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NASA NTRS1973

Preliminary study of supersonic-transport configurations with low values of sonic boom

A parametric study of low-boom supersonic transport airplanes with conventional configurations was made to identify the features of specific configurations that promise relatively low sonic boom overpressures (less than 47.9 N/sq m). The range of values considered was gross weight from 28,300 to 170,000 kg; cruise Mach numbers of 2 to 3.2; and wing loadings of 1436, 2870, and 4309 N/sq m. Fuselage length was varied from 49.1 to 102.4 m and fuselage diameter from 2.75 to 3.98 m. A nominal Mach 2 configuration weighing 56,700 kg and having a wing loading of 2870 N/sq m was selected; and its gross geometric, aerodynamic, and structural features were estimated. At a cruise altitude of 18,300 m, lift-drag ratio was estimated to be 7.35, while sonic boom overpressure was 41.7 N/sq m. Takeoff thrust loading using four afterburning turbojet engines at maximum dry thrust was 0.32. Payload for a 4440-km range was 16.7 percent of gross weight, giving a direct operating cost of 0.82 cent per seat statute mile.

Dugan, J. F., Jr.↗

NASA NTRS2015

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

Olson, Erik D.↗

NASA NTRS2008

Improving the Optical Quality Factor of the WGM Resonator

Resonators usually are characterized with two partially dependent values: finesse (F) and quality factor (Q). The finesse of an empty Fabry-Perot (FP) resonator is defined solely by the quality of its mirrors and is calculated as F=piR(exp 1/2)/(1-R). The maximum up-to-date value of reflectivity R approximately equal to 1 - 1.6 x 10(exp -6) is achieved with dielectric mirrors. An FP resonator made with the mirrors has finesse F=1.9 x 10(exp 6). Further practical increase of the finesse of FP resonators is problematic because of the absorption and the scattering of light in the mirror material through fundamental limit on the reflection losses given by the internal material losses and by thermodynamic density fluctuations on the order of parts in 109. The quality factor of a resonator depends on both its finesse and its geometrical size. A one-dimensional FP resonator has Q=2 F L/lambda, where L is the distance between the mirrors and lambda is the wavelength. It is easy to see that the quality factor of the resonator is unlimited because L is unlimited. F and Q are equally important. In some cases, finesse is technically more valuable than the quality factor. For instance, buildup of the optical power inside the resonator, as well as the Purcell factor, is proportional to finesse. Sometimes, however, the quality factor is more valuable. For example, inverse threshold power of intracavity hyperparametric oscillation is proportional to Q(exp 2) and efficiency of parametric frequency mixing is proportional to Q(exp 3). Therefore, it is important to know both the maximally achievable finesse and quality factor values of a resonator. Whispering gallery mode (WGM) resonators are capable of achieving larger finesse compared to FP resonators. For instance, fused silica resonators with finesse 2.3 x 10(exp 6) and 2.8 x 10(exp 6) have been demonstrated. Crystalline WGM resonators reveal even larger finesse values, F=6.3 x 10(exp 6), because of low attenuation of light in the transparent optical crystals. The larger values of F and Q result in the enhancement of various nonlinear processes. Low-threshold Raman lasing, optomechanical oscillations, frequency doubling, and hyperparametric oscillations based on these resonators have been recently demonstrated. Theory predicts a possibility of nearly 10(exp 14) room-temperature optical Q-factors of optical crystalline WGM resonators, which correspond to finesse levels higher than 10(exp 9). Experiments have shown numbers a thousand times lower than that. The difference occurs due to media imperfections. To substantially reduce the optical losses caused by the imperfections, a specific, multi-step, asymptotic processing of the resonator is implemented. The technique has been initially developed to reduce microwave absorption in dielectric resonators. One step of the process consists of mechanical polishing performed after high temperature annealing. Several steps repeat one after another to lead to significant reduction in optical attenuation and, as a result, to the increase of Q-factor as well as finesse of the resonator which demonstrates a CaF2 WGM resonator with F greater than 10(exp 7) and Q greater than 10(exp 11).

