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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Finding the Pareto front for high-entropy-alloy catalysts

Finding catalysts that have both high activity and high stability presents a long-standing challenge. Since optimizing activity and stability are conflicting objectives, the best one can do is find the Pareto front that yields optimal tradeoffs between these features. On the Pareto front, there is a trade-off where a portion of catalytic activity must be sacrificed to gain further stability and vice versa . Here, we provide a method to optimize the front by designing a multi-objective genetic algorithm that combines machine learning, graph neural network calculations, and density functional calculations. The application considered is the oxygen evolution reaction catalyzed by high-entropy alloys. We find that the Pareto front generally contains alloys with diverse elements, but that enhancing stability inevitably inflicts a toll on activity. We compare the general conclusions of our work to a survey of 545 experiments.

Zhang, Chengyi [Univ. of Auckland (New Zealand)]↗
DOE OSTI2021

Thermodynamic stability versus kinetic accessibility: Pareto fronts for programmable self-assembly

A challenge in designing self-assembling building blocks is to ensure the target state is both thermodynamically stable and kinetically accessible. These two objectives are known to be typically in competition, but it is not known how to simultaneously optimize them. We consider this problem through the lens of multi-objective optimization theory: we develop a genetic algorithm to compute the Pareto fronts characterizing the tradeoff between equilibrium probability and folding rate, for a model system of small polymers of colloids with tunable short-ranged interaction energies. We use a coarse-grained model for the particles' dynamics that allows us to efficiently search over parameters, for systems small enough to be enumerated. For most target states there is a tradeoff when the number of types of particles is small, with medium-weak bonds favouring fast folding, and strong bonds favouring high equilibrium probability. Additionally, the tradeoff disappears when the number of particle types reaches a value m *, that is usually much less than the total number of particles. This general approach of computing Pareto fronts allows one to identify the minimum number of design parameters to avoid a thermodynamic–kinetic tradeoff. However, we argue, by contrasting our coarse-grained model's predictions with those of Brownian dynamics simulations, that particles with short-ranged isotropic interactions should generically have a tradeoff, and avoiding it in larger systems will require orientation-dependent interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Environmental and socio-economic Pareto-front trade-off analysis of U.S. PET packaging material in a circular economy

Various recycling technologies are emerging to implement circular economy in plasticssupply chain systems. However, the environmental and socio-economic trade-offs of in circular economy are not well understood at a systems level. Particularly, quantifying these trade-offs as a function of end-of-life (EOL) management decisions, including transition of recycling technologies, systems level metrics such as circularity, recycled content, and the need for fossil-derived plastics are not well understood. Here, the present study addressed these research gaps by applying a systems analysis modeling approach that utilizes material flow analysis, life cycle assessment, socioeconomic data, and system optimization techniques for polyethylene terephthalate (PET) packaging supply chains in the United States. Pareto-front trade-offs between conflicting environmental and socio-economic impacts as well as those between socioeconomic impacts and circularity were explored using the epsilon constraint method. The Pareto-front trade-off analysis revealed the transition of EOL management strategies for PET packaging systems, including changes in selection of recycling technologies, to aid decision making process by quantifying studied system metrics. Transitioning from environmentally optimal to socio-economically optimal systems led to increased employment (by 17%), wages (by 26%), and revenues (by 6%) but also led to increased global warming potential (GWP; by 65%), energy consumption (by 59%), and reliance on fossil PET in the system (by 78%). Finally, the results show that there is not a unique set of recycling technologies to achieve a sustainable circular economy of PET packaging system, instead it depends on the decision maker’s objectives and targeted metrics of the system.

