Surrogate-based Optimization Research Articles

A study of Stall-Induced Vibrations using Surrogate-Based Optimization

Stall-Induced Vibrations (SIV) are an important design consideration for wind turbine blade design, especially for large, modern, wind turbines with highly flexible blades. Their severity depends on both the inflow and the structural characteristics of the blades. Studying SIV has a high computational cost, because it requires high-fidelity aeroelastic simulations, and potentially a large number of input variables. In an effort to reduce the computational cost of the domain exploration, in this work we have adopted a Surrogate-Based Optimization (SBO) framework. This way, the combination of input variables that lead to SIV can be explored with the minimum number of aeroelastic simulations. The proposed SBO framework can use any type of surrogate model, and leverages Delaunay triangulation to iteratively select samples to refine the surrogate model. The occurrence and severity of SIV on the IEA 10MW turbine is studied in a five variables space consisting of: wind speed, yaw angle, vertical wind shear, wind veer, and atmospheric temperature. A well-trained surrogate model is developed and used to predict the damping ratio of the first blade edgewise mode in the entire inflow space at a reduced computational cost. Sensitivity analysis of the predicted damping ratio shows that yaw angle is the most influential variable, while temperature is the least influential variable in terms of inflow conditions that can lead to the occurrence of SIV. Inflow conditions with a moderate yaw angle (around 10–25 deg), high wind speeds, and moderate to high negative veer are found to lead to severe SIV. This study should serve as a guiding tool to decide the scope of the more computationally expensive simulations such as high-fidelity CFD-based aeroelastic simulations which can provide a more accurate description of SIV.

Impacts of photovoltaic and energy storage system adoption on public transport: A simulation-based optimization approach

Photovoltaic and energy storage system (PESS) adoption in public transport (PT) can offer a promising alternative towards reducing the charging and carbon emission costs of transit agencies. However, the quantitative impacts of PESS on operational cost, carbon emission cost, bus scheduling, and energy management in PT remain unclear. This study is performed with the aim of filling this research gap by presenting an impact analysis framework incorporating multisource datasets and a simulation-based optimization approach. A simulation is designed to capture bus scheduling and energy management on a day-to-day transit operation. A surrogate-based optimization method is adopted to determine an optimal PESS configuration for battery electric bus (BEB) charging stations. A case study is performed by introducing PESS at BEB charging stations in Beijing, China, leveraging historical weather and bus operational data. Compared with conventional charging stations, the novel transit system with PESS reduces the annual charging costs and carbon emissions of a single bus route in this case study by 17.6% and 8.8% on average, respectively. The results suggest that the recycling electricity price of PV generation is the key to influencing charging costs and carbon emissions. Battery capacities also impact the scheduling pattern of PESS considerably. Further comparison across five bus routes in Beijing reveals that the deployment locations of PESS are key decisions influencing the operational cost and carbon emissions in PT at the network level when the investment budget is limited.

Optimization of Savonius wind turbine with additional blades by surrogate model using artificial neural networks

The aim of the current investigation is to obtain the optimum configuration of Savonius wind turbine which results in maximum power coefficient (Cp). In order to achieve that Surrogate-based optimization (SBO) was used for obtaining the optimum values of investigated parameters. Design of experiment (DoE) was applied on four variables which are: the arc angle of original blade (ψ), the shape factor of original blade (p/q), the arc angle of additional blades (β), and the additional blade radii ratio (Rr). Computational fluid dynamics (CFD) simulations using ANSYS FLUENT were conducted to feed the artificial neural networks (ANN) with the sufficient data for training for the traditional and optimized rotors. The considered original blade arc angle (ψ) and the additional blades angle (β) varied from 70° to 180°, the original blade shape factor (p/q) ranges from 0.00 to 0.70, and the additional blade radii ratio (Rr) changes from 0.20 to 1.25 of that of the original blade. The optimized rotor showed a maximum Cp of 0.2836 results in 44.5% increase in Cp over 0.1962 of conventional one for the tip speed ratio (TSR) of 0.75. The maximum increase is 66.12% at TSR = 1.3.