Savchenkov, Anatoliy↗

NASA NTRS2012

A Comprehensive Structural Dynamic Analysis Approach for Multi Mission Earth Entry Vehicle (MMEEV) Development

The anticipated NASA Mars Sample Return Mission (MSR) requires a simple and reliable method in which to return collected Martian samples back to earth for scientific analysis. The Multi-Mission Earth Entry Vehicle (MMEEV) is NASA's proposed solution to this MSR requirement. Key aspects of the MMEEV are its reliable and passive operation, energy absorbing foam-composite structure, and modular impact sphere (IS) design. To aid in the development of an EEV design that can be modified for various missions requirements, two fully parametric finite element models were developed. The first model was developed in an explicit finite element code and was designed to evaluate the impact response of the vehicle and payload during the final stage of the vehicle's return to earth. The second model was developed in an explicit code and was designed to evaluate the static and dynamic structural response of the vehicle during launch and reentry. In contrast to most other FE models, built through a Graphical User Interface (GUI) pre-processor, the current model was developed using a coding technique that allows the analyst to quickly change nearly all aspects of the model including: geometric dimensions, material properties, load and boundary conditions, mesh properties, and analysis controls. Using the developed design tool, a full range of proposed designs can quickly be analyzed numerically and thus the design trade space for the EEV can be fully understood. An engineer can then quickly reach the best design for a specific mission and also adapt and optimize the general design for different missions.

Perino, Scott↗

NASA NTRS1986

Aeroelastic considerations for torsionally soft rotors

A research study was initiated to systematically determine the impact of selected blade tip geometric parameters on conformable rotor performance and loads characteristics. The model articulated rotors included baseline and torsionally soft blades with interchangeable tips. Seven blade tip designs were evaluated on the baseline rotor and six tip designs were tested on the torsionally soft blades. The designs incorporated a systemmatic variation in geometric parameters including sweep, taper, and anhedral. The rotors were evaluated in the NASA Langley Transonic Dynamics Tunnel at several advance ratios, lift and propulsive force values, and tip Mach numbers. A track sensitivity study was also conducted at several advance ratios for both rotors. Based on the test results, tip parameter variations generated significant rotor performance and loads differences for both baseline and torsionally soft blades. Azimuthal variation of elastic twist generated by variations in the tip parameters strongly correlated with rotor performance and loads, but the magnitude of advancing blade elastic twist did not. In addition, fixed system vibratory loads and rotor track for potential conformable rotor candidates appears very sensitive to parametric rotor changes.

Mantay, W. R.↗

NASA NTRS1984

Aeroelastic considerations for torsionally soft rotors

Mantay, W. R.↗

DOE OSTI2025

Mesoscale Linear Elastic Modeling and Homogenization of Marine Energy Composites

The design of fiber-reinforced composite (FRC)-based components for marine energy applications necessitates a fundamental understanding of material properties and the resulting geometry to predict long-term performance. In this work, we present a modeling workflow to predict linear elastic and diffusive bulk properties at the mesoscale for an idealized geometry based on knowledge of fiber and resin properties. A parametric study was performed to identify the key model input parameters that influence bulk properties. Furthermore, we demonstrate how bulk properties can be leveraged in high-fidelity image-based simulations, where imperfections in tow geometry and voids captured during X-ray computed tomography imaging are explicitly represented within the simulation. Bulk properties of interest include moduli, Poisson’s ratios, hygroscopic swelling, diffusivity, and moisture uptake, which are key parameters for characterizing FRC performance within marine environments. Modeling predictions agreed well with experimental data, except for estimating swelling coefficients, likely due to crack accumulation as a function of moisture uptake. The mesoscale modeling workflow ultimately highlights a versatile framework for understanding the influence of material and geometric properties, which can be leveraged to rapidly assess new FRC-based components.

