Data-driven Multiobjective Optimization Research Articles

A data-driven multi-objective optimization approach for enhanced methanol yield and exergy loss minimization in direct hydrogenation of CO[formula omitted]

The stability and control of process industries have historically faced obstacles due to inherent uncertainties in their operations. This work focuses on leveraging machine learning models as a surrogate to facilitate real-time optimization of operating conditions of the direct hydrogenation of CO2 to enhance methanol production while minimizing exergy losses. Numerous studies have explored steady-state exergy analysis and the impact of various process conditions on methanol production. However, there is a notable absence of research investigating the influence of exergy destruction on methanol production under dynamic conditions. Initially, a commercial software Aspen HYSYS was utilized to design, model, and simulate the methanol synthesis plant. Exergy analysis was conducted to quantify the process exergy losses, exergy efficiency, and potential areas for improvement. The process model transitioned to a dynamic mode by incorporating ±5% uncertainty into critical operating conditions, i.e., temperature, pressure, and molar flow rate, simulating real-world variability and resulting in a dataset of 370 samples. Two machine learning models; the Gaussian process regression (GPR) and artificial neural network (ANN) model were developed using the data samples to predict the process exergy losses and molar flow rate of methanol produced. To enhance the predictive capabilities of these deployed models, Bayesian optimization was employed for hyperparameter tuning. The developed models were employed as surrogates in multi-objective genetic algorithm (MOGA) environments with the aim of maximizing the production of methanol with minimum exergy losses under uncertainty. The optimized process conditions, derived from MOGA-based methods, underwent cross-validation using the Aspen model. This analysis revealed that the methanol synthesis plant exhibited an exergy loss of 2425 kW, an exergy efficiency of 97.78%, and an improvement potential of 53.74 kW. The GPR and ANN models demonstrated high correlation coefficients (R2) of 0.9928 and 0.9375, and root mean square error (RMSE) values of 38.93 and 1.122, respectively. Incorporating these machine learning models as surrogates within the optimization frameworks notably outperformed the base case, achieving maximum methanol production while minimizing exergy losses in the process.

Offline Data-Driven Multiobjective Optimization Evolutionary Algorithm Based on Generative Adversarial Network

Usually, data-driven multi-objective optimiza -tion problems (DD-MOPs) are indirectly solved by evolutionary algorithms through the built surrogate model which is well-trained from sample data. However, in most DD-MOPs, only a few available data can be practicably collected from real engineering experiments due to the unaffordable cost and time. The key challenge in such a DD-MOP is to prevent the serious deterioration on the accuracy of the obtained approximate Pareto front. In this paper, two novel strategies, critical fitness for evolutionary algorithms and data augmentation for a surrogate model, are complementarily imposed by a generative adversarial network (GAN) to tackle with the challenges in DD-MOPs. In the critical fitness strategy, a new critical fitness, composed of the critical score from the discriminator of GAN and the prediction value of surrogate model, is proposed to improve the accuracy of approximate Pareto front of a DD-MOP. In the data augmentation strategy, some new samples are synthetized by the generator of GAN to build a better-trained surrogate model. As a result, the GAN concurrently serves the critical fitness strategy and the data augmentation strategy as the roles of “killing two birds with one stone”. The performance of the proposed algorithm for DD-MOPs was well-verified over 26 benchmark problems and successfully applied to discover new NdFeB materials.

Data-Driven Multi-Objective Optimization Approach to Loaded Meshing Transmission Performances for Aerospace Spiral Bevel Gears.

Loaded meshing transmission performance optimization has been an increasingly significant target for the design and manufacturing of aerospace spiral bevel gears with low noise and high strength. An innovative data-driven multi-objective optimization (MOO) method is proposed for the loaded meshing transmission performances of aerospace spiral bevel gears. Data-driven tooth surface modeling is first used to obtain a curvature analysis of loaded contact points. An innovative numerical loaded tooth contact analysis (NLTCA) is applied to develop the data-driven relationships of machine tool settings with respect to loaded meshing transmission performance evaluations. Moreover, the MOO function is solved by using an achievement function approach to accurate machine tool settings output, satisfying the prescribed requirements. Finally, numerical examples are given to verify the proposed methodology. The presented approach can serve as a powerful tool to optimize the loaded meshing transmission performances with higher computational accuracy and efficiency than the conventional methods.

