Search NASASearch

SEARCH · Search NASA

Results for “global optimization”

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 145 records · Page 8

Minimum fuel horizontal flightpaths in the terminal area

The problem of minimum fuel airplane trajectories from arbitrary initial states to be fixed final state is considered. There are four state variables (two position coordinates, heading, and constrained velocity) and two constrained controls (thrust and bank angle). The fuel optimality of circular and straight line flightpaths is examined. Representative extremals (trajectories satisfying the necessary conditions of the minimum principle) of various types are computed and used to evaluate trajectories generated by an on line algorithm. Attention is paid to the existence of Darboux points (beyond which an extremal ceases to be globally optimal). One fuel flow rate model includes a term quadratic in thrust; hence, the optimal thrust is continuous and nonsingular. The other fuel flow rate model is linear in thrust, and consequently the optimal thrust is discontinuous and singular.

Kreindler, E.

Genetic Algorithm for Optimization: Preprocessing with n Dimensional Bisection and Error Estimation

A knowledge of the appropriate values of the parameters of a genetic algorithm (GA) such as the population size, the shrunk search space containing the solution, crossover and mutation probabilities is not available a priori for a general optimization problem. Recommended here is a polynomial-time preprocessing scheme that includes an n-dimensional bisection and that determines the foregoing parameters before deciding upon an appropriate GA for all problems of similar nature and type. Such a preprocessing is not only fast but also enables us to get the global optimal solution and its reasonably narrow error bounds with a high degree of confidence.

Sen, S. K.

Introduction to and comparison of deep learning and optimization approaches to analytical wake modeling of a tilted wind turbine

This paper introduces innovative optimization and deep learning techniques to enhance the prediction of complex wake dynamics in the downstream wind velocity of tilted wind turbines. Traditional methods for calibrating the Bastankhah wake model often lead to increased errors in wind velocity distribution due to overfitting of the local wake characteristics. To address this issue, we propose an additional global optimization step to reduce errors in wind velocity predictions with respect to various wake parameters. Despite this improvement, the Bastankhah model's axisymmetric Gaussian wake shape limits its accuracy for complex wake structures. Therefore, we also propose a deep learning approach, which demonstrates promising results by accurately modeling complex wake shapes across a broader range of tilt angles with minimal computational cost. The deep learning approach achieves near-identical predictions to high-fidelity large-eddy simulations, representing a promising advancement in wake modeling.

17 WIND ENERGY

End to End Optimization of a Mars Hybrid Transportation Architecture

NASA’s Mars Study Capability Team (MSCT) is developing a reusable Mars hybrid transportation architecture in which both chemical and solar electric propulsion systems are used in a single vehicle design to send crew and cargo to Mars. This paper presents a new integrated framework that combines Earth departure/arrival, heliocentric trajectory, Mars orbit reorientation, and vehicle sizing into a single environment and solves the entire mission from beginning to end in an effort to find a globally optimized solution for the hybrid architecture.

Qu, Min

Surrogate modeling and optimization of the leaching process in a rare earth elements recovery plant

Critical minerals (CMs) and Rare Earth Elements (REEs) play a vital role in crucial infrastructure technologies such as renewable energy generation and batteries. Recovering them from waste materials has recently been found to significantly reduce environmental impact and supply chain costs related to these materials. In this work, we investigate surrogate modeling techniques aimed to simplify the modeling, simulation, and optimization of the leaching processes involved in CM and REE recovery flowsheets. As there is currently a lack of systematic studies on this topic, we perform extensive computational testing to ascertain which surrogate models are easier to construct and offer high predictive accuracy. Further, our results suggest that sparse quadratic models balance predictive accuracy and computational efficiency. Training and using these surrogates for global optimization of the leaching process requires two orders of magnitude fewer measurements and is up to four orders of magnitude faster than optimizing the original simulation using equation-oriented optimization or derivative-free optimization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM

An Optimizing Space Data-Communications Scheduling Method and Algorithm with Interference Mitigation, Generalized for a Broad Class of Optimization Problems