computational mechanics↗

NASA NTRS1991

Numerical investigations in three-dimensional internal flows

The present study is a preliminary investigation into the behavior of the flow within a 28 degree total geometric turning angle hypothetical Mach 10 inlet as calculated with the full three-dimensional Navier-Stokes equations. Comparison between the two-dimensional and three-dimensional solutions have been made. The overall compression is not significantly different between the two-dimensional and center plane three dimensional solutions. Approximately one-half to two-thirds of the inlet flow at the exit of the inlet behave nominally two-dimensionally. On the other hand, flow field non-uniformities in the three-dimensional solution indicate the potential significance of the sidewall boundary layer flows ingested into the inlet. The tailoring of the geometry at the inlet shoulder and on the cowl obtained in the two-dimensional parametric design study have also proved to be effective at controlling the boundary layer behavior in the three-dimensional code. The three-dimensional inlet solution remained started indicating that the two-dimensional design had a sufficient margin to allow for three-dimensional flow field effects. Although confidence is being gained in the use of SCRAM3D (three-dimensional full Navier-Stokes code) as applied to similar flow fields, the actual effects of the three-dimensional flow fields associated with sidewalls and wind tunnel installations can require verification with ground-based experiments.

Rose, William C.↗

NASA NTRSDate not supplied

Introducing Tropical Geometric Approaches to Delay Tolerant Networking Optimization

Delay Tolerant Networking (DTN) is the standard approach to the networking of space systems with the goal of supporting the Solar System Internet (SSI). Current space networks have a small scale and often depend on rigorously scheduled (pre-determined) contact opportunities; this manual approach inhibits scalability. The goal of this paper is to recast these scheduling problems in order to apply the optimization machinery of tropical geometry. Contact opportunities in space are dependent on such factors as orbital mechanics and asset availability, which induce time-varying connectivity; indeed, end-to-end connectivity might never occur. Routing optimization within this structure is classically difficult and typically utilizes Dijkstra's algorithm as applied to contact graphs. Alternatively, we follow the successes of tropical geometry in train schedule optimization, job assignments, and even traditional networking, by extending this approach to this more general (i.e. disconnected) problem space. These successes imply tropical geometry provides a useful framework in the context of DTNs, starting with applications to queuing theory and long-haul links. Recently, tropical geometry has been applied to parametric path optimization on graphs with variable edge weights. In this work, we extend these advances to account for the problem of routing in a space network, and find that tropical geometry is well-suited to the challenges offered by this new setting, including contact schedules featuring probabilities. Our approach leverages the combinatorial nature of the problem to give feasible shortest path trees in the presence of variable channel conditions and latency, evolving topologies, and uncertainty inherent in space routing. We discuss our tropical approach to DTN for two Python implementations, a Verilog Tropical ALU implementation, tropical frameworks for other parametric graph problems, and solution stability. Lastly, a program for future work is included to illuminate the path ahead.

Delay Tolerant Networking↗

NASA NTRS2014

A Multiscale Progressive Failure Modeling Methodology for Composites that Includes Fiber Strength Stochastics

A multiscale modeling methodology was developed for continuous fiber composites that incorporates a statistical distribution of fiber strengths into coupled multiscale micromechanics/finite element (FE) analyses. A modified two-parameter Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the statistical distribution of fiber strengths. A parametric study using the NASA Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) was performed to assess the effect of variable fiber strengths on local composite failure within a repeating unit cell (RUC) and subsequent global failure. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a unidirectional SCS-6/TIMETAL 21S metal matrix composite tensile dogbone specimen at 650 degC. Multiscale progressive failure analyses were performed to quantify the effect of spatially varying fiber strengths on the RUC-averaged and global stress-strain responses and failure. The ultimate composite strengths and distribution of failure locations (predominately within the gage section) reasonably matched the experimentally observed failure behavior. The predicted composite failure behavior suggests that use of macroscale models that exploit global geometric symmetries are inappropriate for cases where the actual distribution of local fiber strengths displays no such symmetries. This issue has not received much attention in the literature. Moreover, the model discretization at a specific length scale can have a profound effect on the computational costs associated with multiscale simulations.models that yield accurate yet tractable results.

