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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2025, Vol. 59 Issue (2): 227-248    DOI: 10.3785/j.issn.1008-973X.2025.02.002
    
Review of data-driven intelligent computation and its application
Rui DAI1(),Jing JIE2,Wanliang WANG1,*(),Qianlin YE1,Fei WU1
1. College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China
2. School of Automation and Electrical Engineering, Zhejiang University of Science and Technology, Hangzhou 310023, China
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Abstract  

State-of-the-art data-driven intelligent computations (DDICs) were comprehensively reviewed in order to effectively solve the increasingly complex and expensive optimization problems (EOPs) emerging in real-world applications, which can effectively reduce computing costs and improve solutions. The latest research achievements of DDICs were outlined from both algorithm and application perspectives. Various technical points in generalized DDICs and adaptive DDICs were summarized and categorized. The challenges and opportunities faced by DDICs in solving EOPs were analyzed. Future research potential trends were proposed, such as conducting deeper theoretical analyses, exploring novel learning paradigms, applying these methods in various practical fields, and so on. This aims to provide targeted references and directions for researchers, stimulating innovative ideas to more effectively address the complex EOPs encountered in real-world applications.

Key words： data-driven optimization      surrogate-assisted optimization      intelligent computation      adaptive learning      expensive optimization problem     
Received: 23 February 2024      Published: 11 February 2025
CLC:  TP 301  
Fund:  国家自然科学基金资助项目（61873240）；浙江大学CAD&CG国家重点实验室开放课题资助项目（A2210）；浙江省重点研究发展计划资助项目（2023C03189，2023C01168）.
Corresponding Authors: Wanliang WANG     E-mail: zjudr@zjut.edu.cn;zjutwwl@zjut.edu.cn
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Rui DAI
Jing JIE
Wanliang WANG
Qianlin YE
Fei WU
Cite this article:

Rui DAI,Jing JIE,Wanliang WANG,Qianlin YE,Fei WU. Review of data-driven intelligent computation and its application. Journal of ZheJiang University (Engineering Science), 2025, 59(2): 227-248.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2025.02.002     OR     https://www.zjujournals.com/eng/Y2025/V59/I2/227


数据驱动的智能计算及其应用研究综述

为了有效地解决实际应用中涌现出的越来越复杂的昂贵优化问题（EOPs），全面综述了能够有效降低计算成本和提高求解效率的最新数据驱动智能计算（DDICs）方法. 从算法和应用2个层面系统地概述了最新DDICs的研究成果，归纳和总结了广义DDICs和自适应DDICs中的不同技术点，剖析了DDICs在解决EOPs时所面临的挑战与机遇. 提出未来研究的潜在发展趋势，如进行更深层次的理论分析、探索新颖的学习范式及其在更多不同实际领域中的应用等，旨在为研究者提供有针对性的参考与方向，激发创新思路，从而更有效地应对实际应用中的各种复杂EOPs.