Multi-objective optimization for composition design of civil materials based on data-driven method

The performance of civil materials depends on their compositions. The material design is an important, challenging, and time-consuming work during the construction due to the complex relationship among different compositions and the conflict between properties and economic cost. This study developed a data-driven multi-objective optimization design framework to determine the reasonable material compositions based on laboratory experiment, reduced order model (ROM), and multi-objective optimization (MOO). The ROM was used to capture the complex relationship between the material compositions and the corresponding material performance. The MOO was utilized to determine the pareto optimal solution of compositions in the global space. Taking examples of cement grouts and modified asphalt binders, the develop framework was demonstrated and verified. The developed framework provides an excellent tool for composition design of civil materials.

Treed Gaussian Process Regression for Solving Offline Data-Driven Continuous Multiobjective Optimization Problems.

For offline data-driven multiobjective optimization problems (MOPs), no new data is available during the optimization process. Approximation models (or surrogates) are first built using the provided offline data, and an optimizer, for example, a multiobjective evolutionary algorithm, can then be utilized to find Pareto optimal solutions to the problem with surrogates as objective functions. In contrast to online data-driven MOPs, these surrogates cannot be updated with new data and, hence, the approximation accuracy cannot be improved by considering new data during the optimization process. Gaussian process regression (GPR) models are widely used as surrogates because of their ability to provide uncertainty information. However, building GPRs becomes computationally expensive when the size of the dataset is large. Using sparse GPRs reduces the computational cost of building the surrogates. However, sparse GPRs are not tailored to solve offline data-driven MOPs, where good accuracy of the surrogates is needed near Pareto optimal solutions. Treed GPR (TGPR-MO) surrogates for offline data-driven MOPs with continuous decision variables are proposed in this paper. The proposed surrogates first split the decision space into subregions using regression trees and build GPRs sequentially in regions close to Pareto optimal solutions in the decision space to accurately approximate tradeoffs between the objective functions. TGPR-MO surrogates are computationally inexpensive because GPRs are built only in a smaller region of the decision space utilizing a subset of the data. The TGPR-MO surrogates were tested on distance-based visualizable problems with various data sizes, sampling strategies, numbers of objective functions, and decision variables. Experimental results showed that the TGPR-MO surrogates are computationally cheaper and can handle datasets of large size. Furthermore, TGPR-MO surrogates produced solutions closer to Pareto optimal solutions compared to full GPRs and sparse GPRs.

Accelerated feasible screening of flame-retardant polymeric composites using data-driven multi-objective optimization

The design of flame-retardant polymeric composites (FRPC) with simultaneously satisfied requirements of multiple performances was traditionally costly in both time and economy. In this work, we performed data-driven multi-objective optimization (MOO) of the FRPC to accelerate the discoveries of high-performance composites. Consistent experimental datasets for each of the four target performances: limiting oxygen index, tensile strength, maximum specific optical density, and the total smoke release within the first four minutes, were created on 153 FRPC. Then, decision rules and approximate equations were found by using machine learning to predict the performances, and MOO was achieved by identifying the optimal composites that simultaneously satisfying the requirements by all these models. Considering a huge composition space (nearly 44 thousands of composites), MOO led to the discovery of 149 promising candidates. 10 of them were selected for experimental validation, and most of which were confirmed with excellent overall performances, demonstrating the efficiency of the approach in designing the FRPC for industrial applications.

