Infilling Strategy Research Articles

A Q-learning driven competitive surrogate assisted evolutionary optimizer with multiple oriented mutation operators for expensive problems

Surrogate-assisted evolutionary algorithms (SAEAs) prevail in the solution of computationally expensive optimization problems. However, with the growth of problem scale and complexity, the high-dimensional problem space greatly restricts their effectiveness and applicability. This paper proposes a Q-learning driven competitive surrogate-assisted evolutionary optimizer with multiple oriented mutation operators (CSEO-MOMO) to improve the prediction effectiveness and accuracy of SAEAs in different scenarios of optimization problems. CSEO-MOMO constructs isomorphic models with different complexities during iteration. The Q-learning method is employed to pick the proper model for prediction based on the state feedback of the iterative population. To explore the search space more comprehensively and increase the probability of finding a better solution, two competitive sub-populations coevolve with personalized mutation operators, of which different oriented optimal tractive base vectors are nominated to guide the mutation direction. In addition, a tailored infilling strategy concerning both the performance of the iterative individuals and their spatial distribution is used to winnow out the individuals with great potential for real evaluation. A suit of high-dimensional CEC benchmarks of different properties and an openly shared topology optimization problem are used for the effectiveness and efficiency verification of CSEO-MOMO. The experimental results reveal that CSEO-MOMO trumps seven excellent SAEAs in solving high-dimensional complex problems and possesses better accuracy and robustness under various fitness landscape scenarios. (The relevant MATLAB code of CSEO-MOMO is publicly available in the first author’s GitHub repository: https://github.com/qinna-zhu/CSEO-MOMO.)

Multi-fidelity deep learning for aerodynamic shape optimization using convolutional neural network

Aerodynamic shape design is essential for improving aircraft performance and efficiency. First, this study introduces a data-driven optimization framework utilizing a multi-fidelity convolutional neural network (MFCNN) for aerodynamic shape optimization. To achieve better optimization results with reduced computational cost, the framework dynamically incorporates new data in each optimization cycle. Specifically, it constantly involves the optimal solution from previous cycle as a new high-fidelity sample and employs a low-fidelity infilling strategy that maximizes the minimum Euclidean distance for selecting new low-fidelity samples. Moreover, a standard synthetic benchmark is used to elaborate the procedure of optimization and show the capability and effectiveness of the framework. Finally, the framework is applied to two aerodynamic shape optimization problems: maximizing the lift-to-drag ratio for the Royal Aircraft Establishment 2822 (RAE2822) airfoils and minimizing the cruise drag coefficient for the three-dimensional (3D) drooped and scarfed non-axisymmetric nacelles. The framework increases the lift-to-drag ratio by 51.21% over the baseline and achieves an 18.79% reduction in the cruise drag coefficient for nacelle optimization, outperforming traditional multi-fidelity deep neural network optimization framework. Sufficiently utilizing the implicit relations between different fidelity levels of data through defined local perceptual fields and convolution, our MFCNN-based optimization framework signifies a step forward in the efficiency and accuracy of aerodynamic shape optimization.

A hybrid criterion-based sample infilling strategy for surrogate-assisted multi-objective optimization

A hybrid criterion-based sample infilling strategy for surrogate-assisted multi-objective optimization

Action reliability analysis under random‐interval hybrid uncertainty of chain conveyor based on adaptive intelligent extremum surrogate model

AbstractThe action responses of controlled mechanisms are often multiparametric, nonlinear, and uncertain. Complex dynamics and limited uncertain information pose difficulties for action reliability analysis. This paper develops an adaptive intelligent extremum surrogate model (AIESM) method for the action reliability under random‐interval hybrid uncertainty of a chain conveyor. First, a dynamic model of the chain conveyor is established, which considers the impact and frictional effects within the mechanical system, the regulating effects of the control system, and the external disturbances of the system. After that, a hybrid kernel extreme learning machine optimized by the sparrow search algorithm is employed as an intelligent surrogate model to construct the initial surrogate model from the hybrid uncertain variables to the limit state function (LSF) response and the extremum surrogate model (ESM) from the random variables to the LSF extremum response. An adaptive infilling strategy combining active learning and opposition‐based learning is applied to improve the accuracy and efficiency of the ESM and reduce the estimation error of action reliability. Finally, the action reliability interval bounds are obtained by Monte Carlo simulation based on the ESM. Two numerical examples are presented to illustrate the validity of the AIESM method. The action reliability interval of the chain conveyor provided by the proposed method is [0.9706, 0.9923].