关键词： 数据驱动优化,  代理辅助优化,  智能计算,  自适应学习,  昂贵优化问题 
Fig.1 General flow chart of ICs
Fig.2 Generalized framework of DDICs
元模型应用范围特点
PR/RSM[10]连续问题适合低阶非线性和小规模EOPs；不需要指定参数
GP/Kriging[29]连续问题只适合中低维EOPs；能够提供预测的不确定性
ANN[30]连续问题评估精度高，但需要人为大量试错；训练时间长；鲁棒性差
RBFN[31]连续问题适合中高维EOPs；具有较高的非线性逼近能力；鲁棒性好；可伸缩性强
RF[32]连续问题和离散问题需要调整的参数少；评估精度有待提高
KNN[33]连续问题和离散问题适合高维和多模态EOPs；对异常值不敏感；计算量大；不适合数据不平衡的问题
SVM[34]连续问题和离散问题适合中低维EOPs；鲁棒性差
CNN[35]连续问题和离散问题适合大规模多目标EOPs；能够实现模型并行
GAN[36]离散问题作为分类器，将候选解分为真实和虚假数据，适合大规模的稀疏EOPs；结构复杂，可能存在过拟合问题
EDN[37]连续问题适合高维EOPs；具有很强的可伸缩性；能够提供不确定性
Tab.1 Comparison and analysis of several popular metamodels
Fig.3 Diagram of ensemble learning based on bagging method
测试函数维度CC-DDEADDEA-SEBDDEA-LDGSRK-DDEATT-DDEAMS-DDEO
Ackley1005.78(0.453)6.67(0.534) (+)5.67(0.256) (=)5.32(0.248) (-)4.79(0.213) (-)11.8(1.01) (+)
5004.89(0.471)16.3(0.462) (+)15.7(0.371) (+)7.49(0.278) (+)7.44(0.267) (+)18.1(0.522) (+)
10004.5(0.345)18.5(0.282) (+)18.7(0.191) (+)8.43(0.222) (+)8.21(0.265) (+)18.2(0.567) (+)
Ellipsoid10072.1(15.0)2.53×102(44.3) (+)1.46×102(37.1) (+)83.1(15.9) (+)64.7(12.7) (=)1.27×103(3.41×102) (+)
5001.02×103(2.52×102)1.55×105(2.12×104) (+)1.04×105(1.03×104) (+)8.56×103(6.73×102) (+)8.39×103(9.81×102) (+)2.32×105(4.36×104) (+)
10002.88×103 (6.01×102)9.49×105(9.34×104) (+)7.78×105(5.57×104) (+)4.92×104(5.33×103) (+)4.66×104(3.89×103) (+)7.29×105(5.27×104) (+)
Griewank1001.01(2.55×10-2)17.7(4.27) (+)10.2(1.88) (+)4.2(0.76) (+)4.5(0.554) (+)57.4(9.56) (+)
5001.78(0.273)1.84×103(3.05×102) (+)1.55×103(1.47×102) (+)1.25×102(12.0) (+)1.21×102(12.2) (+)2.47×103(96.6) (+)
10003.71(0.634)6.41×103(6.32×102) (+)5.47×103(4.71×102) (+)3.33×102(36.1) (+)3.31×102(34.9) (+)4.40×103(1.19×102) (+)
Rastrigin1005.39×102(1.01×102)6.81×102 (1.14×102) (+)4.56×102(66.4) (-)4.32×102(53.6) (-)3.11×102(34.6) (-)1.15×103(3.53×102) (+)
5001.74×103(4.22×102)5.56×103(1.69×102) (+)5.45×103(1.39×102) (+)3.78×103(2.37×102) (+)3.89×103(2.09×102) (+)6.04×103(2.45×102) (+)
10002.65×103(4.38×102)1.20×104(2.49×102) (+)1.17×104(2.17×102) (+)8.73×103(3.02×102) (+)8.78×103(2.79×102) (+)1.19×104(3.24×102) (+)
Rosenbrock1003.23×102(41.4)1.78×102(24.3) (?)1.56×102(11.7) (?)2.42×102(33.5) (?)1.43×102(8.53) (?)1.18×103(6.22×102) (+)
5007.77×102(57.4)1.56×104(3.54×103) (+)9.78×103(1.40×103) (+)1.11×103(65.8) (+)1.05×103(47.0) (+)2.44×104(3.47×103) (+)
10001.32×103(87.3)6.17×104(7.01×103) (+)4.27×104(3.29×103) (+)2.36×103(1.74×102) (+)2.28×103(1.48×102) (+)4.52×104(3.04×103) (+)
+/=/?NA14/0/112/1/212/0/311/1/315/0/0
Tab.2 Comparison result of several state-of-the-art DDICs on five benchmark functions
Fig.4 Schematic diagram of multiswarm search process
Fig.5 Diagram of grouping decision variables in cooperation optimization search
Fig.6 Schematic of search process of hierarchical surrogate model
Fig.7 Multitask information sharing framework based on MFEA
Fig.8 Three different methods based on classification
