SEARCH · Search NASA
Results for “multiparametric 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.
Optimal Operation of an Industrial Dividing Wall Column through Multiparametric Programming
Not Available
Benders Decomposition Using Graph Modeling and Multi-Parametric Programming
Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.
Explicit model predictive control through robust optimization
A strategy that calculates an explicit state feedback policy to regulate constrained uncertain discrete‐time uncertain linear systems is presented. We consider uncertain processes, affected by box‐bounded multiplicative uncertainty as well as bounded additive uncertainty with linear state and inputs constraints. The proposed method includes (i) the calculation of a terminal set constraint and (ii) the robust reformulation of state constraints in the prediction horizon. These features allow the derivation of the desired policy by solving a single multiparametric quadratic programming problem that guarantees feasible operation in the presence of uncertainty. Additionally, we employ variable and constraint elimination approaches to enhance the computational performance of the strategy. We demonstrate the steps and benefits of these developments with a numerical example and a chemical engineering case study.
Partition-based Feasible Integer Solution Pre-computation for Hybrid Model Predictive Control
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a static map from the current parameter to a suboptimal integer solution such that the remaining convex program is feasible. Convergence is proved with a new insight that the overlap among the feasible parameter sets of each integer solution governs the partition complexity. The partition is stored as a tree which makes querying the feasible solution efficient. The algorithm can be used to warm start a mixed integer solver with a real-time guarantee or to provide a reference integer solution in several suboptimal MPC schemes. The algorithm is tested on randomly generated systems with up to six states, demonstrating the effectiveness of the approach.
Probabilistic structural analysis by extremum methods
The objective is to demonstrate discrete extremum methods of structural analysis as a tool for structural system reliability evaluation. Specifically, linear and multiobjective linear programming models for analysis of rigid plastic frames under proportional and multiparametric loadings, respectively, are considered. Kinematic and static approaches for analysis form a primal-dual pair in each of these models and have a polyhedral format. Duality relations link extreme points and hyperplanes of these polyhedra and lead naturally to dual methods for system reliability evaluation.
A long-term space astrophysics research program: An x-ray perspective of the components and structure of galaxies
X-ray studies of galaxies by the Smithsonian Astrophysical Observatory (SAO) and MIT are described. Activities at SAO include ROSAT PSPC x-ray data reduction and analysis pipeline; x-ray sources in nearby Sc galaxies; optical, x-ray, and radio study of ongoing galactic merger; a radio, far infrared, optical, and x-ray study of the Sc galaxy NGC247; and a multiparametric analysis of the Einstein sample of early-type galaxies. Activities at MIT included continued analysis of observations with ROSAT and ASCA, and continued development of new approaches to spectral analysis with ASCA and AXAF. Also, a new method for characterizing structure in galactic clusters was developed and applied to ROSAT images of a large sample of clusters. An appendix contains preprints generated by the research.
Radiation Risk Assessment of the Individual Astronaut: A Complement to Radiation Interests at the NIH
Predicting human risks following exposure to space radiation is uncertain in part because of unpredictable distribution of high-LET and low-dose-derived damage amongst cells in tissues, unknown synergistic effects of microgravity upon gene- and protein-expression, and inadequately modeled processing of radiation-induced damage within cells to produce rare and late-appearing malignant cancers. Furthermore, estimation of risks of radiogenic outcome within small numbers of astronauts is not possible using classic epidemiologic study. It therefore seems useful to develop strategies of risk-assessment based upon large datasets acquired from correlated biological models useful for resolving radiogenic risk-assessment for irradiated individuals. In this regard, it is suggested that sensitive cellular biodosimeters that simultaneously report 1) the quantity of absorbed dose after exposure to ionizing radiation, 2) the quality of radiation delivering that dose, and 3) the biomolecular risk of malignant transformation be developed in order to resolve these NASA-specific challenges. Multiparametric cellular biodosimeters could be developed using analyses of gene-expression and protein-expression whereby large datasets of cellular response to radiation-induced damage are analyzed for markers predictive for acute response as well as cancer-risk. A new paradigm is accordingly addressed wherein genomic and proteomic datasets are registered and interrogated in order to provide statistically significant dose-dependent risk estimation in individual astronauts. This evaluation of the individual for assessment of radiogenic outcomes connects to NIH program in that such a paradigm also supports assignment of a given patient to a specific therapy, the diagnosis of response of that patient to therapy, and the prediction of risks accumulated by that patient during therapy - such as risks incurred by scatter and neutrons produced during high-energy Intensity-Modulated Radiation Therapy. Value of assessment of radiogenic outcome for individuals exposed to radiation is suggested to be common to both NASA and NIH.