Optimization of Three-Dimensional Blade and Variable Stators for Efficiency and Stability Enhancement of Multistage Axial Flow Compressor at Variable Speeds

Abstract High efficiency and wide stability at variable speeds are equally important to the design and operation of multistage axial flow compressors. However, published research works on three-dimensional design optimization of compressors are so far mainly limited to a single blade row or stage at design speed due to the curse of dimensionality. Moreover, optimization of variable inlet guide vanes (IGV)/stators for off-design operations is carried out by using a rapid but low-fidelity prediction tool and is generally independent of design optimization of blade geometry. To tackle these issues, a three-dimensional holistic design and adjustment optimization method is developed in which both three-dimensional blade geometry and variable IGV/stators are optimized simultaneously for better efficiency and stability at design and off-design conditions. Metamodel-interpreted data mining method and adaptive infilling strategy are used respectively to enhance the capability of the metamodeling and optimization. The developed method is then applied to a modern highly loaded 3.5-stage transonic axial flow compressor at both design and part-design speeds. The results show that the stall margin is extended from 8.23% to 19.65% at 70% design speed while peak efficiency is slightly improved at design speed. The flow mechanisms responsible for the efficiency enhancement at design speed are mainly associated with the reduced total pressure loss in stators as well as inter- and intra-stage loading redistribution. The stability enhancement at 70% design speed is mainly achieved by loading the front blade rows while unloading the limiting rear blade row through variable IGV/stators adjustment. The developed holistic design and adjustment optimization method with the aid of metamodel-interpreted data mining is of great application value for the design and adjustment of advanced multistage axial flow compressors.

Surrogate-based cyber-physical aerodynamic shape optimization of high-rise buildings using wind tunnel testing

This study proposes a surrogate-based cyber-physical aerodynamic shape optimization (SB-CP-ASO) approach for high-rise buildings under wind loading. Three components are developed in the SB-CP-ASO procedure: (1) an adaptive subtractive manufacturing technique, (2) a high-throughput wind tunnel testing procedure, and (3) a flexible infilling strategy. The downtime of the procedure is minimized through a parallel manufacturing and testing (llM&T) technique. An unexplored double-section setback strategy with various cross-sections and transitions positions is used to demonstrate the performance of the proposed procedure. A total of 173 physical specimens were evaluated to reach the optimization convergence within the reserved testing window. Further analysis of promising shapes considering multiple design wind speeds is suggested to achieve target performance objectives at various hazard levels. Practical information on setback and cross-section modification strategies is discussed based on the optimization results. In comparison with a square benchmark model, the roof drifts for promising candidates with similar building volumes are reduced by more than 70% at wind speeds higher than 50 m/s. This procedure is expected to provide an efficient platform between owners, architects, and structural engineers to identify ideal candidates within a defined design space for real-world applications of high-rise buildings.