测试函数GCS-PSOREMOθ-DAE-DPABMOEACSEAHeEMOEAEDNMOEAKRVEAParEGOKTA2
DTLZ11.430×103
(7.70×101)		1.260×103
(9.63×101)(?)		1.462×103
(8.67×101)(=)		1.440×103
(7.13×101)(=)		1.299×103
(2.72×101)(?)		1.471×103
(6.34×100)(=)		1.502×103
(3.04×101)(+)		1.395×103
(1.55×102)(?)		1.455×103
(9.87×101)(=)		8.246×102
(2.40×100)(?)
DTLZ23.299×10-1
(5.82×10-3)		2.765×100
(2.82×101)(+)		3.563×100
(2.79×10?1)(+)		3.475×100
(2.08×10?1)(+)		2.948×100
(4.99×10?1)(+)		8.328×10?1
(2.26×10?2)(+)		3.154×100
(1.42×10?1)(+)		3.421×100
(4.23×10?2)(+)		3.203×100
(1.98×10?1)(+)		6.644×10?1
(1.31×10?1)(+)
DTLZ34.441×103
(1.97×102)		3.972×103
(2.90×102)(?)		4.409×103
(2.24×102)(=)		4.472×103
(1.21×102)(=)		3.940×103
(1.99×102)(=)		4.600×103
(1.87×102)(=)		4.639×103
(4.84×100)(=)		4.342×103
(2.36×101)(=)		4.568×103
(5.63×101)(=)		2.737×103
(2.45×100)(?)
DTLZ41.258×100
(1.14×10?1)		2.579×100
(2.32×10?1)(+)		3.544×100
(3.80×10?1)(+)		3.457×100
(1.33×10?1)(+)		2.526×100
(8.60×10?2)(+)		1.547×100
(7.89×10?2)(=)		3.595×100
(7.98×10?2)(+)		3.181×100
(1.12×10?1)(+)		3.666×100
(1.03×10?1)(+)		1.447×100
(9.39×10-3)(+)
DTLZ52.372×10-1
(4.83×10?2)		2.631×100
(2.58×10?1)(+)		2.969×100
(3.43×10?1)(+)		3.345×100
(1.61×10?2)(+)		2.739×100
(3.83×10-3)(+)		8.551×10?1
(3.75×10?2)(+)		3.167×100
(1.89×10?2)(+)		3.508×100
(6.06×10?2)(+)		3.248×100
(1.90×10?1)(+)		5.355×10?1
(4.92×10?2)(+)
DTLZ64.456×101
(1.38×10?1)		3.258×101
(1.45×10-2)(?)		4.852×101
(3.51×10?2)(+)		5.092×101
(2.12×10?1)(+)		4.835×101
(3.59×10?1)(+)		5.102×101
(7.25×10?2)(+)		5.005×101
(7.60×10?1)(+)		4.579×101
(7.54×10?1)(=)		4.729×101
(3.19×10?1)(+)		3.333×101
(1.97×100)(?)
DTLZ74.912×10-1
(6.41×10-3)		6.575×101
(5.83×10?1)(+)		7.439×101
(6.33×10?1)(+)		9.862×100
(1.41×10?1)(+)		7.380×100
(7.45×10?1)(+)		8.263×100
(4.03×10?1)(+)		4.312×100
(1.93×10?1)(+)		8.265×10?1
(5.98×10?1)(+)		2.069×100
(5.50×10?1)(+)		6.206×10?1
(3.28×10?1)(+)
WFG12.182×100
(3.97×10?2)		1.797×100
(6.10×10?2)(?)		1.804×100
(8.26×10?2)(?)		2.409×100
(7.57×10?2)(+)		1.668×100
(1.52×10?2)(?)		2.355×100
(5.03×10?2)(+)		1.659×100
(3.49×10?2)(?)		1.643×100
(4.82×10-3)(?)		1.687×100
(4.98×10?2)(?)		2.056×100
(1.13×10?2)(?)
WFG25.132×10-1
(4.74×10?2)		7.437×10?1
(2.64×10?2)(+)		8.407×10?1
(3.95×10?2)(+)		9.977×10?1
(5.90×10?2)(+)		1.0630×100
(2.12×10-2)(+)		8.844×10?1
(1.08×10?1)(+)		1.024×100
(5.08×10?2)(+)		9.647×10?1
(9.93×10?2)(+)		9.064×10?1
(3.59×10?2)(+)		1.174×100
(3.54×10?2)(+)
WFG34.694×10-1
(3.75×10-3)		7.612×10?1
(8.24×10?3)(+)		8.187×10?1
(2.28×10?2)(+)		7.756×10?1
(1.45×10?2)(+)		8.005×10?1
(6.48×10?3)(+)		5.077×10?1
(1.28×10?2)(+)		7.875×10?1
(9.31×10?3)(+)		7.871×10?1
(1.40×10?2)(+)		7.759×10?1
(7.10×10?3)(+)		8.091×10?1
(1.12×10?1)(+)
WFG44.479×10-1
(2.87×10?2)		5.153×10?1
(1.59×10?2)(+)		5.332×10?1
(1.19×10?2)(+)		8.674×10?1
(5.17×10?2)(+)		7.384×10?1
(1.21×10?1)(+)		7.320×10?1
(4.94×10?2)(+)		6.466×10?1
(1.54×10-3)(+)		8.060×10?1