54 - ENVIRONMENTAL SCIENCES/GLOBAL CLIMATE CHANGE ↗
DOE OSTI2022

Low Space Harmonic Content Windings (LSHWs) Applied to Improve the Pareto Front in Design Optimization of Electric Machines

In design optimization of high performance electric machines where the power density is increasingly a key metric, it is often desirable to maximize the average torque output within a given volume. However, if a smooth output is also required, the torque ripple may become a hurdle as it tends to increase with the average torque for conventional windings. A direct benefit of low space harmonic content windings (LSHWs), featuring the suppression or elimination of targeted non-working orders in the winding magnetomotive force (MMF), is the torque ripple reduction. This paper provides a detailed analysis of torque ripple pairs and the space-time harmonic order mapping, with concise results that applies to both distributed windings and fractionalslot concentrated windings (FSCWs) of any slot/pole combination. Metamodel-based optimizations are performed to compare two LSHWs with a conventional winding. Improved Pareto fronts are validated, which confirms higher torque producing capabilities at various torque ripple thresholds for LSHWs.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2026

Active learning enables generation of molecules that advance the known Pareto front

Although generative models hold promise for discovering molecules with optimized desired properties, they often fail to suggest synthesizable molecules that improve upon the properties of the structures represented in the training distribution. We find that this limitation arises not only from the molecule generation process itself, but also from the poor generalization capabilities of molecular property predictors. We address this challenge by creating a closed-loop molecule generation pipeline with iterative retraining on new quantum chemical simulation data. Compared against static, single-pass generative modeling approaches, only our closed-loop iterative workflow generates molecules with properties extending beyond the training distribution (up to 0.44 standard deviations beyond the original range) and achieves a 79% improvement in out-of-distribution molecule classification accuracy. Furthermore, by conditioning molecular generation on thermodynamic stability data obtained during the iterative loop, the proportion of stable and hence potentially synthesizable molecules generated is 3.5x higher than the next-best model.

Chemistry↗
NASA NTRS2003

Evaluation of Genetic Algorithm Concepts Using Model Problems: Multi-Objective Optimization - Part 2

A genetic algorithm approach suitable for solving multi-objective optimization problems is described and evaluated using a series of simple model problems. Several new features including a binning selection algorithm and a gene-space transformation procedure are included. The genetic algorithm is suitable for finding pareto optimal solutions in search spaces that are defined by any number of genes and that contain any number of local extrema. Results indicate that the genetic algorithm optimization approach is flexible in application and extremely reliable, providing optimal results for all optimization problems attempted. The binning algorithm generally provides pareto front quality enhancements and moderate convergence efficiency improvements for most of the model problems. The gene-space transformation procedure provides a large convergence efficiency enhancement for problems with non-convoluted pareto fronts and a degradation in efficiency for problems with convoluted pareto fronts. The most difficult problems --multi-mode search spaces with a large number of genes and convoluted pareto fronts-- require a large number of function evaluations for GA convergence, but always converge.

Holst, Terry L.↗
DOE OSTI2024

Surrogate Model Guided Optimization of Expensive Black-Box Multi-Objective Problems: A Posteriori Methods

Many engineering applications require the simultaneous optimization of multiple conflicting objective functions. Often, these objective functions are evaluated using highly accurate computer simulations that are computationally too expensive to be evaluated hundreds or thousands of times during optimization. Thus, the goal is to find good approximations of the Pareto front using as few of these expensive simulations as possible. Here, we describe an optimization approach based on surrogate models and diverse sampling strategies to accelerate the search for the Pareto solutions. We use a separate surrogate model for approximating each objective function and then we use the surrogate models to inform where additional expensive simulations should be run. The surrogate models are updated in an active learning framework whenever new information from the expensive simulations becomes available. The sampling strategies aim at balancing local improvements of the approximate Pareto front and global exploration to identify the extrema and fill in large gaps of the approximate Pareto front. We demonstrate on a large set of benchmark problems the effectiveness of the method for finding good approximations of the Pareto front.

MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Surrogate-driven design optimization with uncertainty constraints in Monte Carlo simulations

