Surrogate-based Optimization Research Articles

High-dimensional aerodynamic shape optimization framework using geometric domain decomposition and data-driven support strategy for wing design

Traditional aerodynamic shape optimization methods usually suffer from difficulties in optimization and modeling for high-dimensional aerodynamic optimization problems. To overcome these difficulties, a new high-dimensional aerodynamic shape optimization framework is proposed from the perspectives of geometric domain decomposition for dimensionality reduction and a data-driven model support strategy for changing the role of surrogate model and assisting the optimizer. Geometric domain decomposition uses proper orthogonal decomposition to transform the high-dimensional Class-Shape Function Transformation method into low-dimensional geometric modes to reduce design dimensions for parameterizing the geometric shape, which reduces optimization and modeling difficulties. Also, a data-driven support strategy is proposed to improve the effectiveness and efficiency of the optimizer by learning from historical aerodynamic data; this strategy modifies the role of surrogate model in the optimization framework to assist the optimizer; the surrogate model, serving as an auxiliary role, can reduce the dependence on model accuracy, which overcomes the difficulty of high-dimensional modeling to some extent. We applied the developed framework to transonic drag reduction of wings to validate its performance. The optimization results show that the developed framework converges faster and offers better designs compared to direct optimization and state-of-the-art surrogate-based optimization frameworks for high-dimensional aerodynamic shape optimization.

Shock-capturing PID controller for high-order methods with data-driven gain optimization

We present a novel shock-capturing strategy for high-order methods including discontinuous Galerkin (DG) method with data-driven gain optimization. Inspired by the classical control theory, we utilize a proportional–integral–derivative (PID) controller for capturing shock waves with monotonic subcell distributions. The proposed closed-loop control system for shock-capturing, named shock-capturing PID controller (SPID), consists of two key elements: error estimation based on the multi-dimensional limiting strategies (hMLP and hMLP_BD) and shock stabilization using the Laplacian artificial viscosity (LAV). The two elements are combined in a complementary manner to maximize the advantages of limiting strategy and artificial viscosity while overcoming each weakness. First, based on the multi-dimensional limiting process (MLP) condition and the troubled-boundary detector, the estimated error gives a signal to the SPID how much flow variables stray out of monotonic shock profiles. Second, the SPID estimates the amount of artificial viscosity to stabilize the target shock wave and superimposes numerical diffusion to the governing equations in the form of LAV. Each control action of the SPID (i.e., proportional, integral, and derivative) has a distinct role in capturing and stabilizing shock waves. The proportional action determines a minimal amount of background artificial viscosity. The integral action reinforces a shock-stabilizing numerical diffusion where the artificial viscosity by the proportional action alone is insufficient. The derivative action damps out sudden rises of error and spurious oscillations. The SPID incorporates the gain parameters that regulate the impact of each control action, and each gain parameter is determined via a surrogate-based optimization approach utilizing artificial neural networks (ANN). The SPID with the data-driven gain parameters is verified and validated by conducting extensive numerical tests and by comparing the results to other shock-capturing methods (hMLP, hMLP_BD, and Laplacian artificial viscosity). The numerical results demonstrate the excellent performance of SPID in terms of capturing shock waves and stabilizing shock-induced oscillations. Moreover, the SPID successfully preserves unsteady turbulent eddies for large-eddy simulations (LES) of subsonic and supersonic flows and improves convergence characteristics of steady transonic/supersonic flows.

A dynamic aggregation strategy enhanced efficient global optimization algorithm for solving high-dimensional turbomachinery design problems

ABSTRACT To address challenges effectively in turbomachinery design optimization involving high-dimensional ( d ≥ 30 ) expensive black-box problems, a dedicated Efficient Global Optimization (EGO) algorithm is proposed with dynamic aggregation. This specialized approach efficiently navigates optimization tasks with limited sample evaluations. Specifically, the Dynamic Aggregate Efficient Global Optimization (DA-EGO) algorithm decomposes the original high-dimensional design space into low-dimensional subspaces for efficient surrogate-based optimization search, and the optimal solutions of subspaces are combined as an elite-point for the global search. Most importantly, the subspace variables are updated in each iteration, according to the variable interaction analyses in the sub- and full-spaces. The perturbation method and the analysis of variance are used to detect variable interactions. After being validated on 21 benchmark functions ranging from 30 to 90 dimensions, the DA-EGO is used for the optimization of a transonic compressor rotor with 28 variables and a multi-stage compressor optimization with 60 variables. With the above, the effectiveness of the proposed algorithm is well demonstrated.