Multi-fidelity and multi-objective aerodynamic short nacelle shape optimisation under different flight conditions

AbstractThroughout the course of a flight mission, a range of aerodynamic conditions, including design-point conditions and off-design conditions, are encountered. As the bypass ratio increases and the fan-pressure ratio decreases to reduce the engine’s specific fuel consumption, the engine diameters increase, which results in an increase in the nacelle weight and overall drag. To reduce its weight and drag, a shorter nacelle with a length-to-diameter ratio $L/D = 0.35$ is investigated. In this study, an adaptive cokriging-based multi-objective optimisation method is applied to the design of a short aero-engine nacelle. Two nacelle performance metrics were employed as the objective functions for the optimisation routine. The cruise drag coefficient is evaluated under cruise conditions, whereas the intake pressure recovery is evaluated under takeoff conditions. The cokriging metamodel are refined using an effective infilling strategy, where high-fidelity samples are infilled via the modified Pareto fitness, and low-fidelity samples are infilled via the Pareto front. By combining parameterised geometry generation, automated mesh generation, numerical simulations, surrogate model construction, Pareto front exploration based on the non-dominated sorting genetic algorithm-II and sample infilling, an integrated multi-objective optimisation framework for short aero-engine nacelles is developed. Two-objective and three-objective test functions are used to validate the effectiveness of the proposed framework. After the optimisation process, a set of non-dominated nacelle designs is obtained with better aerodynamic performance than the original design, demonstrating the effectiveness of the optimisation framework. Compared with the kriging-based optimisation framework, the cokriging-based optimisation framework outperforms the single-fidelity method with a higher hypervolume value at the same number of iteration loops.

A Generative Approach for Script Event Prediction via Contrastive Fine-Tuning

Script event prediction aims to predict the subsequent event given the context. This requires the capability to infer the correlations between events. Recent works have attempted to improve event correlation reasoning by using pretrained language models and incorporating external knowledge (e.g., discourse relations). Though promising results have been achieved, some challenges still remain. First, the pretrained language models adopted by current works ignore event-level knowledge, resulting in an inability to capture the correlations between events well. Second, modeling correlations between events with discourse relations is limited because it can only capture explicit correlations between events with discourse markers, and cannot capture many implicit correlations. To this end, we propose a novel generative approach for this task, in which a pretrained language model is fine-tuned with an event-centric pretraining objective and predicts the next event within a generative paradigm. Specifically, we first introduce a novel event-level blank infilling strategy as the learning objective to inject event-level knowledge into the pretrained language model, and then design a likelihood-based contrastive loss for fine-tuning the generative model. Instead of using an additional prediction layer, we perform prediction by using sequence likelihoods generated by the generative model. Our approach models correlations between events in a soft way without any external knowledge. The likelihood-based prediction eliminates the need to use additional networks to make predictions and is somewhat interpretable since it scores each word in the event. Experimental results on the multi-choice narrative cloze (MCNC) task demonstrate that our approach achieves better results than other state-of-the-art baselines. Our code will be available at https://github.com/zhufq00/mcnc.

An active learning reliability algorithm using DMSSA‐optimized Kriging model and parallel infilling strategy

AbstractDue to the limited sample sizes and highly complicated performance functions, how to improve the reliability calculation accuracy and efficiency is an important issue for complex equipment working in harsh environments. This paper proposes an active learning reliability algorithm based on the double‐mutation slap swarm algorithm‐optimized (DMSSA) Kriging surrogate model, parallel infilling strategy and subset simulation (SS). In the method, the uniform design (UD) is employed to select the initial sampling points and their real responses of performance functions are estimated. The DMSSA integrates Cauchy and Gauss mutation to explore the optimal hyperparameter of Kriging model with high accuracy. The parallel infilling strategy combines the expected improvement (EI), minimizing prediction (MP) and mean squared error (MSE) criteria to find new sampling points, which are adaptively added into the database in each iteration to update the design of experiment (DoE). Ultimately, the SS method is employed to deal with the small failure probability problems. Five various examples are analyzed to verify the calculation accuracy and efficiency of the proposed method.

