimize the 'unused' or 'wasted' energy while keeping the priority on certain type of load and minimum disturbance of the original optimal schedule determined in the first-stage off-line study. The computational performance of the on-line 'rescheduler' is an important criterion and plays a critical role in the selection of the appropriate tool. The Howard University Center for Energy Systems and Control has developed a hybrid optimization-expert systems based power management program. The pre-scheduler has been developed using a non-linear multi-objective optimization technique called the Outer Approximation method and implemented using the General Algebraic Modeling System (GAMS). The optimization model has the capability of dealing with multiple conflicting objectives viz. maximizing energy utilization, minimizing the variation of load over a day, etc. and incorporates several complex interaction between the loads in a space system. The rescheduling is performed using an expert system developed in PROLOG which utilizes a rule-base for reallocation of the loads in an emergency condition viz. shortage of power due to solar array failure, increase of base load, addition of new activity, repetition of old activity etc. Both the modules handle decision making on battery charging and discharging and allocation of loads over a time-horizon of a day divided into intervals of 10 minutes. The models have been extensively tested using a case study for the Space Station Freedom and the results for the case study will be presented. Several future enhancements of the pre-scheduler and the 'rescheduler' have been outlined which include graphic analyzer for the on-line module, incorporating probabilistic considerations, including spatial location of the loads and the connectivity using a direct current (DC) load flow model.

Momoh, James↗
NASA NTRS1990

An approximation to the outer planet ephemeris errors in JPL's DE 200

The outer planet positions of JPL's recent planetary ephemeris, DE 202, have begun to show significant differences from DE 200, the basic ephemeris of the major national almanacs. The differences DE 202 - DE 200 are plotted and are assumed to approximate the errors of DE 200. For Jupiter, the difference in right ascension varies over the planet's 12 yr period between -0.1 and -0.2 arcsec throughout the century; for Saturn, the right ascension also varies over the 30 yr period, but in addition, shows a drift which reaches -0.25 arcsec at present; for Uranus, the difference is small through the first half of the century, but now has reached -0.4 arcsec; for Neptune, the error was +0.6 arcsec at 1900 and is near -1.0 arcsec by the year 2000; the error for Pluto exceeds +2.0 arcsec by the end of the century and is rapidly increasing. The declination errors are generally periodic and smaller than the right ascensions.

Standish, E. M., Jr.↗
NASA NTRS1974

Hydrogen ionization in the shock layer for entry into the outer planets

Approximate assessments are presented for the chemical state of the shock layer with respect to the hydrogen ionization reaction for representative entries into Saturn, Uranus, and Jupiter. It is shown that, except for a steep entry into the Saturn nominal atmosphere, the computation of all entry probe gascaps for the outer planets can probably be considered on either a frozen or chemical equilibrium basis.

Howe, J. T.↗
NASA NTRS1978

An approximate inviscid radiating flow field analysis for outer planet entry probes

An approximate computational technique has been developed for predicting inviscid, radiating flows about blunt probes entering atmospheres consisting of hydrogen and helium. The technique is rapid and versatile and is well suited for performing parametric trade studies for outer planet entries. Details of the computational technique, the thermodynamic correlations, the 58-step absorption coefficient model and the analytic shock shape equations are discussed. Good comparisons of the radiative heating computed by the approximate method and by detailed calculations are obtained.

Zoby, E. V.↗