Generalized Method of Cells↗

NASA NTRS2003

Using Correlated Photons to Suppress Background Noise

A proposed method of suppressing the effect of background noise in an optical communication system would exploit the transmission and reception of correlated photons at the receiver. The method would not afford any advantage in a system in which performance is limited by shot noise. However, if the performance of the system is limited by background noise (e.g., sunlight in the case of a free-space optical communication system or incoherently scattered in-band photons in the case of a fiber-optic communication system), then the proposed method could offer an advantage: the proposed method would make it possible to achieve a signal-to-noise ratio (S/N) significantly greater than that of an otherwise equivalent background- noise-limited optical communication system based on the classical transmission and reception of uncorrelated photons. The figure schematically depicts a classical optical-communication system and a system according to the proposed method. In the classical system, a modulated laser beam is transmitted along an optical path to a receiver, the optics of which include a narrow-band-pass filter that suppresses some of the background noise. A photodetector in the receiver detects the laser-beam and background photons, most or all of which are uncorrelated. In the proposed system, correlated photons would be generated at the transmitter by making a modulated laser beam pass through a nonlinear parametric down-conversion crystal. The sum of frequencies of the correlated photons in each pair would equal the frequency of the incident photon from which they were generated. As in the classical system, the correlated photons would travel along an optical path to a receiver, where they would be band-pass filtered and detected. Unlike in the classical system, the photodetector in the receiver in this system would be one that intrinsically favors the detection of pairs of correlated photons over the detection of uncorrelated photons. Even though there would be no way of knowing the precise location and time of creation of a given pair of correlated signal photons in the nonlinear down-conversion crystal, the fact that the photons are necessarily created at the same time and place makes it possible to utilize conventional geometrical imaging optics to reunite the photons in coincidence in the receiving photodetector. Because most or all of the signal photons would be correlated while most or all of the noise photons would be uncorrelated, the S/N would be correspondingly enhanced in the photodetector output. An additional advantage to be gained by use of a correlated-photon detector is that it could be capable of recovering the signal even in the presence of background light so bright that a classical uncorrelated-photon detector would be saturated. A blocked-impurity-band (BIB) photodetector that preferentially detects pairs of correlated photons over uncorrelated ones and that operates at a quantum efficiency of 88 percent is commercially available. This detector must be cooled to the temperature of liquid helium to obtain the desired low-noise performance. It is planned to use this detector in a proof-of-principle demonstration. In addition, it may be possible to develop GaN-based photodetectors that could offer the desired low-noise performance at room temperature.

Jackson, Deborah↗

NASA NTRS1985

Conical similarity of shock/boundary-layer interactions generated by swept and unswept fins

A parametric experimental investigation has been made of the class of three-dimensional shock wave/turbulent boundary layer interactions generated by swept and unswept leading-edge fins. The fin sweepback angles were 0-65 deg at 5, 9, and 15 deg angles of attack. Two equilibrium two-dimensional turbulent boundary layers with a freestream Mach number of 2.95 and a Reynolds number of 6.3 x 10 to the 7th/m were used as incoming flow conditions. All of the resulting interactions were found to possess conical symmetry of the surface flow patterns and pressures outside of an initial inception zone. Further, these interactions were found to obey a simple conical similarity rule based on inviscid shock wave strength, irrespective of fin sweepback or angle of attack. This is one of the first demonstrations of similarity among three-dimensional interactions produced by geometrically dissimilar shock generators.