In multi-objective design tasks, the computational cost increases rapidly when high-fidelity simulations are used to evaluate objective functions. Surrogate models help mitigate this cost by approximating the simulation output, simplifying the design process. However, under high uncertainty, surrogate models trained on noisy data can produce inaccurate predictions, as their performance depends heavily on the quality of training data. This study investigates the impact of data uncertainty on two multi-objective design problems modelled using Monte Carlo transport simulations: a neutron moderator and an ion-to-neutron converter. For each, a grid search was performed using five different tally uncertainty levels to generate training data for neural network surrogate models. These models were then optimized using NSGA-III. The recovered Pareto-fronts were analyzed across uncertainty levels: in the moderator problem, normalized hypervolume dropped from 0.886 at 1.0% uncertainty to 0.748 at 10% uncertainty, while in the converter problem it remained near 0.50 for all cases. Average simulation times were also compared to evaluate the trade-off between accuracy and computational cost. Results show that the influence of simulation uncertainty is strongly problem-dependent. In the neutron moderator case, higher uncertainties led to exaggerated objective sensitivities and distorted Pareto-fronts, reducing normalized hypervolume. In contrast, the ion-to-neutron converter task was less affected—low-fidelity simulations produced results similar to those from high-fidelity data. These findings suggest that a fixed-fidelity approach is not optimal. Surrogate models can recover the Pareto-front under noisy conditions, and multi-fidelity studies help identify suitable uncertainty levels for each problem to balance efficiency and accuracy.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2022

An agent-based blackboard system for multi-objective optimization

In the field of multi-objective optimization, there are a multitude of algorithms from which to choose. Each algorithm has strengths and weaknesses associated with the mechanics for finding the Pareto front. Recently, researchers have begun to examine how multi-agent environments can be used to help solve multi-objective optimization problems. In this work, we propose a multi-objective optimization algorithm based on a multi-agent blackboard system (MABS). The MABS framework allows for multiple agents to read and write pertinent optimization problem data to a central blackboard agent. Agents can stochastically search the design space, use previously discovered solutions to explore local optima, or update and prune the Pareto front. A centralized blackboard framework allows the optimization problem to be solved in a cohesive manner and permits stopping, restarting, or updating the optimization problem. The MABS framework is tested against three alternative optimization algorithms across a suite of engineering design problems and typically outperforms the other algorithms in discovering the Pareto front. A parallelizability study is performed where we find that the MABS is able to evaluate a set number of designs, which require an evaluation time ranging from 0 to 300 seconds, quicker than a traditional optimization algorithm: this fact becomes more apparent the longer it takes to evaluate a design. To provide context for the benefits provided by MABS, a real-world nuclear engineering design problem is examined. MABS is used to examine the placement of experiments in a nuclear reactor, where we are able to evaluate hundreds of configurations for experimental placement while maintaining a strict set of safety constraints.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Quantum approximate multi-objective optimization

The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2019

Numerical Investigation and Optimization of a Flushwall Injector for Scramjet Applications at Hypervelocity Flow Conditions

An investigation utilizing Reynolds-averaged simulations (RAS) was performed in order to find optimal designs for an interdigitated flushwall injector suitable for scramjet applications at hypervelocity conditions. The flight Mach number, duct height, spanwise width, and injection angle were the design variables selected to maximize two objective functions: the thrust potential and combustion efficiency. A Latin hypercube sampling design-of-experiments method was used to select design points for RAS. A methodology was developed that automated building geometries and generating grids for each design. The ensuing RAS analysis generated the performance database from which the two objective functions of interest were computed using a one-dimensional performance utility. The data were fitted using four surrogate models: an artificial neural network (ANN) model, a cubic polynomial, a quadratic polynomial, and a Kriging model. Variance-based decomposition showed that both objective functions were primarily driven by changes in the duct height. Multiobjective design optimization was performed for all four surrogate models via a genetic algorithm method. Optimal solutions were obtained at the upper and lower bounds of the flight Mach number range. The Kriging model obtained an optimal solution set that predicted high values for both objective functions. Additionally, three challenge points were selected to assess the designs on the Pareto fronts. Further sampling among the designs of the Pareto fronts are required in order to lower the errors and perform more accurate surrogate-based optimization. sed optimization.

