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A modified trust-region assisted variable-fidelity optimization framework for computationally expensive problems

ENGINEERING COMPUTATIONS 2022年第7期39卷 2733-2754页

作者： Li, Chengshan Dong, Huachao Changan Univ Sch Construct Machinery Xian Peoples R China Changan Univ Autopilot & Maglev Transportat Technol & Equipmen Xian Peoples R China Northwestern Polytech Univ Sch Marine Sci & Technol Xian Peoples R China

Purpose variable-fidelity optimization (VFO) frameworks generally aim at taking full advantage of high-fidelity (HF) and low-fidelity (LF) models to solve computationally expensive problems. The purpose of this paper is to develop a novel modified trust-region assisted variable-fidelity optimization (MTR-VFO) framework that can improve the optimization efficiency for computationally expensive engineering design problems. Design/methodology/approach Though the LF model is rough and inaccurate, it probably contains the gradient information and trend of the computationally expensive HF model. In the proposed framework, the extreme locations of the LF kriging model are firstly utilized to enhance the HF kriging model, and then a modified trust-region (MTR) method is presented for efficient local search. The proposed MTR-VFO framework is verified through comparison with three typical methods on some benchmark problems, and it is also applied to optimize the configuration of underwater tandem wings. Findings The results indicate that the proposed MTR-VFO framework is more effective than some existing typical methods and it has the potential of solving computationally expensive problems more efficiently. Originality/value The extreme locations of LF models are utilized to improve the accuracy of HF models and a MTR method is first proposed for local search without utilizing HF gradient. Besides, a novel MTR-VFO framework is presented which is verified to be more effective than some existing typical methods and shows great potential of solving computationally expensive problems effectively.

关键词： variable-fidelity optimization Kriging Trust-region method Computationally expensive problems Design optimization

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Parametric Modelling and variable-fidelity Bayesian optimization of Aerodynamics for a Reusable Flight Vehicle

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FLUID DYNAMICS 2024年第6期59卷 2083-2095页

作者： Xu, D. Y. Shen, Y. Huang, W. Guo, Z. Y. Zhang, H. Xu, D. F. Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha Hunan Peoples R China Aerosp Syst Engn Shanghai Shanghai Peoples R China

AbstractA variable-fidelity Bayesian optimization approach that leverages low-fidelity data (panel approach) to efficiently establish an initial prior for aerodynamic optimization of reusable flight vehicles is proposed. This approach demonstrates a notable advantage over traditional Bayesian optimization techniques constrained by their reliance on high-fidelity data and the associated computational expenses. A comparative analysis reveals that our approach can identify the optimized solutions that would typically require a substantial amount of data, using only a limited number of high-fidelity samples. While the traditional approach undergoes significant shifts in the search space over 50 iterations due to Bayesian optimization's tendency to explore unknown space, our approach, employing low-fidelity data as an initial prior knowledge, achieves stability within approximately 10 iterations. Notably, with just 50 computational fluid dynamics (CFD) samples (high-fidelity data), the optimized vehicle shape demonstrates significant improvements in the lift-to-drag ratio across a broad range of the attack angles, showing a 9% enhancement at the target lift-to-drag ratio at the 10 degrees attack angle, which is the optimization objective.

关键词： variable-fidelity optimization Bayesian optimization reusable flight vehicle design

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An online variable-fidelity optimization approach for multi-objective design optimization

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2019年第3期60卷 1059-1077页

作者： Shu, Leshi Jiang, Ping Zhou, Qi Xie, Tingli Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Hubei Peoples R China Huazhong Univ Sci & Technol Sch Aerosp Engn Wuhan 430074 Hubei Peoples R China

Multi-objective genetic algorithms (MOGAs) are effective ways for obtaining Pareto solutions of multi-objective design optimization problems. However, the high computational cost of MOGAs limits their applications to practical engineering optimization problems involving computational expensive simulations. To address this issue, a novel variable-fidelity (VF) optimization approach for multi-objective design optimization is proposed, in which a VF metamodel is embedded in the computation process of MOGA to replace the expensive simulation model. The VF metamodel is updated in the optimization process of MOGA, considering the cost of simulation models with different fidelity and the influence of the VF metamodel uncertainty. A normalized distance constraint is introduced to avoid selecting clustered sample points. Four numerical examples and two engineering cases are used to demonstrate the applicability and efficiency of the proposed approach. The results show that the proposed approach can obtain Pareto solutions with good quality and outperforms the other four approaches considered here as references in terms of computational efficiency.

关键词： Multi-objective optimization variable-fidelity optimization Multi-objective genetic algorithms Metamodel uncertainty

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variable-fidelity Design optimization of Antennas with Automated Model Selection 10

Variable-Fidelity Design Optimization of Antennas with Autom...

