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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Estimating the Adequacy of a Multi-Objective Optimization

Multi-objective optimization methods can be criticized for lacking a statistically valid measure of the quality and representativeness of a solution. This stance is especially relevant to metaheuristic optimization approaches but can also apply to other methods that typically might only report a small representative subset of a Pareto frontier. Here we present a method to address this deficiency based on random sampling of a solution space to determine, with a specified level of confidence, the fraction of the solution space that is surpassed by an optimization. The Superiority of Multi-Objective Optimization to Random Sampling, or SMORS method, can evaluate quality and representativeness using dominance or other measures, e.g., a spacing measure for high-dimensional spaces. SMORS has been tested in a combinatorial optimization context using a genetic algorithm but could be useful for other optimization methods.

42 ENGINEERING↗
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↗
DOE OSTI2022

LINAC OPTICS OPTIMIZATION WITH MULTI-OBJECTIVE OPTIMIZATION

The beamline design of recirculating linacs requires special attention to avoid beam instabilities due to RF wakefields. A proposed high-energy, multi-pass energy recovery demonstration at CEBAF uses a low beam current. Stronger focusing at lower energies is necessary to avoid beam breakup(BBU) instabilities, even with this small beam current. The CEBAF linac optics optimization balances over-focusing at higher energies and beta excursions at lower energies. Using proper mathematical expressions, linac optics optimization can be achieved with evolutionary algorithms. Here, we present the optimization process of North Linac optics using multi-objective optimization.

Neththikumara, I.↗
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↗
NASA NTRS2019

Time-varying Weights in Multi-Objective Optimal Control for Flexible Wing Aircraft

A multi-objective optimal control technique is modified to accommodate changing cost function weights and is used to control a flexible wing aircraft model. Variation of the weights is used to adjust the relative importance of each objective according to either a prescribed function of time or of the state. Several techniques for obtaining a practical approximation to the optimal control solution are presented, and stability of a specific weight structure with the optimal controller is demonstrated. Functionality of the multi-objective control design with weight variation is demonstrated in simulation of a flexible wing transport aircraft and is shown to improve performance over the fixed weight version both at a constant flight condition and across changing flight conditions.

Hashemi, Kelley E.↗
NASA NTRS2022

A Reinforcement Learning Hyper-Heuristic in Multi-Objective Optimization with Application to Structural Damage Identification

Multi-objective optimization allows satisfying multiple decision criteria concurrently, and generally yields multiple solutions. It has the potential to be applied to structural damage identification applications which are oftentimes under-determined. How to achieve high-quality solutions in terms of accuracy, diversity, and completeness is a challenging research subject. The solution techniques and parametric selections are believed to be problem specific. In this research, we formulate a reinforcement learning hyper-heuristic scheme to work coherently with the single-point search algorithm MOSA/R (Multi-Objective Simulated Annealing Algorithm based on Re-seed). The four low-level heuristics proposed can meet various optimization requirements adaptively and autonomously using the domination amount, crowding distance, and hypervolume calculations. The new approach exhibits improved and more robust performance than AMOSA, NSGA-II, and MOEA/D when applied to benchmark test cases. It is then applied to an active damage interrogation scheme for structural damage identification where solution diversity/completeness and accuracy are critically important. Results show that this approach can successfully include the true damage scenario in the solution set identified. The outcome of this research can potentially be extended to a variety of applications.

Pei Cao↗
DOE OSTI2024

Utilizing waste heat in wastewater treatment plants for water desalination: Modeling and Multi-Objective optimization of a Multi-Effect desalination system using Decision Tree Regression and Pelican optimization algorithm

This paper examines the feasibility of using waste heat from wastewater treatment plants (WWTPs) for water desalination. A model was developed to utilize waste heat from the gensets at As Samra WWTP in Jordan, using real data and TRNSYS® software to calculate available waste heat. The desalination process was then modeled with ASPEN PLUS® software, focusing on multi-effect desalination (MED). Both series and parallel configurations for the MED system were compared. The study investigated the effects of system feeding flow rate, feeding pressure, and heat input on productivity, performance ratio, and recovery ratio. The study also introduces a novel optimization technique combining machine learning and modern optimization algorithms to maximize system productivity and performance. Initially, a decision tree regression (DTR) model is developed to establish relationships between key independent variables (flow rate, feed pressure, and heat input) and dependent variables (productivity, performance ratio, and recovery ratio). The Pelican Optimization Algorithm (POA) is then used to identify the optimal values of the independent variables for maximum productivity and performance. The results show that using a series configuration yields a system productivity of 3984.2 kg/hr, a performance ratio of 3.78, and a recovery ratio of 0.991 at a feed flow rate of 4000 kg/hr, feed pressure of 3 bars, and heat input of 719 kW. Optimal productivity (4421 kg/hr), performance ratio (3.81), and recovery ratio (0.851) are achieved at a feed flow rate of 5166 kg/hr, feed pressure of 3.2 bars, and heat input of 794 kW. In conclusion, the techno-economic assessment indicates a levelized cost of water of 1.63 USD/m 3 for parallel configurations and 1.65 USD/m 3 for series configurations, with a payback period of less than two years.