NASA's space data-communications infrastructure-the Space Network and the Ground Network-provide scheduled (as well as some limited types of unscheduled) data-communications services to user spacecraft. The Space Network operates several orbiting geostationary platforms (the Tracking and Data Relay Satellite System (TDRSS)), each with its own servicedelivery antennas onboard. The Ground Network operates service-delivery antennas at ground stations located around the world. Together, these networks enable data transfer between user spacecraft and their mission control centers on Earth. Scheduling data-communications events for spacecraft that use the NASA communications infrastructure-the relay satellites and the ground stations-can be accomplished today with software having an operational heritage dating from the 1980s or earlier. An implementation of the scheduling methods and algorithms disclosed and formally specified herein will produce globally optimized schedules with not only optimized service delivery by the space data-communications infrastructure but also optimized satisfaction of all user requirements and prescribed constraints, including radio frequency interference (RFI) constraints. Evolutionary algorithms, a class of probabilistic strategies for searching large solution spaces, is the essential technology invoked and exploited in this disclosure. Also disclosed are secondary methods and algorithms for optimizing the execution efficiency of the schedule-generation algorithms themselves. The scheduling methods and algorithms as presented are adaptable to accommodate the complexity of scheduling the civilian and/or military data-communications infrastructure within the expected range of future users and space- or ground-based service-delivery assets. Finally, the problem itself, and the methods and algorithms, are generalized and specified formally. The generalized methods and algorithms are applicable to a very broad class of combinatorial-optimization problems that encompasses, among many others, the problem of generating optimal space-data communications schedules.

ground stations

Decomposition and Algorithmic Approaches for Solving Large-Scale Process Family Design Problems

Our most recent work expands the water desalination case study from 76 variants to 10,897 variants using the equation-oriented model built in Pyomo as part of the PARETO project. Using the discretization formulation presented in Stinchfield (2024a), rather than solving for all 10,897 variants simultaneously, we decompose the formulation into subproblems containing subsets of variants from the process family. We solve the overall problem with Progressive Hedging (PH) deployed in parallel on a distributed HPC cluster using the open-source Python package mpi-sppy (Knueven et al., 2023). This approach allowed us to solve this process family design problem to ~1.5% relative optimality gap in about 5 hours; in comparison, Gurobi reached ~50% relative optimality gap in about 6 hours (Stinchfield et al., 2024b). However, this approach still requires discretization of the common unit module design ranges; additionally, PH acts as a heuristic for MILP’s with gap-closing capabilities. Ideally, we would not have to use ML surrogates or discretization to solve this problem, instead solving the process family design problem with the equation-oriented model directly to achieve the most accurate results. However, recall that we did not consider solving the MINLP directly due to complexity and size. In this work, we aim to decompose and solve this large-scale MINLP using a Structured Nonlinear Global Optimization algorithm presented by Cao and Zavala (2019).

Stinchfield, Georgia

Feeding Ten Billion People Is Possible Within Four Terrestrial Planetary Boundaries

Global agriculture puts heavy pressure on planetary boundaries, posing the challenge to achieve future food security without compromising Earth system resilience. On the basis of process-detailed, spatially explicit representation of four interlinked planetary boundaries (biosphere integrity, land-system change, freshwater use, nitrogen flows) and agricultural systems in an internally consistent model framework, we here show that almost half of current global food production depends on planetary boundary transgressions. Hotspot regions, mainly in Asia, even face simultaneous transgression of multiple underlying local boundaries. If these boundaries were strictly respected, the present food system could provide a balanced diet (2,355 kcal per capita per day) for 3.4 billion people only. However, as we also demonstrate, transformation towards more sustainable production and consumption patterns could support 10.2 billion people within the planetary boundaries analysed. Key prerequisites are spatially redistributed cropland, improved water–nutrient management, food waste reduction and dietary changes. Adoption of the Sustainable Development Goals by all nations in 2015 is the first ever commitment to a world development path that safeguards the stability of the Earth system as a prerequisite for meeting universal human standards1. The longstanding challenge of achieving food security through sustainable agriculture is particularly acute in this context as world agriculture is a leading cause for the current transgressions of multiple planetary boundaries (PBs) globally and regionally2–5. The PB framework is a comprehensive scientific attempt to synoptically define our planet’s biogeophysical limits to anthropogenic interference. It suggests bounds to nine interacting processes that together delineate a Holocene-like Earth system state. The Holocene is chosen as the reference state as it is the only period known to provide a safe operating space for a world population of several billion people, and according to a precautionary principle, the PBs are set in sufficient distance from processes that may critically undermine Earth system resilience and global sustainability. A challenging question, thus, is whether human development goals such as food security can be met while maintaining multiple PBs along with their subglobal manifestations. Further PB transgressions could jeopardize the chances of providing sufficient food for a world population projected to be wealthier and reach >9 billion by 2050. This conundrum portrays a tradeoff between Earth’s biophysical carrying capacity and humankind’s rising food demand, calling in response for radical rethinking of food production and consumption patterns6–9. Yield gap closures, avoidance of excessive input use, shifts towards less resource-demanding diets, food waste reductions and efficient international trade are crucial options for sustainably increasing the food supply10–15. For example, enhancing water-use efficiency on irrigated and rain-fed farms can triple or quadruple crop yields in low-performing systems, suggesting possible global gains of >20% (ref. 16). Even higher gains appear feasible through globally optimized configurations of the land-use pattern17, and cutting food losses by half could generate food for another billion people18. Thus, collective large-scale implementation of such options could sustain food for a further growing world population19. Yet achieving this within a safe operating space as defined by PBs requires not only a halt to but actually a reversal of existing PB transgressions. Previous studies suggest that such a reconciliation might be possible, but these were based on aggregate representations of PBs (not accounting for the spatial patterns of limits, transgressions and interactions) or considered only one boundary in isolation17,20–23. Here, we systematically quantify to what extent current food production depends on local to global transgressions of the PBs for biosphere integrity, land-system change, freshwater use and nitrogen (N) flows, along with the potential of a range of solutions to avoid these transgressions and still increase food supply (Table 1). To this end, we configured an internally consistent process-based model of the terrestrial biosphere including agriculture (LPJmL) with multiple spatially distributed PBs and their interactions. LPJmL is among the longest-established and best-evaluated biosphere models, showing robust performance regarding simulation of, for example, carbon, water and crop yield dynamics (Supplementary Figs. 1 and 2 and Supplementary Table 1; see ref. 24 for a comprehensive benchmarking and Supplementary Methods for more detail on model evaluations). In principle following established definitions4, we refine the computation of some PBs with respect to their regional patterns and interactions (Methods), providing globally gridded precautionary limits to human interference with the Earth system at a level of great detail. In particular, we account for the evidence that many PBs need to be represented spatially explicitly4 to cover their