Data-driven multi-objective optimization for electric vehicle charging infrastructure

This paper presents a data-driven methodology combining simulation and multi-objective optimization to efficiently implement transportation policy commitments, using as a case study the electric vehicle (EV) charging infrastructure in Newcastle upon Tyne, United Kingdom. The methodology leverages a baseline simulation model developed by our industry partner, Arup Group Limited, to estimate EV demand and quantities from 2020 to 2050. Four future energy scenarios are considered, and a multi-objective optimization approach is employed to determine the optimal types, locations, and quantities of charging points, along with the corresponding total capital and operational expenditures and charging point operating hours. Quantitatively, the variations of the portions of different types of charging points for the four scenarios are relatively small and within 3% range of the total number of charging points. The optimal solutions put priority on the slower charging points, with faster charging points having smaller portions each around 10%-13%.

A data-driven multi-objective optimization framework for determining the suitability of hydrogen fuel cell vehicles in freight transport

In order to evaluate suitability of battery electric vehicles (BEVs) and hydrogen fuel cell vehicles (HFCVs) in freight transport systems, this paper proposes a data-driven and simulation-based multi-objective optimization method to deploy charging/refueling facilities for BEVs/HFCVs. The model considers three objectives, namely minimizing total system cost, maximizing service reliability, and minimizing greenhouse gas (GHG) emissions. In particular, a data-driven micro-simulation approach is developed to simulate the operation of freight transport systems with different vehicle and facility types based on the analysis of a one-week Global Positioning System (GPS) trajectory dataset containing 63,000 freight vehicles in Beijing. With the model, we compare the suitability of BEVs and HFCVs within three typical scenarios, i.e., BEVs coupled with Charging Stations (BEV-CS), BEVs coupled with Battery Swap Stations (BEV-BSS), and HFCVs coupled with Hydrogen Refueling Stations (HFCV-HRS). The results suggest that BEV-CS has the lowest total system cost: its system cost is 62.5% and 90.3% of the costs in BEV-BSS and HFCV-HRS, respectively. BEV-BSS has the lowest delay time: its delay time is 62.1% and 86.0% of the delay times in BEV-CS and HFCV-HRS, respectively. HFCV-HRS has the lowest GHG emissions: its emissions are 37.3% and 46.9% of the emissions in BEV-CS and BEV-BSS, respectively. The results are expected to be helpful for policy making and infrastructure planning in promoting the development of alternative fuel vehicles.

A data-driven robust design optimization method and its application in compressor blade

The probability-based robust optimization methods require a large amount of sample data to build probability distribution models of uncertain parameters. However, it is a common situation that only scarce sampled data are available in practice due to expensive tests. This study proposes a data-driven robust optimization framework by embedding a novel uncertainty quantification (UQ) method, which can quantify the uncertainty based on the statistical moments of scarce input data. The computational robustness and accuracy of the developed UQ methods are validated. Then, the data-driven multi-objective optimization framework is applied to improve the mean performance and aerodynamic robustness of a two-dimensional compressor blade with real stagger angle errors. Uncertainty analysis shows that there is a probability of 47.55% to deviate from the nominal total pressure loss coefficient by more than 1% for the actual performance values at high positive incidence i=7° condition. In the optimization process, the total pressure loss coefficient is selected as the objective function, while the static pressure ratio is used as a constraint. The Gaussian process regression model is trained to improve the robust optimization efficiency. The robust optimization is conducted under the most sensitive conditions. Optimized results indicate that compared with the nominal blade, the mean performance of the selected robust blades is increased by 10.9%, 8.56%, and 0.83%; the performance dispersion is decreased by 19.0%, 24.8%, and 35.3%, respectively. The optimized results can provide useful references for the robust design of compressor blades.