42 ENGINEERING↗
DOE OSTI2025

Harnessing the power of gradient-based simulations for multi-objective optimization in particle accelerators

Abstract Particle accelerator operation requires simultaneous optimization of multiple objectives. Multi-objective optimization (MOO) is particularly challenging due to trade-offs between the objectives. Evolutionary algorithms, such as genetic algorithms (GAs), have been leveraged for many optimization problems, however, they do not apply to complex control problems by design. This paper demonstrates the power of differentiability for solving MOO problems in particle accelerators using a deep differentiable reinforcement learning (DDRL) algorithm. We compare the DDRL algorithm with model-free reinforcement learning (MFRL), GA, and Bayesian optimization (BO) for simultaneous optimization of heat load and trip rates in the continuous electron beam accelerator facility. The underlying problem enforces strict constraints on both individual states and actions as well as cumulative (global) constraints on energy requirements of the beam. Using historical accelerator data, we develop a physics-based surrogate model which is differentiable and allows for back-propagation of gradients. The results are evaluated in the form of a Pareto-front with two objectives. We show that the DDRL outperforms MFRL, BO, and GA on high dimensional problems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Parallel Variable Population Multi-Objective Optimizer (pvpmoo) v1.0

This is a parallel variable population multi-objective optimizer with an adaptive unified differential evolution algorithm or a genetic algorithm. It can also be used for single objective optimization. Some features of this code include: 1) The population size varies from generation to generation to save the total # of objective function evaluations. 2) The population is uniformly distributed to a number of parallel processors for simultaneous objective function evaluation. 3) The objective function evaluation can be attained from an external simulation program with control variables in its input file and objectives calculated from its output files. 4) The optimizer includes an adaptive unified differential evolution algorithm and a real value genetic algorithm. The parameters in the unified differential evolution algorithm can be chosen to attain any mutation schemes in the published literature.

Qiang, Ji↗
NASA NTRS2019

Multi-Objective Optimal Control of the 6-DoF Aeroservoelastic Common Research Model with Aspect Ratio 13.5 Wing

A new 6-DoF aeroservoelastic (ASE) Common Research Model (CRM) provided by The Boeing Company with aspect ratio 13.5 and 17 control surfaces per wing is utilized to demonstrate combined tracking and optimal multi-objective control. The multi-objective controller is derived on the closed loop tracking controller, and utilizes state and gust estimates provided by an extended state observer. Various methods of model reduction useful for control and estimation are presented. A computationally efficient MATLAB/Simulink simulation is presented which includes actuator dynamics, rate and deflection saturation limits, and gust disturbance inputs. The platform is used to demonstrate excellent 6-DoF tracking control performance coupled with the multi-objective controller, which is shown to effectively reduce structural mode movement, wing root bending moment, and drag. State and gust estimation is also shown to perform well, even when derived and/or implemented with significantly fewer states than the original full-sized model.

Drew, Michael C.↗
DOE OSTI2020

Evolutionary multi-objective optimization and Pareto-frontal uncertainty quantification of interatomic forcefields for thermal conductivity simulations

Predictive Molecular Dynamics simulations of thermal transport require forcefields that can simultaneously reproduce several structural, thermodynamic and vibrational properties of materials like lattice constants, phonon density of states, and specific heat. This requires a multi-objective optimization approach for forcefield parameterization. Existing methodologies for forcefield parameterization use ad-hoc and empirical weighting schemes to convert this into a single-objective optimization problem. Here, we provide and describe software to perform multi-objective optimization of Stillinger–Weber forcefields (SWFF) for two-dimensional layered materials using the recently developed 3rd generation non-dominated sorting genetic algorithm (NSGA-III). NSGA-III converges to the set of optimal forcefields lying on the Pareto front in the multi-dimensional objective space. This set of forcefields is used for uncertainty quantification of computed thermal conductivity due to variability in the forcefield parameters. We demonstrate this new optimization scheme by constructing a SWFF for a representative two-dimensional material, 2H-MoSe 2 and quantifying the uncertainty in their computed thermal conductivity.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2022