HyDesign: a tool for sizing optimization of grid-connected hybrid power plants including wind, solar photovoltaic, and lithium-ion batteries

Abstract. Hybrid renewable power plants consisting of collocated wind, solar photovoltaic (PV), and lithium-ion battery storage connected behind a single grid connection can provide additional value to the owners and society in comparison to individual technology plants, such as those that are only wind or only PV. The hybrid power plants considered in this article are connected to the grid and share electrical infrastructure costs across different generation and storing technologies. In this article, we propose a methodology for sizing hybrid power plants as a nested-optimization problem: with an outer sizing optimization and an internal operation optimization. The outer sizing optimization maximizes the net present values over capital expenditures and compares it with standard designs that minimize the levelized cost of energy. The sizing problem formulation includes turbine selection (in terms of rated power, specific power, and hub height), a wind plant wake loss surrogate, simplified wind and PV degradation models, battery degradation, and operation optimization of an internal energy management system. The problem of outer sizing optimization is solved using a new parallel “efficient global optimization” algorithm. This new algorithm is a surrogate-based optimization method that ensures a minimal number of model evaluations but ensures a global scope in the optimization. The methodology presented in this article is available in an open-source tool called HyDesign. The hybrid sizing algorithm is applied for a peak power plant use case at different locations in India where renewable energy auctions impose a monetary penalty when energy is not supplied at peak hours. We compare the hybrid power plant sizing results when using two different objective functions: the levelized cost of energy (LCoE) or the relative net present value with respect to the total capital expenditure costs (NPV/CH). Battery storage is installed only on NPV/CH-based designs, while the hybrid design, including wind, solar, and battery, only occurs on the site with good wind resources. Wind turbine selection on this site prioritizes cheaper turbines with a lower hub height and lower rated power. The number of batteries replaced changes at the different sites, ranging between two or three units over the lifetime. A significant oversizing of the generation in comparison to the grid connection occurs on all NPV/CH-based designs. As expected LCoE-based designs are a single technology with no batteries.

Mixed-integer optimisation of graph neural networks for computer-aided molecular design

ReLU neural networks have been modelled as constraints in mixed integer linear programming (MILP), enabling surrogate-based optimisation in various domains and efficient solution of machine learning certification problems. However, previous works are mostly limited to MLPs. Graph neural networks (GNNs) can learn from non-euclidean data structures such as molecular structures efficiently and are thus highly relevant to computer-aided molecular design (CAMD). We propose a bilinear formulation for ReLU Graph Convolutional Neural Networks and a MILP formulation for ReLU GraphSAGE models. These formulations enable solving optimisation problems with trained GNNs embedded to global optimality. We apply our optimisation approach to an illustrative CAMD case study where the formulations of the trained GNNs are used to design molecules with optimal boiling points.

A Study on the Surrogate-Based Optimization of Flexible Wings Considering a Flutter Constraint

Accounting for aeroelastic phenomena, such as flutter, in the conceptual design phase is becoming more important as the trend toward increasing the wing aspect ratio forges ahead. However, this task is computationally expensive, especially when utilizing high-fidelity simulations and numerical optimization. Thus, the development of efficient computational strategies is necessary. With this goal in mind, this work proposes a surrogate-based optimization (SBO) methodology for wing design using a predefined machine learning model. For this purpose, a custom-made Python framework was built based on different open-source codes. The test subject was the classical Goland wing, parameterized to allow for SBO. The process consists of employing a Latin Hypercube Sampling plan and subsequently simulating the resulting wing on SHARPy to generate a dataset. A regression-based machine learning model is then used to build surrogate models for lift and drag coefficients, structural mass, and flutter speed. Finally, after validating the surrogate model, a multi-objective optimization problem aiming to maximize the lift-to-drag ratio and minimize the structural mass is solved through NSGA-II, considering a flutter constraint. This SBO methodology was successfully tested, reaching reductions of three orders of magnitude in the optimization computational time.