Adaptive ensemble surrogate-based optimization and analysis of forklift pallet racks

As an important part of the lifting platform of pallet forklift trucks, how to reduce the deformation of the pallet rack under working conditions while reducing the mass to ensure the safety performance of forklift trucks is the most concerning issue in the design of forklift truck structure. The pallet rack structure is complex, and optimizing simulation using traditional high-precision simulation models takes much time and effort. Therefore, this paper takes the lifting platform of an unmanned AVG forklift truck as the research object and establishes a parametric model of the pallet rack using the 3D modelling software SolidWorks and the finite element analysis software ANSYS to carry out static analysis of it. Optimization design variables are selected, a single surrogate model and ensemble surrogate model are chosen for various surrogate model techniques, a small number of sample points are used to construct a low-precision model, and adaptive infilling technology is used to improve the model accuracy, and the structure is optimized, and the results show that, while the pallet rack structure meets the requirements of light weight and strength, the mass is reduced by 1.2%, and the morphology is reduced by 17.2%. Moreover, a global sensitivity analysis of each design parameter was carried out under the guidance of the surrogate model, highlighting the most influential design variable as the height of the channel steel and establishing the design variables that should be taken into account in the structural design. This paper compares the performance of the mainstream single-surrogate model and ensemble-surrogate model as well as the adaptive infilling strategy in engineering design and proves that the surrogate model optimization method has a certain guiding significance for the structural optimization design of pallet racking.

An Adaptive Two-Stage Kriging-Based Infilling Strategy for Efficient Multi-Objective Global Optimization

Abstract Most practical multi-objective optimization problems are often characterized by two or more expensive and conflicting objectives, which require time-consuming simulations. Commonly used algorithms construct a surrogate model of each objective function from a few high-fidelity solutions. In order to further decrease the computational burden, adaptive infilling strategies for multi-objective problems are developed to guide the next infilling design for expensive evaluation and update the surrogate model as well as the Pareto front in an iterative manner. In this paper, a multi-objective infilling strategy integrating the Kriging model with a two-stage infilling framework is proposed, termed as ATKIS. This method allows exploitation and exploration alternately to pinpoint the infilling solution for improving the Pareto set and avoiding local over-exploitation simultaneously. At the local exploitation stage, Kriging-based prediction and uncertainty estimation are combined with Non-dominant Ranking and Minimum Relative Distance theories for determining a new design solution, which has maximum improvement relative to the current Pareto set. At the global exploration stage, Voronoi tessellation theory is employed to search for the sparsest position in the design space for a new evaluation. The proposed method is compared with five recent infilling strategies to investigate the performance of infilling ability using several numerical benchmarks. The experimental results show that the proposed method outperforms the other three strategies in improving both effectiveness and robustness using the improvement of hypervolume as the evaluating indicator. In addition, a lightweight optimization design of hoist sheaves shows that the proposed method can deal with real engineering problems, while significantly reducing the computational time and the number of expensive simulations of samples.

Sequential approximate optimization with adaptive parallel infill strategy assisted by inaccurate Pareto front

Sequential Approximate Optimization (SAO) has been widely used in engineering optimization design problems to improve efficiency. The infilling strategy is one of the critical techniques of the SAO, which is of paramount importance to the surrogate model accuracy and optimization efficiency. In this paper, an adaptive parallel infill strategy for surrogate-based single-objective optimization is proposed within a multi-objective optimization framework to balance exploration and exploitation during the optimization process. Within this method, an inaccurate Pareto Front is adopted to assist the infilling of the sampling points. The proposed SAO method with its adaptive parallel sampling strategy is tested on several numerical test cases and an engineering test case with the optimization results compared to state-of-the-art optimization algorithms. The results show that the proposed SAO with the adaptive parallel sampling strategy possesses excellent performance and better stability.

Research on infilling strategy in surrogate-aided optimization for axial compressor blades

The hybrid Voronoi-Latin Hypercube Sampling (Voronoi-LHS) method is proposed for the surrogate-aided optimization of the axial compressor blades. The hybrid method is first applied to the fundamental test cases. The analytical results show that, compared with the Voronoi and LHS strategies, the hybrid method generally improves the robustness and convergency. Then the multi-objective genetic algorithm (MOGA) in conjunction with the artificial neural network (ANN) is applied to optimize the aerodynamic performance of an axial compressor rotor. Before the optimization process, the hybrid Voronoi-LHS sample infilling method is employed to refine the ANN surrogate model. Considering the typical intake distortion, the sweep and lean distributions of this rotor are optimized to pursue the maximum total pressure ratio and adiabatic efficiency. The results show that the optimization significantly improves the pressure ratio, efficiency and surge margin of the compressor with low computing cost.