Multiple Thermal Parameter Inversion for Concrete Dams Using an Integrated Surrogate Model

An efficient and accurate method for concrete thermal parameter inversion is essential to guarantee the reliable and prompt thermal analysis results of dams. Traditional inversion methods either suffer from low analysis efficiency or are limited in accuracy. Thus, this paper presents a method for multiple thermal parameter inversion based on an integrated surrogate model (ISM) and the Jaya algorithm. This method replaces finite element analysis with an ISM incorporating three machine learning algorithms, Kriging, support vector regression (SVR), and radial basis function (RBF), to describe the mapping relationship between thermal parameters and structure temperature responses. The input datasets for model training and testing are generated by a uniform design approach. Subsequently, a simple and efficient global optimization algorithm, Jaya, is used to identify the thermal parameters by minimizing the error between calculated and monitored temperatures. The effectiveness and practicality of this method are verified by applying monitored data of two strength grades of concrete in a dam. The verification results indicate that the proposed approach can obtain more accurate inversion results than the above individual models. Compared with these models, the inversion errors using ISM are reduced by 8.45%, 3.93% and 20.85%, respectively for C35 concrete, and by 6.53%, 23.82% and 44.43%, respectively for C40 concrete. Additionally, this approach maintains the powerful computational efficiency of surrogate-based optimization, and compared to the methods that directly invert using swarm intelligence algorithms, the analysis efficiency is improved by about 111.7 times.

The first AI4TSP competition: Learning to solve stochastic routing problems

This paper reports on the first international competition on AI for the traveling salesman problem (TSP) at the International Joint Conference on Artificial Intelligence 2021 (IJCAI-21). The TSP is one of the classical combinatorial optimization problems, with many variants inspired by real-world applications. This first competition asked the participants to develop algorithms to solve an orienteering problem with stochastic weights and time windows (OPSWTW). It focused on two learning approaches: surrogate-based optimization and deep reinforcement learning. In this paper, we describe the problem, the competition setup, and the winning methods, and give an overview of the results. The winning methods described in this work have advanced the state-of-the-art in using AI for stochastic routing problems. Overall, by organizing this competition we have introduced routing problems as an interesting problem setting for AI researchers. The simulator of the problem has been made open-source and can be used by other researchers as a benchmark for new learning-based methods. The instances and code for the competition are available at https://github.com/paulorocosta/ai-for-tsp-competition.

Surrogate-Based Design Optimization of a H-Darrieus Wind Turbine Comparing Classical Response Surface, Artificial Neural Networks, and Kriging

Clean energy sources like wind energy have been receiving much attention, and great emphasis has been given to the design and optimization of horizontal axis wind turbines, but just as important are the vertical axis wind turbines that can be used for generating energy for small businesses, houses, and buildings. This article sought to study the optimal geometrical parameters of a H-Darrieus vertical axis wind turbine using surrogate-based optimization with three different types of surrogate models and compared them. Airfoil chord and thickness were chosen as the design variables and respective ranges set at 0.32-0.6 m and 0.04-0.16 m. All evaluations are carried out for a tip-speed ratio of 1.5. Three different surrogate models were used and compared, namely a quadratic polynomial response surface, an artificial neural network based on radial basis functions called Extreme Learning Machine and a Kriging interpolator. Surrogates were constructed based on an initial sample data distributed according to a full factorial design. A test set was designed to evaluate the accuracy of the surrogates. Both training and testing data sets were generated using 2D CFD modeling to reduce computational cost. From the test set, Extreme Learning Machine surrogate showed the smallest RMSE of 11.24%, followed by Kriging, at 17.64%, and Response Surface of 22.17%. For the optimal designs the same pattern ensued, with optimal power coefficient overestimated by 8.7% for the response surface surrogate, followed by 3.12% and 2.17% for the Kriging interpolator and the Extreme Learning Machine, respectively. Power coefficient curves comparing the three optimal geometries from each surrogate were calculated and plotted. Optimal turbine obtained from Kriging surrogate optimization process resulted in a 7.92% increase in the Cp, whilst Extreme Learning Machine and Response Surface resulted in a 7.86% and 4.29% increase, respectively, all when compared to baseline CFD model. Concluding guidelines are that the quadratic polynomial response surface may not be the best alternative when dealing with complex non-linear relationships as typically present in VAWT simulations. Superior techniques such as Extreme Learning Machine and Kriging could be more suitable for this application.