Settles, G. S.↗

NASA NTRS2011

Saturn Ring Data Analysis and Thermal Modeling

CIRS, VIMS, UVIS, and ISS (Cassini's Composite Infrared Specrtometer, Visual and Infrared Mapping Spectrometer, Ultra Violet Imaging Spectrometer and Imaging Science Subsystem, respectively), have each operated in a multidimensional observation space and have acquired scans of the lit and unlit rings at multiple phase angles. To better understand physical and dynamical ring particle parametric dependence, we co-registered profiles from these three instruments, taken at a wide range of wavelengths, from ultraviolet through the thermal infrared, to associate changes in ring particle temperature with changes in observed brightness, specifically with albedos inferred by ISS, UVIS and VIMS. We work in a parameter space where the solar elevation range is constrained to 12 deg - 14 deg and the chosen radial region is the B3 region of the B ring; this region is the most optically thick region in Saturn's rings. From this compilation of multiple wavelength data, we construct and fit phase curves and color ratios using independent dynamical thermal models for ring structure and overplot Saturn, Saturn ring, and Solar spectra. Analysis of phase curve construction and color ratios reveals thermal emission to fall within the extrema of the ISS bandwidth and a geometrical dependence of reddening on phase angle, respectively. Analysis of spectra reveals Cassini CIRS Saturn spectra dominate Cassini CIRS B3 Ring Spectra from 19 to 1000 microns, while Earth-based B Ring Spectrum dominates Earth-based Saturn Spectrum from 0.4 to 4 microns. From our fits we test out dynamical thermal models; from the phase curves we derive ring albedos and non-lambertian properties of the ring particle surfaces; and from the color ratios we examine multiple scattering within the regolith of ring particles.

Saturn's rings↗

DOE OSTI2025

Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements

The adaptive variational quantum dynamics simulation (AVQDS) method performs real-time evolution of quantum states using automatically generated parametrized quantum circuits that often contain substantially fewer gates than Trotter circuits. Here we report an improved version of the method, which we call AVQDS(T), by porting the tiling efficient trial circuits with rotations implemented simultaneously technique. The algorithm adaptively adds layers of disjoint unitary gates to the ansatz circuit so as to keep the McLachlan distance, a measure of the accuracy of the variational dynamics, below a fixed threshold. Here we perform benchmark noiseless AVQDS(T) simulations of quench dynamics in local spin models and compare with an alternative adaptive variational approach on quantum resource requirement. Quantum dynamical simulations implementing realistic noise channels are also reported. Finally, we propose a way to substantially alleviate the measurement overhead of AVQDS(T) while maintaining high accuracy by synergistically integrating quantum circuit calculations on quantum processing units with classical calculations using, e.g., tensor networks to evaluate the quantum geometric tensor. We showcase that this approach enables AVQDS(T) to deliver more accurate results than simulations using a fixed ansatz of comparable final depth for a significant time duration with fewer quantum resources.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2010

Thermal Analysis of the Advanced Technology Large Aperture Space Telescope (ATLAST) 8 Meter Primary Mirror

The Advanced Technology Large Aperture Space Telescope (ATLAST) preliminary design concept consists of an 8 meter diameter monolithic primary mirror enclosed in an insulated, optical tube with stray light baffles and a sunshade. ATLAST will be placed in orbit about the Sun-Earth L2 and will experience constant exposure to the sun. The insulation on the optical tube and sunshade serve to cold bias the telescope which helps to minimize thermal gradients. The primary mirror will be maintained at 280K with an active thermal control system. The geometric model of the primary mirror, optical tube, sun baffles, and sunshade was developed using Thermal Desktop(R) SINDA/FLUINT(R) was used for the thermal analysis and the radiation environment was analyzed using RADCAD(R). A XX node model was executed in order to characterize the static performance and thermal stability of the mirror during maneuvers. This is important because long exposure observations, such as extra-solar terrestrial planet finding and characterization, require a very stable observatory wave front. Steady state thermal analyses served to predict mirror temperatures for several different sun angles. Transient analyses were performed in order to predict thermal time constant of the primary mirror for a 20 degree slew or 30 degree roll maneuver. This paper describes the thermal model and provides details of the geometry, thermo-optical properties, and the environment which influences the thermal performance. All assumptions that were used in the analysis are also documented. Parametric analyses are summarized for design parameters including primary mirror coatings and sunshade configuration. Estimates of mirror heater power requirements are reported. The thermal model demonstrates results for the primary mirror heated from the back side and edges using a heater system with multiple independently controlled zones.