Multi-fidelity convolutional neural network surrogate model for aerodynamic optimization based on transfer learning

In aerodynamic shape optimization, a high-fidelity (HF) simulation is generally more accurate but more time-consuming than a low-fidelity (LF) simulation. To take advantage of both HF and LF simulations, a multi-fidelity convolutional neural network (CNN) surrogate model with transfer learning (MFCNN-TL) is proposed, which integrates different fidelity information through fine-tuning and adaptively learns their nonlinear mapping. The proposed surrogate model provides a new optimization framework, which maps the relation between shape parameters and aerodynamic performance. In the optimization framework, the HF model with a fine grid and the LF model with a coarse grid is used, respectively. In each optimization iteration, a multi-fidelity infilling strategy is adopted, and HF samples and LF samples are added to update the surrogate model. Finally, it is applied to the aerodynamic shape optimization of NACA0012 airfoil and RAE2822 airfoil. The optimization results show that the proposed MFCNN-TL surrogate model can significantly reduce the calculation cost and improve the optimization efficiency compared with the single-fidelity surrogate model.

A fast active learning method in design of experiments: multipeak parallel adaptive infilling strategy based on expected improvement

A fast active learning method in design of experiments: multipeak parallel adaptive infilling strategy based on expected improvement

A Single- and Multi-objective Optimization Algorithm for Electromagnetic Devices Assisted by Adaptive Kriging Based on Parallel Infilling Strategy

A computationally efficient surrogate model is suggested to approximate the objective and constraint function values, which replace expensive evaluation of the objective and constraint function values in numerical simulation-based optimization. Kriging surrogate model has been widely used in surrogate-based design optimization (SBDO) to replace the highly nonlinear black-box functions. In this paper, a novel adaptive Kriging model based on parallel infilling strategy is proposed to improve both the numerical accuracy and efficiency of the SBDO methods. The parallel infilling strategy consists of two parts: local sampling and globaluthor sampling. In the local sampling, new additional sampling points are generated only within a limited region that is determined according to the optimal point at the last iteration, while in global sampling they are generated based on the fitting error estimation in the whole region. The effectiveness of the proposed algorithm is verified through applications to analytical functions. Then the algorithm is applied to the multi-objective optimal design of an ironless permanent magnet synchronous linear motor.

Multi-fidelity deep neural network surrogate model for aerodynamic shape optimization

In the present study, an effective optimization framework of aerodynamic shape design is established based on the multi-fidelity deep neural network (MFDNN) model. The objective of the current work is to construct a high-accuracy multi-fidelity surrogate model correlating the configuration parameters of an aircraft and its aerodynamic performance by blending different fidelity information and adaptively learning their linear or nonlinear correlation without any prior assumption. In the optimization framework, the high-fidelity model using a CFD evaluation with fine grid and the low-fidelity model using the same CFD model with coarse grid are applied. Moreover, in each optimization iteration, the high-fidelity infilling strategy by adding the current optimal solution of surrogate model into the high-fidelity database is applied to improve the surrogate accuracy. The low-fidelity infilling strategy which can generate the solutions distributed uniformly in the whole design space is used to update the low-fidelity database for avoiding local optimum. Then, the proposed multi-fidelity optimization framework is validated by two standard synthetic benchmarks. Finally, it is applied to the high-dimensional aerodynamic shape optimization of a RAE2822 airfoil parameterized by 10 design variables and a DLR-F4 wing-body configuration parameterized by 30 design variables. The optimization results demonstrate that the proposed multi-fidelity optimization framework can remarkably improve optimization efficiency and outperform the single-fidelity method.