Advancing surrogate-based optimization of time-expensive environmental problems through adaptive multi-model search

Advancing surrogate-based optimization of time-expensive environmental problems through adaptive multi-model search

Rotary hearth furnace for steel solid waste recycling: Mathematical modeling and surrogate-based optimization using industrial-scale yearly operational data

The presence of zinc in byproduct dust produced during steel production poses a challenge to resource management and can have adverse environmental effects. This study investigates the dezincification behavior of a commercial-scale rotary hearth furnace used to recycle the byproduct dust. A mathematical model of iron-ore/carbon-composite pellets was developed, incorporating a one-dimensional dynamic model to examine the non-uniform distribution of temperature and solid weight fraction. The Arrhenius kinetics of the ZnO reduction reaction (ZnO + CO → Zn + CO2) was fitted using operational data yielding estimated parameters of 163.6 kJ mol−1 and 868.6 m s−1. The simulation results of our study showed good agreement with the operational data from the furnace, with a relative error of 10%. Six factors were identified as having an impact on the dezincification ratio, with the most significant being operational time, particle size, temperature, C/O ratio, porosity, and emissivity in descending order. The mathematical model was used to examine two scenarios of environmental problems and derive optimal solutions for each. Our results show that extreme gradient boosting using operating temperature, operating duration, and C/O ratio as trained variables was the most accurate in predicting dezincification and metallization, resulting in a 33% increase in waste recycling through surrogate-based optimization. The Pareto front analysis highlights the importance of considering the net impact of carbon emissions, total production cost, and solid waste penalties together.

Electric bus charging facility planning with uncertainties: Model formulation and algorithm design

This paper investigates the electric bus charging facility planning (EB-CFP) problem for a bus transit company operating a heterogeneous electric bus (EB) fleet to provide public transportation services, taking into account uncertainties in both EB travel time and battery degradation. The goal of the EB-CFP problem is to determine the number and type of EB chargers that should be deployed at bus terminals and depots to meet daily EB charging demand while minimizing total cost. The problem is formulated as a two-stage stochastic programming model, with the first stage determining the EB charger deployment scheme and the second stage estimating the EB daily operational cost with respect to a predetermined EB trip timetable for a given EB charger deployment scheme. To effectively address the second stage problem, a multi-agent EB transit simulation system that mimics the daily EB operation process is developed. We then design two heuristic methods, the reinforcement learning (RL)-based method and the surrogate-based optimization (SBO), that use the developed multi-agent EB transit simulation system to solve the two-stage stochastic programming model for large-scale instances. Lastly, we run a series of experiments on a fictitious EB transit network and a real-world EB transit network in Singapore to evaluate the performance of the models and algorithms. In order to improve the performance of the EB transit system, some managerial insights are also provided to urban bus transit companies.

Surrogate-based optimization for variational quantum algorithms

Variational quantum algorithms are a class of techniques intended to be used on near-term quantum computers. The goal of these algorithms is to perform large quantum computations by breaking the problem down into a large number of shallow quantum circuits, complemented by classical optimization and feedback between each circuit execution. One path for improving the performance of these algorithms is to enhance the classical optimization technique. Given the relative ease and abundance of classical computing resources, there is ample opportunity to do so. In this work, we introduce the idea of learning surrogate models for variational circuits using few experimental measurements, and then performing parameter optimization using these models as opposed to the original data. We demonstrate this idea using a surrogate model based on kernel approximations, through which we reconstruct local patches of variational cost functions using batches of noisy quantum circuit results. Through application to the quantum approximate optimization algorithm and preparation of ground states for molecules, we demonstrate the superiority of surrogate-based optimization over commonly-used optimization techniques for variational algorithms.