Gerten, Dieter

Improvement of Automated POST Case Success Rate Using Support Vector Machines

During early conceptual design of complex systems, concept down selection can have a large impact upon program life-cycle cost. Therefore, any concepts selected during early design will inherently commit program costs and affect the overall probability of program success. For this reason it is important to consider as large a design space as possible in order to better inform the down selection process. For conceptual design of launch vehicles, trajectory analysis and optimization often presents the largest obstacle to evaluating large trade spaces. This is due to the sensitivity of the trajectory discipline to changes in all other aspects of the vehicle design. Small deltas in the performance of other subsystems can result in relatively large fluctuations in the ascent trajectory because the solution space is non-linear and multi-modal [1]. In order to help capture large design spaces for new launch vehicles, the authors have performed previous work seeking to automate the execution of the industry standard tool, Program to Optimize Simulated Trajectories (POST). This work initially focused on implementation of analyst heuristics to enable closure of cases in an automated fashion, with the goal of applying the concepts of design of experiments (DOE) and surrogate modeling to enable near instantaneous throughput of vehicle cases [2]. Additional work was then completed to improve the DOE process by utilizing a graph theory based approach to connect similar design points [3]. The conclusion of the previous work illustrated the utility of the graph theory approach for completing a DOE through POST. However, this approach was still dependent upon the use of random repetitions to generate seed points for the graph. As noted in [3], only 8% of these random repetitions resulted in converged trajectories. This ultimately affects the ability of the random reps method to confidently approach the global optima for a given vehicle case in a reasonable amount of time. With only an 8% pass rate, tens or hundreds of thousands of reps may be needed to be confident that the best repetition is at least close to the global optima. However, typical design study time constraints require that fewer repetitions be attempted, sometimes resulting in seed points that have only a handful of successful completions. If a small number of successful repetitions are used to generate a seed point, the graph method may inherit some inaccuracies as it chains DOE cases from the non-global-optimal seed points. This creates inherent noise in the graph data, which can limit the accuracy of the resulting surrogate models. For this reason, the goal of this work is to improve the seed point generation method and ultimately the accuracy of the resulting POST surrogate model. The work focuses on increasing the case pass rate for seed point generation.

Zwack, Matthew R.

Numerical Computation of a Continuous-thrust State Transition Matrix Incorporating Accurate Hardware and Ephemeris Models

A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.