Soft and transferable pseudopotentials from multi-objective optimization

Ab initio pseudopotentials are a linchpin of modern molecular and condensed matter electronic structure calculations. In this work, we employ multi-objective optimization to maximize pseudopotential softness while maintaining high accuracy and transferability. To accomplish this, we develop a formulation in which softness and accuracy are simultaneously maximized, with accuracy determined by the ability to reproduce all-electron energy differences between Bravais lattice structures, whereupon the resulting Pareto frontier is scanned for the softest pseudopotential that provides the desired accuracy in established transferability tests. We employ an evolutionary algorithm to solve the multi-objective optimization problem and apply it to generate a comprehensive table of optimized norm-conserving Vanderbilt (ONCV) pseudopotentials (https://github.com/SPARC-X/SPMS-psps). Here, we show that the resulting table is softer than existing tables of comparable accuracy, while more accurate than tables of comparable softness. The potentials thus afford the possibility to speed up calculations in a broad range of applications areas while maintaining high accuracy.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Multi-objective optimization with an integrated electromagnetics and beam dynamics workflow

In particle accelerators, RF cavities are used to accelerate charged particle beams to designed high energy for physical applications. In a typical accelerator design, the optimization of RF cavities and the optimization of beam dynamics are carried out in separate studies. For a more general and unrestricted accelerator design, a coupled optimization of the RF cavities and the beam parameters is required. For this coupled optimization problem, we have developed an integrated electromagnetics and beam dynamics workflow management system. Within this system, the geometries for a set of cavity components are first adjusted; the field modes are then computed with an electromagnetics program, and imported into a beam dynamics program for beam dynamics simulation. This workflow is encapsulated into a parallel multi-objective optimizer to achieve the integrated accelerator design optimization. A multi fidelity strategy is developed to improve the speed of the optimizer. Furthermore, this integrated global optimization capability is illustrated using a photoinjector design example and yields an improved design.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

NSGA-PINN: A Multi-Objective Optimization Method for Physics-Informed Neural Network Training

This paper presents NSGA-PINN, a multi-objective optimization framework for the effective training of physics-informed neural networks (PINNs). The proposed framework uses the non-dominated sorting genetic algorithm (NSGA-II) to enable traditional stochastic gradient optimization algorithms (e.g., ADAM) to escape local minima effectively. Additionally, the NSGA-II algorithm enables satisfying the initial and boundary conditions encoded into the loss function during physics-informed training precisely. We demonstrate the effectiveness of our framework by applying NSGA-PINN to several ordinary and partial differential equation problems. In particular, we show that the proposed framework can handle challenging inverse problems with noisy data.

Lu, Binghang (ORCID:0009000160016632)↗
NASA NTRSDate not supplied

Multi-Objective Optimal Control of High Aspect Ratio Wing Wind Tunnel Model

This paper presents the design of a multi-objective optimal controller for the 13.5 aspect ratio Common Research Model (CRM) wind tunnel model. A Pareto front analysis is performed to provide the optimal tradeoff between the competing objectives - gust load alleviation, maneuver load alleviation, and drag minimization - so that the weighting matrices for the control law are selected optimally. Also presented are two formulations of the controller: a state feedback with Kalman filter design, and an output feedback form where sensors are used directly for feedback control. The controller demonstrates a reduced peak-to-peak strain of 45.78% while also reducing drag and mean bending moment. An output feedback formulation for gust load alleviation is formulated and produces a 53% reduction in the strain response due to a gust input.

Gust Load Alleviation↗
DOE OSTI2025

Data imbalance in drug response prediction: multi-objective optimization approach in deep learning setting

Abstract Drug response prediction (DRP) methods tackle the complex task of associating the effectiveness of small molecules with the specific genetic makeup of the patient. Anti-cancer DRP is a particularly challenging task requiring costly experiments as underlying pathogenic mechanisms are broad and associated with multiple genomic pathways. The scientific community has exerted significant efforts to generate public drug screening datasets, giving a path to various machine learning models that attempt to reason over complex data space of small compounds and biological characteristics of tumors. However, the data depth is still lacking compared to application domains like computer vision or natural language processing domains, limiting current learning capabilities. To combat this issue and improves the generalizability of the DRP models, we are exploring strategies that explicitly address the imbalance in the DRP datasets. We reframe the problem as a multi-objective optimization across multiple drugs to maximize deep learning model performance. We implement this approach by constructing Multi-Objective Optimization Regularized by Loss Entropy loss function and plugging it into a Deep Learning model. We demonstrate the utility of proposed drug discovery methods and make suggestions for further potential application of the work to achieve desirable outcomes in the healthcare field.

Biochemistry & Molecular Biology↗