Surrogate-based optimization of capture chromatography platforms for the improvement of computational efficiency

In this work, we discuss the use of surrogate functions and a new optimization framework to create an efficient and robust computational framework for process design. Our model process is the capture chromatography unit operation for monoclonal antibody purification, an important step in biopharmaceutical manufacturing. Simulating this unit operation involves solving a system of non-linear partial differential equations, which can have high computational cost. We implemented surrogate functions to reduce the computational time and make the framework more attractive for industrial applications. This strategy yielded accurate results with a 93% decrease in processing time. Additionally, we developed a new optimization framework to reduce the number of simulations needed to generate a solution to the optimization problem. We demonstrate the performance of our new framework, which uses MATLAB built-in tools, by comparing its performance against individual optimization algorithms for problems with integer, continuous, and mixed-integer variables.

An efficient method for helicopter fuselage shape optimization

PurposeThis paper aims to develop a new method of fuselage drag optimization that can obtain results faster than the conventional methods based on full computational fluid dynamics (CFD) calculations and can be used to improve the efficiency of preliminary design.Design/methodology/approachAn efficient method for helicopter fuselage shape optimization based on surrogate-based optimization is presented. Two numerical simulation methods are applied in different stages of optimization according to their relative advantages. The fast panel method is used to calculate the sample data to save calculation time for a large number of sample points. The initial solution is obtained by combining the Kriging surrogate model and the multi-island genetic algorithm. Then, the accuracy of the solution is determined by using the infill criteria based on CFD corrections. A parametric model of the fuselage is established by several characteristic sections and guiding curves.FindingsIt is demonstrated that this method can greatly reduce the calculation time while ensuring a high accuracy in the XH-59A helicopter example. The drag coefficient of the optimized fuselage is reduced by 13.3%. Because of the use of different calculation methods for samples, this novel method reduces the total calculation time by almost fourfold compared with full CFD calculations.Originality/valueTo the best of the authors’ knowledge, this is the first study to provide a novel method of fuselage drag optimization by combining different numerical simulation methods. Some suggestions on fuselage shape optimization are given for the XH-59A example.

Multi-fidelity surrogate-based optimal design of road vehicle suspension systems

Ride comfort is a relevant performance for road vehicles. The suspension system can filter vibration caused by the uneven road to improve ride comfort. Optimization of the road vehicle suspension system has been extensively studied. As detailed models require significant computational effort, it becomes increasingly important to develop an efficient optimization framework. In this work, a multi-fidelity surrogate-based optimization framework based on the Approximate Normal Constraint method and Extended Kernel Regression surrogate modeling method is proposed and applied. An analytical model and a multi-body model of the suspension system are used as the low-fidelity and high-fidelity models, respectively. Compared with other well-known methods, the proposed method can provide good accuracy and high efficiency. In addition, the proposed method is applied to different types of vehicle suspension optimization problems and shows good robustness and efficiency.

Computational framework for efficient high-fidelity optimization of bio-inspired propulsion and its application to accelerating swimmers

A new computational framework for high-fidelity optimization of kinematic gaits during self-propelled undulatory swimming is developed. A computational framework utilizes a spectral-element method on moving body-fitted grids for a simulation of self-propelled swimming, and a surrogate-based optimization (SBO) procedure. A new volume-conservation method for reconstruction of a swimmer's geometry during the undulatory motion is proposed to ensure numerical stability of the fluid-structure interaction solver in an incompressible flow framework. A surrogate-based optimization algorithm that utilizes a Kriging response surface method is adopted and further developed in this work to manage the optimization process in the presence of physiological constraints on the fish body motion. A grid convergence of the optimization results is established, and the influence of the polynomial refinement on the results of optimization procedure is assessed. The increase in polynomial order does not change the optimum gaits of locomotion or relative efficiency rankings between the modes, but it results in slightly lower predicted efficiency for all the modes. The optimum solution is characterized by a kinematic gait that generates the reverse Karman vortex street associated with high propulsive efficiency. Efficiency of sub-optimum modes is found to increase with both the tail amplitude and the effective flapping length of the swimmer, and a new scaling law is proposed to capture these trends. Lastly, the SBO algorithm converged to an optimized gate with significantly less function evaluations than typically observed for evolutionary algorithms. This suggests that the SBO framework is a well suited alternative for high-fidelity optimization of fluid and structure problems.