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10th European Conference on Antennas and Propagation (EuCAP)

作者： Koziel, Slawomir Bekasiewicz, Adrian Reykjavik Univ Engn Optimizat & Modeling Ctr IS-101 Reykjavik Iceland

ISBN: (纸本)9788890701863

Computationally efficient design optimization of antenna structures can be realized using variable-fidelity EM simulations, where most of the operations are performed at the level of a coarse-discretization EM model (referred to as the lowfidelity model) with occasional reference to the high-fidelity one, for the sake of model correction and design verification. An important issue is an appropriate selection of the low-fidelity model in terms of its speed and accuracy. It is typically controlled by adjusting discretization density of the structure at hand. Using the model that is too coarse may lead to unreliable design and divergence of the optimization algorithm. If the model is too fine, the computational cost of the design process increases. So far, the model selection has been realized interactively through visual inspection of the model responses. In this paper, an automated procedure for low-fidelity model setup has been proposed based on statistical analysis of correlations between the models of various fidelities. Using an example of a dielectric resonator antenna we demonstrate that our approach allows for selecting the optimal discretization level of the lowfidelity model that results in a good compromise between the cost and reliability of the design process.

关键词： Antenna design simulation-driven design variable-fidelity optimization low-fidelity models model selection feature-based optimization

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Efficient Incremental variable-fidelity Machine-Learning-Assisted Hybrid optimization and Its Application to Multiobjective Antenna Design

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 2024年第12期72卷 9347-9354页

作者： Chen, Weiqi Wu, Qi Han, Biying Yu, Chen Wang, Haiming Hong, Wei Southeast Univ Sch Informat Sci & Engn Nanjing 211189 Peoples R China Southeast Univ State Key Lab Millimeter Waves Nanjing 211189 Peoples R China Purple Mt Labs Nanjing 211111 Peoples R China

Online-model-based machine-learning-assisted optimization (MLAO) methods are widely used to reduce the computational burden of complex electromagnetic (EM) optimization problems. Multidesign parameter and multiobjective EM problems are common in engineering practice. As the problem design dimensionality increases, the training time of the surrogate model in the optimization process becomes nonnegligible. The performance of optimization algorithms degrades for high design dimensions and multiple objectives, and many full-wave simulation calculations are required before convergence. In this work, an incremental variable-fidelity machine-learning-assisted hybrid optimization (IVF-MLAHO) algorithm is proposed to solve a multiobjective EM problem with medium-scale (i.e., 20-50) design variables. First, reliable variable-fidelity models are used for initial sampling to reduce the computational cost of sampling. Then, in the training process, incremental learning or retraining is adaptively selected to update the surrogate models, which reduces the training burden. Furthermore, a hybrid global multiobjective and local single-objective optimization algorithm is adopted to markedly improve the convergence performance. Finally, the superiority of the IVF-MLAHO algorithm is verified on a substrate-integrated waveguide (SIW) broadband millimeter-wave slot antenna array, in which the training time is greatly reduced.

关键词： Computational modeling optimization Training Predictive models Data models Antennas and propagation Adaptation models Machine learning algorithms Antenna arrays Millimeter wave technology Antenna design incremental learning machine learning multiobjective optimization variable-fidelity optimization

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variable-fidelity Design optimization of Antennas with Automated Model Selection

Variable-Fidelity Design Optimization of Antennas with Autom...

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European Conference on Antennas and Propagation

作者： Slawomir Koziel Adrian Bekasiewicz Engineering Optimization & Modeling Center Reykjavik University 101 Iceland

ISBN: (纸本)9781509022342

Computationally efficient design optimization of antenna structures can be realized using variable-fidelity EM simulations, where most of the operations are performed at the level of a coarse-discretization EM model (referred to as the low-fidelity model) with occasional reference to the high-fidelity one, for the sake of model correction and design verification. An important issue is an appropriate selection of the low-fidelity model in terms of its speed and accuracy. It is typically controlled by adjusting discretization density of the structure at hand. Using the model that is too coarse may lead to unreliable design and divergence of the optimization algorithm. If the model is too fine, the computational cost of the design process increases. So far, the model selection has been realized interactively through visual inspection of the model responses. In this paper, an automated procedure for low-fidelity model setup has been proposed based on statistical analysis of correlations between the models of various fidelities. Using an example of a dielectric resonator antenna we demonstrate that our approach allows for selecting the optimal discretization level of the low-fidelity model that results in a good compromise between the cost and reliability of the design process.

关键词： Antenna design feature-based optimization low-fidelity models model selection simulation-driven design variable-fidelity optimization

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Pumping optimization of Coastal Aquifers Using Seawater Intrusion Models of variable-fidelity and Evolutionary Algorithms

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WATER RESOURCES MANAGEMENT 2019年第2期33卷 555-568页

作者： Christelis, Vasileios Mantoglou, Aristotelis Natl Tech Univ Athens Lab Reclamat Works & Water Resources Management Sch Rural & Surveying Engn Athens Greece British Geol Survey Environm Sci Ctr Nottingham England

variable-fidelity modelling has been utilized in several engineering optimization studies to construct surrogate models. However, similar approaches have received much less attention in coastal aquifer management problems. A variable-fidelity optimization framework was developed utilizing a lower-fidelity and computationally cheap model of seawater intrusion, based on the sharp interface assumption, and a simple correction process. The variable-fidelity method was compared to the direct optimization with the high-fidelity variable density and salt transport model and to conventional surrogate-based optimization. The surrogate-based approaches were embedded into the operations of an evolutionary algorithm to implement an efficient online update of the surrogate models and control the feasibility of the optimal solutions. Multiple independent optimization runs were performed to provide more insightful comparison outcomes. Although the variable-fidelity method found a better optimum than the conventional approach, the overall sample statistics showed that the surrogate-based optimization frameworks performed equally well and provided good approximations to the high-fidelity solution. Despite the potential for an improved exploration of the optimal search space by using the variable-fidelity method, the conventional approach had a 30% faster average convergence time.