Shenoy, Rajiv R.↗
NASA NTRS2019

Numerical Investigation and Optimization of a Flushwall Injector for Scramjet Applications at Hypervelocity Flow Conditions

An investigation utilizing Reynolds-averaged simulations (RAS) was performed in order to demonstrate the use of design and analysis of computer experiments (DACE) methods in Sandia’s DAKOTA software package for surrogate modeling and optimization. These methods were applied to a flow- path fueled with an interdigitated flushwall injector suitable for scramjet applications at hyper- velocity conditions and ascending along a constant dynamic pressure flight trajectory. The flight Mach number, duct height, spanwise width, and injection angle were the design variables selected to maximize two objective functions: the thrust potential and combustion efficiency. Because the RAS of this case are computationally expensive, surrogate models are used for optimization. To build a surrogate model a RAS database is created. The sequence of the design variables comprising the database were generated using a Latin hypercube sampling (LHS) method. A methodology was also developed to automatically build geometries and generate structured grids for each design point. The ensuing RAS analysis generated the simulation database from which the two objective functions were computed using a one-dimensionalization (1D) of the three-dimensional simulation data. The data were fitted using four surrogate models: an artificial neural network (ANN), a cubic polynomial, a quadratic polynomial, and a Kriging model. Variance-based decomposition showed that both objective functions were primarily driven by changes in the duct height. Multiobjective design optimization was performed for all four surrogate models via a genetic algorithm method. Optimal solutions were obtained at the upper and lower bounds of the flight Mach number range. The Kriging model predicted an optimal solution set that exhibited high values for both objective functions. Additionally, three challenge points were selected to assess the designs on the Pareto fronts. Further sampling among the designs of the Pareto fronts may be required to lower the surrogate model errors and perform more accurate surrogate-model-based optimization.

Shenoy, Rajiv R.↗
DOE OSTI2024

Optimization of the Second Target Station cold source moderators using an automated workflow

The Second Target Station (STS) at the US Department of Energy’s Oak Ridge National Laboratory is designed to become the world’s highest peak-brightness spallation source of cold neutrons. Successful completion of the STS, which is currently in the preliminary design phase, will provide transformative new capabilities to examine novel materials for future technologies. At STS, neutrons will be generated by spallation reactions in a solid tungsten target. They will be moderated and thermalized in two cold (20 K) para-hydrogen moderators. Careful optimization of these moderators is essential to the project’s success. To find optimal moderator designs, an advanced optimization workflow integrates high-fidelity neutronics calculations using the Monte Carlo N-Particle (MCNP) transport code MCNP6.2 with state-of-the-art optimization algorithms in the Dakota optimization toolkit. For each design iteration, a parametrized solid CAD geometry is generated in Creo and automatically converted into an unstructured mesh geometry by Attila 4MC for the neutronics calculation with MCNP. Iterations repeat until optimal designs are found. Herein this paper presents the results of a sensitivity and optimization study for the cylindrical and tube moderators. Both moderators can be optimized for maximum peak brightness, maximum time-integrated brightness, or any combination between these extremes. Maximum peak brightness is achieved by using smaller optimal dimensions of the moderators, whereas maximum time-integrated brightness is achieved by using larger dimensions. A Pareto front details the designs that optimally balance both brightness metrics. The Pareto front can be found in only 40–110 iterations with 4–5 design parameters when using the efficient global and Pareto-set optimization algorithms in Dakota. Additionally, important engineering constraints can be taken into account, such as the coupling between the cylindrical moderator radius and aluminum vessel wall thicknesses required to ensure structural integrity of the vessels. This interaction has a significant impact on the resulting optimal designs. Our new, highly efficient, fully automated optimization workflow will be used to optimize additional STS components in the future and can be adopted for design and optimization studies at other experimental neutron and accelerator facilities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS2015

Vibroacoustic Tailoring of a Rod-Stiffened Composite Fuselage Panel with Multidisciplinary Considerations

An efficient multi-objective design tailoring procedure seeking to improve the vibroacoustic performance of a fuselage panel while maintaining or reducing weight is presented. The structure considered is the pultruded rod stitched efficient unitized structure, a highly integrated composite structure concept designed for a noncylindrical, next-generation flight vehicle fuselage. Modifications to a baseline design are evaluated within a six-parameter design space including spacing, flange width, and web height for both frame and stringer substructure components. The change in sound power radiation attributed to a design change is predicted using finite-element models sized and meshed for analyses in the 500 Hz, 1 kHz, and 2 kHz octave bands. Three design studies are carried out in parallel while considering a diffuse acoustic field excitation and two types of turbulent boundary-layer excitation. Kriging surrogate models are used to reduce the computational costs of resolving the vibroacoustic and weight objective Pareto fronts. The resulting Pareto optimal designs are then evaluated under a static pressurization ultimate load to assess structural strength and stability. Results suggest that choosing alternative configurations within the considered design space can reduce weight and improve vibroacoustic performance without compromising strength and stability of the structure under the static load condition considered, but the tradeoffs are significantly influenced by the spatial characteristics of the assumed excitation field.