A NON-NESTED INFILLING STRATEGY FOR MULTIFIDELITY BASED EFFICIENT GLOBAL OPTIMIZATION

Efficient Global Optimization (EGO) has become a standard approach for the global optimization of complex systems with high computational costs. EGO uses a training set of objective function values computed at selected input points to construct a statistical surrogate model, with low evaluation cost, on which the optimization procedure is applied. The training set is sequentially enriched, selecting new points, according to a prescribed infilling strategy, in order to converge to the optimum of the original costly model. Multi-fidelity approaches combining evaluations of the quantity of interest at different fidelity levels have been recently introduced to reduce the computational cost of building a global surrogate model. However, the use of multi-fidelity approaches in the context of EGO is still a research topic. In this work, we propose a new effective infilling strategy for multi-fidelity EGO. Our infilling strategy has the particularity of relying on non-nested training sets, a characteristic that comes with several computational benefits. For the enrichment of the multi-fidelity training set, the strategy selects the next input point together with the fidelity level of the objective function evaluation. This characteristic is in contrast with previous nested approaches, which require estimation all lower fidelity levels and are more demanding to update the surrogate. The resulting EGO procedure achieves a significantly reduced computational cost, avoiding computations at useless fidelity levels whenever possible, but it is also more robust to low correlations between levels and noisy estimations. Analytical problems are used to test and illustrate the efficiency of the method. It is finally applied to the optimization of a fully nonlinear fluid-structure interaction system to demonstrate its feasibility on real large-scale problems, with fidelity levels mixing physical approximations in the constitutive models and discretization refinements.

Lightweight design of cylindrical stiffened shells in launch vehicles by a dual-elite population sequential approximation optimization approach

A nonlinear displacement-controlled loading dynamic method is employed to investigate the deformed shape evolution of stiffened shells from prebuckling to postbuckling field until collapse. Because of the time-consuming postbuckling analysis, the dual-elite population sequential approximation optimization (SAO) approach is proposed. A novel determination method of Gaussian kernel widths based on moment estimates is proposed to enhance the augmented radial basis function surrogate model. A novel adaptive parallel infilling strategy is then developed to balance the capabilities of local and global optimization. A dual-elite population strategy is further developed to exploit the information from already acquired sampling points. Finally, the framework of the proposed SAO approach, which is implemented in a distributed parallel way on high-performance clusters to further diminish computation costs, is presented. The efficiency of the algorithm is validated by the postbuckling lightweight optimization of a cylindrical stiffened shell, resulting in a reduction of 12.3% of the initial weight.

Kriging-assisted Discrete Global Optimization (KDGO) for black-box problems with costly objective and constraints

In this paper, a Kriging-assisted discrete global optimization method is presented for computationally expensive black-box problems. KDGO employs Kriging to approximate the landscape of a black-box model, and utilizes a novel infilling strategy to capture the promising discrete samples. In the infilling strategy, a multi-start knowledge mining approach is introduced, including Optimization, Projection, Sampling and Selection. Firstly, a multi-start optimization is used to capture the promising solutions in the continuous design range. Secondly, all these potential solutions are projected to a predefined matrix and a grid sampling method suitable for low and high-dimensional space is proposed to get the promising discrete samples. Thereafter, the k-nearest neighbors (KNN) search strategy and expected improvement (EI) criterion are jointly used to select the candidate samples. The algorithm keeps running to update Kriging and find the most promising samples until the satisfactory solution is obtained. KDGO is primarily developed to solve time-consuming black-box problems with various discrete cases including binary, integer, non-integer, uni/multimodal and box/inequality-constrained types. After the comparison tests on 20 representative benchmark cases, KDGO proves that it can build a reasonable balance between exploitation and exploration. Besides, compared with the existing 6 methods, KDGO has significant advantages on computational efficiency and robustness. Finally, KDGO is used for structure optimization of a blended-wing-body underwater glider, and gets the satisfactory design.