Managing network congestion with link-based incentives: A surrogate-based optimization approach

Incentive-based travel demand management (IBTDM) programs endow monetary incentives to encourage travel demand redistribution across space and time. They are more appealing than alternatives such as congestion charging because commuters do not need to pay out of pocket. However, such congestion-alleviation solutions are usually managed by small private companies with constrained incentive budgets. Thus, the incentive should be wisely determined so that a limited incentive budget can be effectively used to fulfill maximum social welfare while maintaining the financial health of the IBTDM program. It is essential to know whether IBTDM is financially sound—that is, whether financial investment in IBTDM will lead to more than the equivalent value in total system travel time reduction. However, optimizing the link-based endowment scheme in a large-scale network is challenging because 1) the objective function and the budget constraint are both characterized by expensive-to-evaluate functions without closed form, and 2) it is a large-scale optimization problem that contains massive amount of decision variables. In this study, a computationally efficient surrogate-based optimization framework that is suitable for high-dimensional problems is proposed. A simulation-based dynamic traffic assignment model is used to evaluate the performance of transportation systems, and a Kriging model with partial least squares acts as the surrogate to approximate the simulation model. The results show that the optimal network-wide link-based incentive scheme improves the performance of the system. The higher the incentive budget, the more effective the incentive and the lower the marginal utility of the incentive. Furthermore, in a well-designed incentive scheme, a $1M investment in IBTDM would lead to much more than the equivalent of $1M in total system travel time reduction, which proves the economic viability of IBTDM and provides support for its promotion. IBTDM implemented within smaller regions and tighter incentive budgets produces higher utility ratios.

Multi-objective optimization of transpiration cooling for high pressure turbine vane

Transpiration cooling is a promising cooling measure for high-temperature components in gas turbines. Although the flow and heat transfer characteristics of transpiration cooling have been investigated in several experimental and numerical researches, the design optimization of transpiration cooling is less studied until now. In this paper, a multi-objective optimization framework based on the ANN surrogate model and the NSGA-Ⅱ is built to optimize the transpiration cooling of C3X turbine vane. The transpiration cooled C3X vane consists of multiple porous zones whose porosities could be different and are treated as the design parameters. The optimization objectives are minimum area-averaged vane surface temperature and minimum aerodynamic loss. A total of 960 CFD simulations are conducted to prepare the sample dataset. After the validation of the surrogate-based optimization framework, the Pareto front is obtained as an output. Three representative Pareto-optimal points are chosen from the Pareto front, considering the best cooling performance, the lowest aerodynamic loss, and a balance between them. The porosity distributions and coolant allocations, the cooling performances, and the aerodynamic losses for the three Pareto points are discussed, and the involved flow and heat transfer characteristics are analyzed. The results reveal that to reach a balance between the cooling efficiency and the aerodynamic loss for an optimal transpiration cooled C3X vane, coolant should be appropriately distributed to the leading edge, as well as zones immediately downstream of the leading edge.

Data-driven surrogate model for aerodynamic design using separable shape tensor method

In the context of increasing dimensionality of design variables and the complexity of constraints, the efficacy of Surrogate-Based Optimization (SBO) is limited. The traditional linear and nonlinear dimensionality reduction algorithms are mainly to decompose the mathematical matrix composed of design variables or objective functions in various forms, the smoothness of the design space cannot be guaranteed in the process, and additional constraint functions need to be added in the optimization, which increases the calculation cost. This study presents a new parameterization method to improve both problems of SBO. The new parameterization is addressed by decoupling affine transformations (dilation, rotation, shearing, and translation) within the Grassmannian submanifold, which enables a separate representation of the physical information of the airfoil in a high-dimensional space. Building upon this, Principal Geodesic Analysis (PGA) is employed to achieve geometric control, compress the design space, reduce the number of design variables, reduce the dimensions of design variables and enhance predictive performance during the surrogate optimization process. For comparison, a dimensionality reduction space is defined using 95% of the energy, and RAE 2822 for transonic conditions are used as demonstrations. This method significantly enhances the optimization efficiency of the surrogate model while effectively enabling geometric constraints. In three-dimensional problems, it enables simultaneous design of planar shapes for various components of the aircraft and high-order perturbation deformations. Optimization was applied to the ONERA M6 wing, achieving a lift-drag ratio of 18.09, representing a 27.25% improvement compared to the baseline configuration. In comparison to conventional surrogate model optimization methods, which only achieved a 17.97% improvement, this approach demonstrates its superiority.