Allen, Albert R.↗
DOE OSTI2022

Optimization of Water-Alternating-CO2 Injection Field Operations Using a Machine-Learning-Assisted Workflow

Summary This paper will present a robust workflow to address multiobjective optimization (MOO) of carbon dioxide (CO2)-enhanced oil recovery (EOR)-sequestration projects with a large number of operational control parameters. Farnsworth unit (FWU) field, a mature oil reservoir undergoing CO2 alternating water injection (CO2-WAG) EOR, will be used as a field case to validate the proposed optimization protocol. The expected outcome of this work would be a repository of Pareto-optimal solutions of multiple objective functions, including oil recovery, carbon storage volume, and project economics. FWU’s numerical model is used to demonstrate the proposed optimization workflow. Because using MOO requires computationally intensive procedures, machine-learning-based proxies are introduced to substitute for the high-fidelity model, thus reducing the total computation overhead. The vector machine regression combined with the Gaussian kernel (Gaussian-SVR) is used to construct proxies. An iterative self-adjusting process prepares the training knowledge base to develop robust proxies and minimizes computational time. The proxies’ hyperparameters will be optimally designed using Bayesian optimization to achieve better generalization performance. Trained proxies will be coupled with multiobjective particle swarm Optimization (MOPSO) protocol to construct the Pareto-front solution repository. The outcomes of this workflow will be a repository containing Pareto-optimal solutions of multiple objectives considered in the CO2-WAG project. The proposed optimization workflow will be compared with another established methodology using a multilayer neural network (MLNN) to validate its feasibility in handling MOO with a large number of parameters to control. Optimization parameters used include operational variables that might be used to control the CO2-WAG process, such as the duration of the water/gas injection period, producer bottomhole pressure (BHP) control, and water injection rate of each well included in the numerical model. It is proved that the workflow coupling Gaussian-SVR proxies and the iterative self-adjusting protocol is more computationally efficient. The MOO process is made more rapid by squeezing the size of the required training knowledge base while maintaining the high accuracy of the optimized results. The outcomes of the optimization study show promising results in successfully establishing the solution repository considering multiple objective functions. Results are also verified by validating the Pareto fronts with simulation results using obtained optimized control parameters. The outcome from this work could provide field operators an opportunity to design a CO2-WAG project using as many inputs as possible from the reservoir models. The proposed work introduces a novel concept that couples Gaussian-SVR proxies with a self-adjusting protocol to increase the computational efficiency of the proposed workflow and to guarantee the high accuracy of the obtained optimized results. More importantly, the workflow can optimize a large number of control parameters used in a complex CO2-WAG process, which greatly extends its utility in solving large-scale MOO problems in various projects with similar desired outcomes.

Energy & Fuels↗
DOE OSTI2022

Consideration of alternative coolants in AGR-like FHR designs

Replacing carbon-dioxide coolant in AGR-like reactor with molten salt significantly affects the reactor performance characteristics. Hence, a new core design is needed. In this work, a Multi-Objective Particle Swarm Optimisation is used to identify the most favourable configurations for a new system layout. The performed analysis examines each configuration with respect to its thermal-hydraulic performance to assess the power uprate potential which is limited by multiple temperature constraints (e.g. fuel centreline and cladding temperatures as well as the coolant freezing/boiling). The estimated maximum power was then used in the fuel burnup calculations, from which a discharge burnup and cycle average Coolant Temperature Coefficients (CTC) were obtained. As a result of the optimisation process, several families of possible solutions were identified, which form an optimal Pareto Front. The most attractive configurations in terms of achievable power density, however, were not necessarily on the Pareto front. Several coolant options are examined and compared in this paper. The newly identified design options have the potential to achieve power density that is higher than that of a typical AGR by up to a factor of five while maintaining negative CTC through the burnup cycle. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