Multi-objective optimization of the cathode catalyst layer micro-composition of polymer electrolyte membrane fuel cells using a multi-scale, two-phase fuel cell model and data-driven surrogates

Polymer electrolyte membrane fuel cells (PEMFCs) are considered a promising alternative to internal combustion engines in the automotive sector. Their commercialization is mainly hindered due to the cost and effectiveness of using platinum (Pt) in them. The cathode catalyst layer (CL) is considered a core component in PEMFCs, and its composition often considerably affects the cell performance (Vcell) also PEMFC fabrication and production Cstack costs. In this study, a data-driven multi-objective optimization analysis is conducted to effectively evaluate the effects of various cathode CL compositions on Vcell and Cstack. Four essential cathode CL parameters, i.e., platinum loading (LPt), weight ratio of ionomer to carbon (wtI/C), weight ratio of Pt to carbon (wtPt/c), and porosity of cathode CL (εcCL), are considered as the design variables. The simulation results of a three-dimensional, multi-scale, two-phase comprehensive PEMFC model are used to train and test two famous surrogates: multi-layer perceptron (MLP) and response surface analysis (RSA). Their accuracies are verified using root mean square error and adjusted R2. MLP which outperforms RSA in terms of prediction capability is then linked to a multi-objective non-dominated sorting genetic algorithm II. Compared to a typical PEMFC stack, the results of the optimal study show that the single-cell voltage, Vcell is improved by 28 mV for the same stack price and the stack cost evaluated through the U.S department of energy cost model is reduced by $5.86/kW for the same stack performance.

Data-Driven Multiobjective Optimization for Massive MIMO and Hyperdensification Empowered 5G Planning under Realistic Network Environment

To accommodate the increasing data rate demand, the fifth-generation (5G) cellular network came up with new technological advancements including massive multiple-input multiple-output (massive MIMO) and hyperdensification which can significantly boost network capacity. On the other hand, the introduction of these technologies along with their heterogeneity brings a challenge in terms of network operators’ need to identify a cost-effective optimal deployment approach which is hardly entertained by the legacy planning and optimization method. Hence, to leverage the core benefits of those technologies in a cost-effective manner, we need a holistic planning framework that takes into account their coverage, capacity and cost impact, and realistic spatiotemporal distribution of users. In this work, we present a data-driven multiobjective optimization planning framework that can be used not only for small cells but also for massive MIMO. The planning framework is illustrated using a 5G planning case study for a service area in Addis Ababa, Ethiopia, considering its realistic network data that is collected from the network management system and different potential identified deployment options. Ray tracing is employed to compute propagation, and users and demands are distributed based on the realistic network data. A two-stage optimization and a joint optimization are applied to identify points that provide optimal network performance. Simulation results reveal that the planning method provides Pareto points for different deployment options that can significantly improve the performance of the existing network while reducing the total network cost.

Data-Driven Multi-Objective Optimization Tactics for Catalytic Asymmetric Reactions Using Bisphosphine Ligands.

Optimization of the catalyst structure to simultaneously improve multiple reaction objectives (e.g., yield, enantioselectivity, and regioselectivity) remains a formidable challenge. Herein, we describe a machine learning workflow for the multi-objective optimization of catalytic reactions that employ chiral bisphosphine ligands. This was demonstrated through the optimization of two sequential reactions required in the asymmetric synthesis of an active pharmaceutical ingredient. To accomplish this, a density functional theory-derived database of >550 bisphosphine ligands was constructed, and a designer chemical space mapping technique was established. The protocol used classification methods to identify active catalysts, followed by linear regression to model reaction selectivity. This led to the prediction and validation of significantly improved ligands for all reaction outputs, suggesting a general strategy that can be readily implemented for reaction optimizations where performance is controlled by bisphosphine ligands.