Hornsby, Linda↗

NASA NTRSDate not supplied

Icing Physics Studies Using the 3D SIDRM Test Article: Aerodynamic and Supercooled Liquid Icing Analysis

In-flight icing is an important safety issue and is a factor that affects aircraft design and performance. Newer regulations are driving a need for improvements in airframe and engine icing simulation capability. Experimental data is required for development of icing physics models and simulation validation. To that end, this paper presents the analysis of the supercooled liquid icing data subset from tests conducted in 2022 at the NASA Icing Research Tunnel that studied both supercooled water and ice-crystal icing. The test article that was utilized replicated 3D geometrical features of an inter-compressor duct and strut region of a turbofan engine. The surfaces of the Simulated Inter-compressor Duct Research Model (SIDRM) can be heated to simulate the warm surfaces of the turbofan inter-compressor duct. The test article is instrumented with pressure taps, heaters, heat flux gauges, and thermocouples, while a 3D laser scanner, cameras, and a scale to measure ice mass were utilized to characterize the icing behavior. The aim of these tests was to generate ice accretions on the SIDRM test article under well-characterized supercooled liquid icing and ice crystal icing conditions. This paper discusses measurements related to aerodynamic testing and supercooled liquid icing tests that were conducted. Aerodynamic measurements were analyzed and compared to computational simulations and were found to be in good agreement for the range of airspeeds (50 to 230 knots) and angles of attack (0 to 4°) tested. Various parametric sweeps were conducted during the supercooled liquid icing portion of the test entry (cloud median volumetric diameter ranged from 15 to 90 µm, total air temperature from -3 to -17 °C, angle of attack from 0 to 4°, and accretion time from 5 to 20 min). These sweeps were performed to measure that parameter’s impact on ice accretion size, location (icing extent), characteristics (such as glaze/rime ice and shedding behavior), and test article surface temperature. Analysis of the test data showed that clouds composed of larger drops, colder air temperatures, smaller angles of attack, and longer spray times were the primary parameters that resulted in accretions with greater ice mass. Test article angle of attack and cloud droplet size influenced the location of ice accretion as these two parameters directly impact collection efficiency. With respect to icing characteristics, total air temperature dictated icing type, and smaller cloud drop size along with warmer air temperatures resulted in greater amounts of ice shedding. Surface temperature increased during ice accretion from the release of latent (fusion) heat, where total air temperature and cloud drop size impacted the amount of surface temperature change. The icing measurements collected during the SIDRM tests will be used to develop and validate 3D computational engine icing tools, such as GlennICE, that predictively assesses the onset and growth of ice. One of the goals of the sponsoring NASA project is to develop simulation models and tools that can assist in the design and certification of engines for flight in icing conditions in a cost effective way.

supercooled liquid icing↗

NASA NTRS2018

Modeling Fiber Kinking at the Microscale and Mesoscale

A computational micromechanics (CMM) model is employed to interrogate the assumptions of a recently developed mesoscale continuum damage mechanics (CDM) model for fiber kinking. The CMM model considers an individually discretized three dimensional fiber and surrounding matrix accounting for nonlinearity in the fiber, matrix plasticity, fiber/matrix interface debonding, and geometric nonlinearity. Key parameters of the CMM model were measured through experiments. In particular, a novel experimental technique to characterize the in situ longitudinal compressive strength of carbon fibers through indentation of micropillars is presented. The CDM model is formulated on the basis of Budiansky's fiber kinking theory (FKT) with a constitutive deformation-decomposition approach to alleviate mesh size sensitivity. In contrast to conventional mesoscale CDM models that prescribe a constitutive response directly, the response of the proposed model is an outcome of material nonlinearity and large rotations of the fiber direction following FKT. Comparison of the predictions from the CMM and CDM models shows remarkable correlation in strength, post-peak residual stress, and fiber rotation, with less than 10% difference between the two models in most cases. Additional comparisons are made with several fiber kinking models proposed in the literature to highlight the efficacy of the two models. Finally, the CMM model is exercised in parametric studies to explore opportunities to improve the longitudinal compression strength of a ply through the use of nonconventional microstructures.

Herraez, Miguel↗

DOE OSTI2025

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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