An Improved Approach for Reducing the Dimensionality of Wing Aerodynamic Optimization Considering Longitudinal Stability

The wing aerodynamic shape optimization is a typical high-dimensional problem with numerous independent design variables. Researching methods to reduce the dimensionality of optimization from the perspective of aerodynamic characteristics is necessary. One traditional aerodynamic-based approach decouples the wing’s camber and thickness according to the thin airfoil theory, but it has limitations due to unclear application scope and effectiveness. This paper proposes an improved approach that determines the values of certain thickness variables based on a data-driven aerodynamic characteristics model before optimization, which considers longitudinal stability. By reducing the number of design variables, the dimensionality of optimization is decreased effectively. The derivation of the improved approach is accomplished through the design of experiments, parametric modeling, computational fluid dynamics, and sensitivity analysis. The effectiveness of the improved approach is validated by applying it to the aerodynamic optimization of an ONERA-M6 wing in subsonic flow based on the surrogate-based optimization algorithm. The results demonstrate that the improved approach significantly accelerates the optimization process while maintaining global effectiveness.

Surrogate-based optimisation of process systems to recover resources from wastewater

Wastewater systems are transitioning towards integrative process systems to recover multiple resources whilst simultaneously satisfying regulations on final effluent quality. This work contributes to the literature by bringing a systems-thinking approach to resource recovery from wastewater, harnessing surrogate modelling and mathematical optimisation techniques to highlight holistic process systems. A surrogate-based process synthesis methodology was presented to harness high-fidelity data from black box process simulations, embedding first principles models, within a superstructure optimisation framework. Modelling tools were developed to facilitate tailored derivative-free optimisation solutions widely applicable to black box optimisation problems. The optimisation of a process system to recover energy and nutrients from a brewery wastewater reveals significant scope to reduce the environmental impacts of food and beverage production systems. Additionally, the application demonstrates the capabilities of the modelling methodology to highlight optimal processes to recover carbon, nitrogen, and phosphorous resources whilst also accounting for uncertainties inherent to wastewater systems.

An optimization framework for wind farm layout design using CFD-based Kriging model

Wind farm layout optimization (WFLO) seeks to alleviate the wake loss and maximize wind farm power output efficiency, and is a crucial process in the design and planning of wind energy projects. Since the optimization algorithms typically require thousands of numerical evaluations of the wake effects, conventional WFLO studies are usually carried out with the low-fidelity analytical wake models, while the higher-fidelity computational-fluid-dynamics-based (CFD-based) methods are seldom used due to the excessive computational cost. In this paper, we develop a self-adaptive optimization framework for wind farm layout design using CFD-based Kriging model to maximize the annual energy production (AEP) of wind farms. This surrogate-based optimization (SBO) framework uses latin hypercube sampling to generate a group of wind farm layout samples, based on which CFD simulations with the turbines modeled as actuator disks are carried out to obtain the corresponding AEPs. This initial wind farm layout dataset is used to train the Kriging model, which is then integrated with an optimizer based on genetic algorithm (GA). As the optimization progresses, the intermediate optimal layout designs are again fed into the dataset to re-train the Kriging model. Such adaptive update of wind farm layout dataset continues until the algorithm converges to the optimal layout design. To evaluate the performance of the proposed SBO framework, we apply it to four representative wind farm cases. Compared to the conventional staggered layout along the dominant wind direction, the optimized wind farm produces significantly higher total AEP, which is more evenly distributed among the turbines. In particular, the SBO framework requires significantly smaller number of CFD calls to yield the optimal layouts that generates almost the same AEP with the direct CFD-GA method. Further analysis on the velocity fields show that the optimization framework always attempts to locate the downstream turbines away from the wakes of upstream ones along the dominant wind directions. The proposed CFD-based surrogate model provides a more accurate and flexible alternative to the conventional analytical-wake-model-based methods in WFLO tasks, and has the potential to be used for designing efficient wind farm projects.

Efficient sampling techniques for surrogate-based optimization with thermoelastic application

In many real-life models, the objective function may be very expensive to calculate or sometimes a black-box function. Therefore, a surrogate model is required to reduce the cost of the calculations. To build a robust surrogate model, a good sampling technique is needed. This paper suggests two new sampling techniques for surrogate-based optimization, depending on four random walk steps, which in turn give a good chance for building an accurate approximation for the original function. In addition to that, one of these new sampling techniques has a new feature that was not used before. The main advantage of our two suggested sampling techniques is that there is no optimization subproblem will be solved for the next sample point, which in turn saves CPU time. Furthermore, we applied our two sampling techniques to a 1D thermal shock problem for a half-space in the context of the fractional order theory of thermoelasticity to reduce the number of function evaluations and consequently CPU time. Laplace transform techniques are used to obtain the solution of the system in the frequency domain. Applying our algorithms to the few points obtained by using Laplace’s inverse, we can reach the optimal solution for all functions filed. The predictions of our techniques are discussed and compared with the classical method. 2D and 3D graphs are plotted for our numerical results. The temperature, displacement, and stress distributions are computed and represented graphically for different times and several fractional parameters.