Surrogate-based optimization approach for capacitated hub location problem with uncertainty

CJ Logistics has started to consider opening single new hub facility to expand the current transportation network system. This naturally leads to formulating a research question “where should the new hub facility be located in South Korea to minimize total transportation cost of the network system operated by the company?”. This research aims to answer the question by proposing a surrogate-based optimization approach. In addition to finding an optimal location of the new hub facility, this research performs sensitivity analysis to study the correlation between hub capacity (i.e., the source of uncertainty) and transportation cost. The results indicate that (1) total transportation cost after the establishment of the new hub facility at the optimal location is reduced by approximately 14% compared to the current transportation network system and (2) the currently operated hub facility located in Daejeon has the greatest influence on total transportation cost; while the existing hub facilities located in Cheongwon, Yongin, and Gunpo have little impact on total transportation cost after the construction of the new hub facility. It is expected that the outcome of this research helps the company systematically manage the transportation network system when the new hub facility is constructed.

Integrated approach based on surrogate optimization and CFD for the design of helical turbulators

The present work describes an accurate tool based on numerical simulations and genetic algorithms, which is able to automatically choose the turbulator geometrical parameters with helical profile that optimize both the heat exchanged and the pressure losses with a low computation cost. In particular, the proposed methodology is assessed in the design of turbulators for the smoke-pipe of a steam boiler. The flue gases behavior is modeled with the compressible Reynolds-Averaged Navier–Stokes equations, coupled with transport equations for non-reacting chemical species. The optimization employs a surrogate-based optimization, where the single and multi objective genetic algorithm are applied to a response surface. Different objective functions from literature to drive the optimization process are compared, e.g, the heat exchange efficiency, the total entropy generation number, the merit function, and the net profit and total cost per unit transferred heat load. Even if these functions have been yet investigated in different works, showing pros and cons, it is still not clear from a practical point of view, which one should be used for a shape optimization process. The results suggest the use of a different objective function if the main goal is to maximize the heat exchanged and/or to minimize the pressure losses, with similar performance of the parameters based on the laws of thermodynamics or also on economic considerations. Furthermore, the results prove the higher fidelity of numerical simulations in the estimation of the Nusselt number and the friction factor in comparison with empirical correlations. The significance of the present work lies in the proof of the low computational cost and easy application of a shape optimization process for the design-of-things based on numerical simulations.

Optimized hydrodynamic interactions in phalanx school arrays of accelerated thunniform swimmers

Optimal fish array hydrodynamics in accelerating phalanx schools are investigated through a computational framework which combines high fidelity Computational Fluid Dynamics (CFD) simulations with a gradient free surrogate-based optimization algorithm. Critical parameters relevant to a phalanx fish school, such as midline kinematics, separation distance and phase synchronization, are investigated in light of efficient propulsion during an accelerating fish motion. Results show that the optimal midline kinematics in accelerating phalanx schools resemble those of accelerating solitary swimmers. The optimal separation distance in a phalanx school for thunniform biologically-inspired swimmers is shown to be around 2L (where L is the swimmer’s total length). Furthermore, separation distance is shown to have a stronger effect, ceteris paribus, on the propulsion efficiency of a school when compared to phase synchronization.