关键词： Seawater intrusion Pumping optimization Surrogate modelling variable-fidelity optimization

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variable-fidelity multipoint aerodynamic shape optimization with output-based adapted meshes

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AEROSPACE SCIENCE AND TECHNOLOGY 2020年 105卷

作者： Chen, Guodong Fidkowski, Krzysztof J. Univ Michigan Dept Aerosp Engn Ann Arbor MI 48109 USA

This paper presents a method to control the discretization error in multipoint aerodynamic shape optimization using output-based adapted meshes. The meshes are adapted via adjoint-based error estimates, taking into account both the objective and constraint output errors. A multi-fidelity optimization framework is then developed by taking advantage of the variable fidelity offered by adaptive meshes. The objective functional and its sensitivity at each design point (operating condition) are first evaluated on the same initial coarse mesh, which is then subsequently adapted for each design point individually as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. As the shape approaches the optimal design, the mesh at each design point becomes finer, in regions necessary for that particular operating condition. The multi-fidelity framework is tightly coupled with the objective error estimation to ensure the optimization accuracy at each fidelity. Computational savings arise from a reduction of the mesh size when the design is far from optimal and avoiding an exhaustive search on low-fidelity meshes. The proposed method is demonstrated on multipoint drag minimization problems of a transonic airfoil with lift and area constraints. Improved accuracy and efficiency are shown compared to traditional fixed-fidelity optimization with a fixed computational mesh. (C) 2020 Elsevier Masson SAS. All rights reserved.

关键词： Multipoint optimization variable-fidelity optimization Discretization error Adjoint-based error estimation Mesh adaptation

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variable-fidelity expected improvement method for efficient global optimization of expensive functions

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STRUCTURAL AND MULTIDISCIPLINARY optimization 2018年第4期58卷 1431-1451页

作者： Zhang, Yu Han, Zhong-Hua Zhang, Ke-Shi Northwestern Polytech Univ Sch Aeronaut Natl Key Lab Sci & Technol Aerodynam Design & Res Xian 710072 Shaanxi Peoples R China

The efficient global optimization method (EGO) based on kriging surrogate model and expected improvement (EI) has received much attention for optimization of high-fidelity, expensive functions. However, when the standard EI method is directly applied to a variable-fidelity optimization (VFO) introducing assistance from cheap, low-fidelity functions via hierarchical kriging (HK) or cokriging, only high-fidelity samples can be chosen to update the variable-fidelity surrogate model. The theory of infilling low-fidelity samples towards the improvement of high-fidelity function is still a blank area. This article proposes a variable-fidelity EI (VF-EI) method that can adaptively select new samples of both low and high fidelity. Based on the theory of HK model, the EI of the high-fidelity function associated with adding low- and high-fidelity sample points are analytically derived, and the resulting VF-EI is a function of both the design variables x and the fidelity level l. Through maximizing the VF-EI, both the sample location and fidelity level of next numerical evaluation are determined, which in turn drives the optimization converging to the global optimum of high-fidelity function. The proposed VF-EI is verified by six analytical test cases and demonstrated by two engineering problems, including aerodynamic shape optimizations of RAE 2822 airfoil and ONERA M6 wing. The results show that it can remarkably improve the optimization efficiency and compares favorably to the existing methods.

关键词： Efficient global optimization Surrogate model variable-fidelity optimization Expected improvement Kriging

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Adaptive Model Refinement with Batch Bayesian Sampling for optimization of Bio-inspired Flow Tailoring

Adaptive Model Refinement with Batch Bayesian Sampling for O...

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AIAA Aviation Forum and Exposition

作者： Ghassemi, Payam Lulekart, Sumeet Sanjay Chowdhury, Souma Univ Buffalo Dept Mech & Aerosp Engn Buffalo NY 14260 USA

ISBN: (数字)9781624105890

ISBN: (纸本)9781624105890

This paper presents an advancement of a model-independent surrogate based optimization method with adaptive sampling, known as Adaptive Model Refinement. The primary advancement relates to the capability to identify optimum location to add new samples. To this end, a new variable fidelity optimization method is proposed, where the timing of refinement and the number of infill points are determined based on the existing work in adaptive model refinement, and the location of the infill points are uniquely decided by integrating a GP-based criteria (\q-EI") adopted from Bayesian optimization. Preliminary optimization runs showcase the achievement of up to 9% of drag reduction.

关键词： variable-fidelity optimization Surrogate-Based optimization Bayesian optimization Bio-inspired Fluid Dynamics Passive Flow Control Riblets

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