A Novel Multi-Fidelity Surrogate for Efficient Turbine Design Optimization

Abstract To solve the turbine design optimization problems efficiently, surrogate-based optimization algorithms are frequently used. To further reduce the cost of turbine design, the multi-fidelity surrogate (MFS)-based optimization is proposed by the researchers, who resort to augmenting the small number of expensive high-fidelity (HF) samples by a large portion of low-fidelity (LF) but cheap samples in surrogate modeling and optimization process. Nonetheless, according to our observations, the MFS-based optimization sometimes can only have better convergence rate at the early stage of optimization process, but yielding worse final solution than the single-fidelity surrogate (SFS)-based optimization that uses high-fidelity samples alone. The reason behind can be explained as follows. With the increase of HF samples in the optimization process, the LF samples can cause negative effect and therefore misleading the optimization search. To address the above issue, an ensemble weighted multi-fidelity surrogate (EMFS) is proposed. Specifically, the density-based spatial clustering of applications with noise is used to detect the region where the MFS cannot build a more accurate surrogate, and a local SFS is built there. Then, an EMFS is built by combining the MFS and SFS with adaptive weights, which is used to guide the optimization process. The related algorithm is named as multi- and single-fidelity surrogate fused optimization (MSFO). Through tests on GE-E3 blade optimization and the film cooling layout design of a turbine endwall, the effectiveness of proposed MSFO is well demonstrated.

Investigating surrogate-based hybrid acquisition processes. Application to Covid-19 contact mitigation

Surrogate models are built to produce computationally efficient versions of time-complex simulation-based objective functions so as to address expensive optimization. In surrogate-assisted evolutionary computations, the surrogate model evaluates and/or filters candidate solutions produced by evolutionary operators. In surrogate-driven optimization, the surrogate is used to define the objective function of an auxiliary optimization problem whose resolution generates new candidates. In this paper, hybridization of these two types of acquisition processes is investigated with a focus on robustness with respect to the computational budget and parallel scalability. A new hybrid method based on the successive use of acquisition processes during the search outperforms competing approaches regarding these two aspects on the Covid-19 contact mitigation problem. To further improve the generalization to larger ranges of search landscapes, another new hybrid method based on the dispersion metric is proposed. The integration of landscape analysis tools in surrogate-based optimization seems promising according to the numerical results reported on the CEC2015 test suite.

Robust optimization of geoenergy production using data-driven deep recurrent auto-encoder and fully-connected neural network proxy

Robust and efficient optimization of post-history well production schedule under history-matched geomodel known as closed-loop production management is crucial to achieve reasonable and reliable decision-making for subsurface geoenergy resources (e.g., oil/gas resources, geothermal, natural gas hydrate, etc.) recovery in petroleum industry. The procedure generally consists of a cycling implementation of geomodel history matching and production schedule optimization through repeatedly simulating high-fidelity reservoir models and therefore needs almost infeasible computation cost particularly for field-scale oil production scenario. Through hybridizing deep recurrent neural network and particle-swarm optimization algorithm, we present a novel data-driven computation framework for robust post-history production optimization without explicitly performing history matching. In the proposed framework, we develop a hybrid neural network proxy model, which combines recurrent autoencoder (RAE) and fully-connected neural network (FCNN), referred to as RAE-FCNN. The RAE structure can extract latent information from time-series history data, and the FCNN structure can map the combination of extracted latent variables by RAE and post-history well-control sequence to net present value (NPV). The trained RAE-FCNN proxy model can predict NPV values corresponding to the history measurements and user-specific post-history well controls. In the robust optimization framework, the averaged NPV over an ensemble of noisy history measurements are regarded as the objective function while the post-history well-controls are chosen as the decision variables. The proposed surrogate-based optimization framework has been demonstrated on two waterflooding reservoir production cases, e.g., a 2D synthetic Gaussian model and a 3D benchmaRk channelized EGG model.The decision variables considered in optimization are the injection rates with linear bound constraints at the injectors. In comparison with the optimization results by high-fidelity reservoir models, solely 1000 high-fidelity reservoir models for both cases are sufficient to train accurate proxy model and achieve satisfactory post-history production optimization results. Our proposed deep-learning-based optimization method can effectively make full use of history data to predict post-history oil well production without the need of computationally expensive history matching step, which enables us to achieve quick decision-making and risk evaluation for close-loop waterflooding reservoir production management and optimization.