Low Thrust

Computation of optimal output-feedback compensators for linear time-invariant systems

The control of linear time-invariant systems with respect to a quadratic performance criterion was considered, subject to the constraint that the control vector be a constant linear transformation of the output vector. The optimal feedback matrix, f*, was selected to optimize the expected performance, given the covariance of the initial state. It is first shown that the expected performance criterion can be expressed as the ratio of two multinomials in the element of f. This expression provides the basis for a feasible method of determining f* in the case of single-input single-output systems. A number of iterative algorithms are then proposed for the calculation of f* for multiple input-output systems. For two of these, monotone convergence is proved, but they involve the solution of nonlinear matrix equations at each iteration. Another is proposed involving the solution of Lyapunov equations at each iteration, and the gradual increase of the magnitude of a penalty function. Experience with this algorithm will be needed to determine whether or not it does, indeed, possess desirable convergence properties, and whether it can be used to determine the globally optimal f*.

Platzman, L. K.

The Global Geodetic Observing System: Space Geodesy Networks for the Future

Ground-based networks of co-located space geodetic techniques (VLBI, SLR, GNSS. and DORIS) are the basis for the development and maintenance of the International Terrestrial Reference frame (ITRF), which is our metric of reference for measurements of global change, The Global Geodetic Observing System (GGOS) of the International Association of Geodesy (IAG) has established a task to develop a strategy to design, integrate and maintain the fundamental geodetic network and supporting infrastructure in a sustainable way to satisfy the long-term requirements for the reference frame. The GGOS goal is an origin definition at 1 mm or better and a temporal stability on the order of 0.1 mm/y, with similar numbers for the scale and orientation components. These goals are based on scientific requirements to address sea level rise with confidence, but other applications are not far behind. Recent studies including one by the US National Research Council has strongly stated the need and the urgency for the fundamental space geodesy network. Simulations are underway to examining accuracies for origin, scale and orientation of the resulting ITRF based on various network designs and system performance to determine the optimal global network to achieve this goal. To date these simulations indicate that 24 - 32 co-located stations are adequate to define the reference frame and a more dense GNSS and DORIS network will be required to distribute the reference frame to users anywhere on Earth. Stations in the new global network will require geologically stable sites with good weather, established infrastructure, and local support and personnel. GGOS wil seek groups that are interested in participation. GGOS intends to issues a Call for Participation of groups that would like to contribute in the network implementation and operation. Some examples of integrated stations currently in operation or under development will be presented. We will examine necessary conditions and challenges in designing a co-location station.

Pearlman, Michael

Engineering calculations for communications satellite systems planning

Computer-based techniques for optimizing communications-satellite orbit and frequency assignments are discussed. A gradient-search code was tested against a BSS scenario derived from the RARC-83 data. Improvement was obtained, but each iteration requires about 50 minutes of IBM-3081 CPU time. Gradient-search experiments on a small FSS test problem, consisting of a single service area served by 8 satellites, showed quickest convergence when the satellites were all initially placed near the center of the available orbital arc with moderate spacing. A transformation technique is proposed for investigating the surface topography of the objective function used in the gradient-search method. A new synthesis approach is based on transforming single-entry interference constraints into corresponding constraints on satellite spacings. These constraints are used with linear objective functions to formulate the co-channel orbital assignment task as a linear-programming (LP) problem or mixed integer programming (MIP) problem. Globally optimal solutions are always found with the MIP problems, but not necessarily with the LP problems. The MIP solutions can be used to evaluate the quality of the LP solutions. The initial results are very encouraging.

Reilly, C. H.

Neural architecture search via similarity adaptive guidance

Evolutionary neural network architecture search (ENAS) has attracted the attention of many experts due to its global optimization capabilities to automatically search for convolutional neural network architectures based on the target task. The current search space for ENAS is not to design a fully structured network, but to search for smaller cell architectures to reduce search costs. However, blind search strategies do not effectively utilize the potential experience of the population. In order to utilize the potential experience learned by the current population to guide the evolutionary search of the population, we propose a similarity guided neural network architecture search algorithm based on cell architecture, which utilizes the similarity between pairwise architectures in the population as empirical knowledge learned by the population. Our proposed algorithm provides a novel method for calculating architecture similarity, which calculates architecture similarity separately from the cell and macro-structure. Then we decouple the connections and operations in the cell and calculate connection and operation similarity separately. In addition, we propose adaptive similarity selection and binary tournament selection strategies to enhance the algorithm’s global and local search capabilities and effectively explore the search space. Finally, we design an improved single-point crossover operator to enhance the local search ability of the evolutionary operator. The experimental results show that SAGNAS is a competitive algorithm that achieves 97.44% and 81.60% in CIFAR10 and CIFAR100 with only 1.9 GPU-days spent.