Data-driven multi-objective optimization with neural network-based sensitivity analysis for semiconductor devices

Statistical modeling and optimization are critical for product quality management and technology development in the manufacturing industry. As the emerging device appears and technology advances, it consists of highly-correlated multivariate parameters and has a non-linear relationship. Moreover, technology development requires extensive cost and effort, and often it takes several years to establish a physical model after the advent of new technology. Thus, this paper presents an effective data-driven multi-objective optimization with neural network-based sensitivity analysis for semiconductor devices before explicitly developing a physical or compact model. Sensitivity analysis allows a quick search for influential parameters and selects design parameter candidates for a customized solution. Then, the selected parameters are adjusted to maintain within the set range by the scaled sensitivities and to have robustness against noise. It optimizes design variables to meet performance and variation requirements simultaneously, considering correlation between parameters. Therefore, multi-objective solutions hold physical consistency and are found with ¡ 1.7% error. The proposed method is efficient in computational time, which is significantly reduced by more than 80% compared to Bayesian optimization for process optimization. This approach is a general methodology applicable to various industries besides the semiconductor field. Finally, we expect this study to help shorten development time and improve yield through customized multi-objective solutions.

A data-driven multi-objective optimization framework for optimal integration planning of solid-state transformer fed energy hub in a distribution network

This study proposes an optimal planning technique for a solid-state transformer (SST) fed hybrid energy hub consisting of a wind turbine distributed generator (WTDG) and a battery energy storage system (BESS) in a distribution network (DN). The energy exchange within the energy hub and with the utility grid is regulated by an efficient energy management plan (EMP). The simultaneous planning of a WTDG-BESS energy hub in a DN fed through an SST is a challenging combinatorial optimization problem. It is not only about capacity allocation and placement, but also about charging and discharging dispatches of BESSs under dynamically altering system parameters with the intermittent nature of WTDG outputs and the operational limits of the system itself. As a result, simultaneous allocation becomes a mixed integer nonlinear programming (MINLP) problem, with the operational aspect acting as a limitation for the planning aspect and adding to the complexity of the problem. While the power flow takes into consideration the operational losses of the traditional distribution transformers (DT), the optimization problem reduces voltage deviations and energy losses of the DN. A 33-bus radial DN was used to test the proposed technique, and the outcomes of various case studies are included. The MINLP problem was addressed using the non-dominated sorted genetic algorithm (NSGA-II) in the MATLAB R2020a platform. The outcomes of the evaluation show an energy loss reduction (ELR) of 62%, while a voltage profile improvement (VPI) of 69% is obtained.

Data-driven multi-objective optimization of ultralight hierarchical origami-corrugation meta-sandwich structures

With advantages in stiffness, strength, and energy absorption, hierarchical origami-corrugation meta-sandwich (HOCM) structures are envisioned as a novel ultralight multifunctional sandwich construction for various practical applications. Firstly, the macro-equivalent compressive modulus is analytically derived using a two-level homogenization approach. The HOCM samples manufactured by selective laser melting are then tested under quasi-static out-of-plane compressive loading. A representative volume element model is proposed for finite element simulations to explore further the compressive performance, with good agreement achieved between measurements and simulations. Influences of critical geometric parameters on compressive properties, including initial failure modes, specific peak strength (SPS) and specific energy absorption (SEA), are numerically analyzed. Subsequently, the surrogate model based on a fully connected neural network algorithm is selected as the machine learning strategy to approximate the SPS and SEA, with cross-validation conducted to verify its accuracy. Finally, a multi-objective optimization method incorporating the surrogate model and the non-dominated sorting genetic algorithm II is implemented to carry out optimal design for HOCM structures possessing simultaneous superior SPS, SEA with assured stiffness. Such a data-driven optimization procedure based on the machine learning method exhibits high accuracy for strongly nonlinear problems, especially for SEA in current work, leading to highly efficient optimization.

Probabilistic Selection Approaches in Decomposition-Based Evolutionary Algorithms for Offline Data-Driven Multiobjective Optimization

In offline data-driven multiobjective optimization, no new data are available during the optimization process. Approximation models, also known as surrogates, are built using the provided offline data. A multiobjective evolutionary algorithm can be utilized to find solutions by using these surrogates. The accuracy of the approximated solutions depends on the surrogates and approximations typically involve uncertainties. In this article, we propose probabilistic selection approaches that utilize the uncertainty information of the Kriging models (as surrogates) to improve the solution process in offline data-driven multiobjective optimization. These approaches are designed for decomposition-based multiobjective evolutionary algorithms and can, thus, handle a large number of objectives. The proposed approaches were tested on distance-based visualizable test problems and the DTLZ suite. The proposed approaches produced solutions with a greater hypervolume, and a lower root mean squared error compared to generic approaches and a transfer learning approach that do not use uncertainty information.