Kriging-Based Space Exploration Global Optimization Method in Aerodynamic Design

For complicated aerodynamic design problems, the efficient global optimization method suffered from the defect of the incorrect portrayal of the design space, resulting in bad global convergence and efficiency performance. To this end, a Kriging-based global optimization method, named the Kriging-based space exploration method (KSE), was proposed in this paper. It selected multiple promising local minima and classified them into partially and fully explored minima in terms of the fitting quality of the surrogate model. Then, the partially explored minima would be furtherly exploited. During the local search, an enhanced trust-region method was adopted to make deep exploitation. By combining local and global searches, the proposed method could improve the fitting quality of the surrogate model and the optimization efficiency. The KSE was compared to other global surrogate-based optimization methods on 12 bound-constrained testing functions with 2 to 16 design variables and 2 aerodynamic optimization problems with 24 to 77 design variables. The results indicated that the KSE generally took fewer function evaluations to find the global optima or reach the target value in most test problems, holding better efficiency and robustness.

A spur to molecular geometry optimization: Gradient-enhanced universal kriging with on-the-fly adaptive ab initio prior mean functions in curvilinear coordinates.

We present a molecular geometry optimization algorithm based on the gradient-enhanced universal kriging (GEUK) formalism with ab initio prior mean functions, which incorporates prior physical knowledge to surrogate-based optimization. In this formalism, we have demonstrated the advantage of allowing the prior mean functions to be adaptive during geometry optimization over a pre-fixed choice of prior functions. Our implementation is general and flexible in two senses. First, the optimizations on the surrogate surface can be in both Cartesian coordinates and curvilinear coordinates. We explore four representative curvilinear coordinates in this work, including the redundant Coulombic coordinates, the redundant internal coordinates, the non-redundant delocalized internal coordinates, and the non-redundant hybrid delocalized internal Z-matrix coordinates. We show that our GEUK optimizer accelerates geometry optimization as compared to conventional non-surrogate-based optimizers in internal coordinates. We further showcase the power of the GEUK with on-the-fly adaptive priors for efficient optimizations of challenging molecules (Criegee intermediates) with a high-accuracy electronic structure method (the coupled-cluster method). Second, we present the usage of internal coordinates under the complete curvilinear scheme. A complete curvilinear scheme performs both surrogate potential-energy surface (PES) fitting and structure optimization entirely in the curvilinear coordinates. Our benchmark indicates that the complete curvilinear scheme significantly reduces the cost of structure minimization on the surrogate compared to the incomplete curvilinear scheme, which fits the surrogate PES in curvilinear coordinates partially and optimizes a structure in Cartesian coordinates through curvilinear coordinates via the chain rule.

An efficient geometric constraint handling method for surrogate-based aerodynamic shape optimization

Handling a large number of geometric constraints brings a big challenge to the surrogate-based aerodynamic shape optimization (ASO) driven by computational fluid dynamics (CFD). It is not feasible to calculate the geometric constraint functions directly during the sub-optimization of a surrogate-based optimization, as the geometric constraint functions are to be evaluated thousands of times for each updating cycle and the total cost of a number of cycles can be prohibitive. This article proposes an efficient method of handling geometric constraints within the framework of a surrogate-based optimization to address this problem. The core idea is to use the Kreisselmeier-Steinhauser (KS) method to aggregate all geometric constraints into one that can be approximated by a cheap surrogate model, in order to avoid the large computational cost associated with tremendous calculation of geometric constraint values. The proposed method is verified by an analytical test case. Then, the proposed method is demonstrated and compared with the methods of building surrogate models of all geometric constraints and calculating all geometric constraints directly during each sub-optimization by drag minimizations of NACA0012 air foil and ONERA M6 wing in transonic flows. To investigate the ability of the proposed method for handling various geometric constraints, drag minimization of CRM wing in viscous transonic flow driven by CFD is performed. Results show that the proposed method can dramatically improve the optimization efficiency of ASO with the number of geometric constraints ranging from 15 to 1429 and the number of types of geometric constraints up to 3, which offers great potential for handling a larger number and more types of geometric constraints.