97 MATHEMATICS AND COMPUTING

Influence of counterion substitution on the properties of imidazolium-based ionic liquid clusters

Due to their unique physiochemical properties that may be tailored for specific purposes, ionic liquids (ILs) have been investigated for various applications, including chemical separations, catalysis, energy storage, and space propulsion. The different cations and anions comprising ILs may be selected to optimize a range of desired properties, such as thermal stability, ionic conductivity, and volatility, leading to the designation of certain ILs as designer “green” solvents. The effect of counterions on the properties of ILs is of both fundamental scientific interest and technological importance. Herein, we report a systematic experimental and theoretical investigation of the size, charge, stability toward dissociation, and geometric/electronic structure of 1-ethyl-3-methyl imidazolium (EMIM)-based IL clusters containing two different atomic counterions (i.e., bromide [Br − ] and iodide [I − ]). This work extends our studies of EMIM + cations with atomic chloride (Cl − ) and molecular tetrafluoroborate (BF 4 − ) anions reported previously by Baxter et al. [Chem. Mater. 34, 2612 (2022)] and Zhang et al . [J. Phys. Chem. Lett. 11, 6844 (2020)], respectively. Distributions of anionic IL clusters were generated in the gas phase using electrospray ionization and characterized by high mass resolution mass spectrometry, energy-resolved collision-induced dissociation, and negative ion photoelectron spectroscopy experiments. The experimental results reveal anion-dependent trends in the size distribution, relative abundance, ionic charge state, stability toward dissociation, and electron binding energies of the IL clusters. Complementary global optimization theory provides molecular-level insights into the bonding and electronic structure of a selected subset of clusters, including their low energy structures and electrostatic potential maps, and how these fundamental characteristics are influenced by anion substitution. Collectively, our findings demonstrate how the fundamental properties of ILs, which determine their suitability for many applications, may be tuned by substituting counterions. These observations are critical in the sub-nanometer cluster size regime where phenomena do not scale predictably to the bulk phase, and each atom counts toward determining behavior.

cluster

ARPA-E Grid Optimization (GO) Competition Challenge 2

The ARPA-E Grid Optimization (GO) Competition Challenge 2, from 2020 to 2021, expanded upon the problem posed in Challenge 1 by adding adjustable transformer tap ratios, phase shifting transformers, switchable shunts, price-responsive demand, ramp rate constrained generators and loads, and fast-start unit commitment. Furthermore, Challenge 2 was a maximization problem while Challenge 1 was a minimization problem. Specifically, the economic surplus, defined as the benefit of serving load minus the cost of generation, is being maximized. It was expected that the objective value of a given solution should be positive, representing economic gain, but negative objectives from poor solutions were possible. The two code submission feature of Challenge 1 was maintained. Additionally, Divisions 3 and 4 within the competition permitted on/off switching of transmission lines (Divisions 1 and 2 did not). After the initial release of the Problem Formulation on 7/20/2020, ARPA-E Director Lane Genatowski announced Challenge 2 on 9/12/2020. The final May 31, 2021, version of the Problem Formulation was 97 pages long with 299 equations. The Challenge proceeded with 2 non-prize Events and 2 prize Events. Teams receiving Challenge 1 FOA awards and prize money were required to use the prize money to fund their Challenge 2 efforts (Georgia Institute of Technology, Global Optimal Technology, Inc., Lawrence Livermore National Laboratory, Lehigh University, Northwestern University, Artelys, Columbia, Pearl Street Technologies, Pennsylvania State University, and University of Colorado Boulder). For more information on the competition and challenge 2 see the "GO Competition Challenge 2 Information" resource below. Challenge 1 and Challenge 3 information can be found in the resources linked below.

ACOPF

Accelerating the Structure Exploration of Diverse Bi–Pt Nanoclusters via Physics‐Informed Machine Learning Potential and Particle Swarm Optimization

Bimetallic Bi–Pt nanoclusters exhibit diverse structural motifs, including core-shell, Janus, and mixed alloy configurations, due to the unique bonding characteristics between Bi and Pt atoms. Using density functional theory refinements from ChIMES physically machine-learned potential and CALYPSO particle swarm optimization global searches, 34 Bi20-Pt20 nanoclusters are systematically classified. The results reveal that Bi atoms predominantly occupy surface sites, driven by charge transfer effects. Cohesive energy trends alone prove insufficient for structure differentiation, necessitating a data-driven approach employing principal component analysis and K-means clustering. Furthermore, vibrational, electronic, and infrared spectral analyses provide additional insights into structure-property relationships. The findings offer an original framework for the automated classification and analysis of bimetallic nanoclusters, enhancing the understanding of their stability and functional properties.

bimetallic nanoparticles