Accelerated design for magnetic high entropy alloys using data-driven multi-objective optimization

High entropy alloys (HEAs) with excellent combination performance of magnetic and mechanical properties were rationally designed via intelligent algorithms combined with metallurgical knowledge.

An Online Data-Driven Multi-Objective Optimization of a Permanent Magnet Linear Synchronous Motor

In this article, an online data-driven multi-objective optimization is proposed to suppress the undesired thrust ripple and improve the average thrust of the permanent magnet linear synchronous motor (PMLSM). A two-loop optimization process is adopted, and the first loop is designed to achieve a higher accuracy of the Kriging models by adding points based on expected improvement (EI) criteria. Through the first loop, the Kriging models achieve a significant increase in the prediction accuracy from 76% to 99.7%. Then, the second loop runs to optimize the PMLSM by using the Kriging assisted multi-objective particle swarm optimization (MOPSO) method. The results show that the optimized PMLSM successfully achieve a 64% reduction in the thrust ripple and a 6.6% increase in the average thrust compared with the original PMLSM.

Multi-objective data-driven optimization for improving deep brain stimulation in Parkinson’s disease

Objective. Deep brain stimulation (DBS) is an effective treatment for Parkinson’s disease (PD) but its success depends on a time-consuming process of trial-and-error to identify the optimal stimulation settings for each individual patient. Data-driven optimization algorithms have been proposed to efficiently find the stimulation setting that maximizes a quantitative biomarker of symptom relief. However, these algorithms cannot efficiently take into account stimulation settings that may control symptoms but also cause side effects. Here we demonstrate how multi-objective data-driven optimization can be used to find the optimal trade-off between maximizing symptom relief and minimizing side effects. Approach. Cortical and motor evoked potential data collected from PD patients during intraoperative stimulation of the subthalamic nucleus were used to construct a framework for designing and prototyping data-driven multi-objective optimization algorithms. Using this framework, we explored how these techniques can be applied clinically, and characterized the design features critical for solving this optimization problem. Our two optimization objectives were to maximize cortical evoked potentials, a putative biomarker of therapeutic benefit, and to minimize motor potentials, a biomarker of motor side effects. Main Results. Using this in silico design framework, we demonstrated how the optimal trade-off between two objectives can substantially reduce the stimulation parameter space by 61 ± 19%. The best algorithm for identifying the optimal trade-off between the two objectives was a Bayesian optimization approach with an area under the receiver operating characteristic curve of up to 0.94 ± 0.02, which was possible with the use of a surrogate model and a well-tuned acquisition function to efficiently select which stimulation settings to sample. Significance. These findings show that multi-objective optimization is a promising approach for identifying the optimal trade-off between symptom relief and side effects in DBS. Moreover, these approaches can be readily extended to newly discovered biomarkers, adapted to DBS for disorders beyond PD, and can scale with the development of more complex DBS devices.

Data-driven multi-objective optimization of laser welding parameters of 6061-T6 aluminum alloy

In this paper, a data-driven multi-objective optimization approach using optimal Latin hypercube sampling (OLHS), Kriging (KRG) metamodel and the non-dominated sorting genetic algorithm II (NSGA-II) is presented for the laser welding process parameters on 6061-T6 aluminum alloy. The experiments are designed by OLHS and carried out to obtain the data results. The complex relationship between the process parameters and the bead profile geometry is established by KRG using the data results. The accuracy of the established KRG metamodel is validated using experiments. Then, NSGA-II is used to explore the design space and search the Pareto optimal solutions of process parameters. Besides, the validation experiments were carried out to obtain ideal LW bead profile, which shows that the approach can bring dependable guidance for LW experiments.