Automotive disc-brake squeal noise modeling for shape optimization under uncertainties

Disc-brake systems in automotive vehicles tend to exhibit undesirable squeal noise during braking operations. Although this noise does not affect braking efficiency, it creates noise pollution and poses problems from a sales point of view since noise is commonly associated with malfunction by consumers. Squeal noise can be minimized by optimizing the shape of the system's mechanical parts. However, uncertainties related to manufacturing processes inevitably affect the system's response, and must be considered. The presented work aims at numerically quantifying and minimizing disc-brake squeal noise in the presence of uncertain parameters. A simplified disc-brake model is constructed using the novel Isogeometric Analysis method which is well-suited to shape optimization problems. The prediction of squeal noise propensity is based on the fact that squeal noise is directly related to unstable structural modes and uses Complex Eigenvalue Analysis to determine the extent of squeal occurrences. A surrogate-based optimization strategy is used to handle the high computational cost in the context of optimization, as well as to propagate uncertainties. The constructed model shows good capability for representation and quantification of squeal noise phenomena. A Pareto front of robust squeal minimizing shapes is obtained through the proposed approach.

Surrogate-based optimization for the worst-case prediction regarding a flexible structure impacted by wind gusts

The paper is a follow-up of the recent study on the assessment of discrete wind gust parameters impacting a flexible lightweight structure as a first step towards the evaluation of the worst-case scenario caused by strong wind gusts (JWEIA 231, 105207, 2022). The present study goes beyond by suggesting an optimization framework which allows to determine the worst-case scenario automatically. For this purpose, a stochastic response surface algorithm with a surrogate model based on radial basis functions is chosen. The algorithm relies on costly evaluations of the objective function, which consist of CPU-time intensive fully coupled fluid–structure interaction (FSI) high-fidelity simulations including the pre- and post-processing of the results. Besides the parallelization of the coupled FSI solver, a parallel version of the optimization algorithm allows to carry out several costly evaluations simultaneously. The Metric Stochastic Response Surface algorithm determines the worst case fast. Then, it continues to explore the optimization space to ensure that the global extremum is reached. A sensitivity study on relevant parameters of the optimization algorithm is conducted. Typically, for the present FSI setup, an optimization run takes one week with 6 evaluations in parallel to compute 100 different configurations. The worst case is found after about one third of the evaluations. The increase of parallel evaluations drastically reduces the wall-clock time, but the worst case is found later after half of the evaluations. This later finding is due to the parallel nature of the algorithm. Finally, the various sources of uncertainties that arise throughout the entire procedure are assessed and discussed.

Surrogate-based optimization design for surface texture of helical pair in helical hydraulic rotary actuator

A good surface texture design can effectively improve the tribological performance of the helical pair within a helical hydraulic rotary actuator(HHRA). However, the optimization design process can be time-consuming due to the multiple design variables involved and the complexity of the mathematical model. This paper proposes a modified efficient global optimization (MEGO) method for solving such demanding surface texture design challenges. The MEGO utilizes a Kriging model with the optimized Latin hypercube sampling (OLHS) for initial sampling and the proposed modified expected improvement (MEI) function for sequential sampling. A comparative study of several global optimization algorithms with the MEGO on the surface texture design is performed. Subsequently, surrogate-based optimization and parameter analysis are carried out, resulting in the identification of an optimal set of texture parameters. The findings reveal the superiority of the MEGO in both model prediction accuracy and refinement of minima. Moreover, compared to the base design, the friction coefficient can be reduced by up to 45.2%.

Adaptive Latin Hypercube Sampling for a Surrogate-Based Optimization with Artificial Neural Network

A significant number of sample points are often required for surrogate-based optimization when utilizing process simulations to cover the entire system space. This necessity is particularly pronounced in complex simulations or high-dimensional physical experiments, where a large number of sample points is essential. In this study, we have developed an adaptive Latin hypercube sampling (LHS) method that generates additional sample points from areas with the highest output deviations to optimize the required number of samples. The surrogate model used for the optimization problem is artificial neural networks (ANNs). The standard for measuring solution accuracy is the percent error of the optimal solution. The outcomes of the proposed algorithm were compared to those of random sampling for validation. As case studies, we chose three different chemical processes to illustrate problems of varying complexity and numbers of variables. The findings indicate that for all case studies, the proposed LHS optimization algorithm required fewer sample points than random sampling to achieve optimal solutions of similar quality. To extend the application of this methodology, we recommend further applying it to fields beyond chemical engineering and higher-dimensional problems.