(2.65×10?2)(+)		7.955×10?1
(7.37×10?2)(+)		1.192×100
(1.86×10?1)(+)
WFG57.514×10?1
(4.15×10?3)		7.118×10-1
(1.08×10?2)(?)		8.667×10?1
(2.52×10?2)(+)		8.680×10?1
(9.44×10?3)(+)		8.421×10?1
(8.99×10-3)(+)		8.499×10?1
(1.92×10?2)(+)		7.966×10?1
(1.23×10?2)(+)		8.567×10?1
(3.36×10?2)(+)		8.694×10?1
(4.78×10?2)(+)		1.074×100
(6.19×10?2)(+)
WFG67.067×10-1
(5.15×10-3)		8.849×10?1
(1.80×10?2)(+)		1.005×100
(1.91×10?2)(+)		1.020×100
(2.22×10?2)(+)		9.376×10?1
(2.18×10?2)(+)		9.552×10?1
(6.49×10?2)(+)		9.506×10?1
(9.03×10?3)(+)		1.022×100
(2.26×10?2)(+)		1.050×100
(1.04×10?2)(+)		1.177×100
(1.67×10?2)(+)
WFG74.891×10-1
(2.21×10-3)		6.705×10?1
(1.39×10?2)(+)		6.744×10?1
(1.69×10?2)(+)		6.684×10?1
(1.13×10?2)(+)		7.467×10?1
(7.27×10?2)(+)		6.378×10?1
(1.30×10?2)(+)		6.788×10?1
(4.60×10?3)(+)		6.911×10?1
(5.11×10?3)(+)		7.013×10?1
(4.11×10?2)(+)		6.016×10?1
(1.29×10?2)(+)
WFG85.743×10-1
(3.63×10-3)		7.288×10?1
(1.13×10?2)(+)		7.220×10?1
(1.21×10?2)(+)		7.415×10?1
(1.66×10?2)(+)		7.355×10?1
(1.59×10?2)(+)		6.903×10?1
(2.04×10?2)(+)		7.308×10?1
(8.46×10?3)(+)		7.243×10?1
(1.53×10?2)(+)		7.916×10?1
(2.12×10?2)(+)		5.781×10?1
(2.27×10?2)(=)
WFG96.573×10-1
(9.88×10-3)		7.288×10?1
(1.13×10?2)(+)		9.203×10?1
(1.48×10?2)(+)		9.387×10?1
(2.54×10?2)(+)		9.114×10?1
(2.92×10?2)(+)		9.022×10?1
(3.36×10?2)(+)		9.515×10?1
(1.61×10?2)(+)		9.380×10?1
(1.69×10?2)(+)		9.708×10?1
(3.85×10?2)(+)		6.672×10?1
(6.40×10?2)(=)
+/=/?NA11/0/513/2/114/2/013/1/213/3/014/1/112/2/213/2/110/2/4
Tab.3 Mean and standard deviation of IGD values obtained by ten multi-objective DDICs on DTLZ and WFG problems
Fig.9 Optimization framework of online DDICs
Fig.10 Implementation process of adaptive DDIC
Fig.11 Adaptive selection process of optimization operator or surrogate model
序号应用领域问题算法目标约束优化算子代理模型
1创伤系统设计离散SA-NSGA-II[10]多无NSGA-IIPR
1创伤系统设计离散RF-CMOCO[54]多不等式MOEARF
2建筑节能设计连续DSCPSO-EMM[153]单无PSORBFN
3天线设计连续improved MOEA/D[154]多不等式MOEA/DBPNN
3天线设计连续SAEA-HAS[142]单无GARBFN
3天线设计连续APSO-mixP[155]单无PSOKriging
4张力/压缩弹簧设计连续MS-MTGAwA[84]单等式GARBFN
5桁架结构设计离散KDPDE[156]单不等式+等式DEKriging
5桁架结构设计离散SADE-MI[157]单不等式DERBFN
6翼型设计离散SA-MPSO[59]单无PSORBFN
6翼型设计离散SA-TSDE[48]单不等式DERBFN
6翼型设计离散SAEA-DBLL[91]多无RVEARBFN
6翼型设计离散DSAEA-PS[99]多无NSGA-IIKriging+GP
6翼型设计离散SAOR-MOEA[121]多无MOEARBFN
7车辆设计连续K-CSEA[158]多无RVEAKriging
7车辆设计连续AMOS[143]多不等式MOEAPR+Kriging+RBFN
8减速机设计连续SACOS[159]单不等式CSORBFN
9船舶设计连续eToSA-DE[53]单不等式DEGP
10供应链系统优化连续CDE[160]单无DERF
11污水处理过程优化连续RLPSO[30]单不等式PSOANN
11污水处理过程优化连续DOC[161]多不等式MOPSOFNN
12车间与资源调度连续PAEM-LSTM[134]多不等式MOEALSTM
12车间与资源调度离散SACS[33]单不等式+等式ACOKNN
12车间与资源调度离散RATSJOP[162]单不等式+等式GARF
13神经网络架构搜索离散SHEALED[24]单无DE+GARBFN
13神经网络架构搜索离散SHCHO[69]单无DECNN
13神经网络架构搜索混合SHEDA[25]单无EDAKriging
14能源与电力系统连续SAMTO[77]单无MFEARBFN
14能源与电力系统连续SAFDR[163]单无PSOGP
15油藏产量连续IDRCEA[125]单无DERBFN+KNN
16无线传感器系统连续SAPPE[164]单无PPERBFN
17自动团队组装游戏离散DDEA-DLS[57]单等式DELSTM
18交通信号配时离散CL-DDEA[50]单等式DE孪生RBFN
Tab.4 Practical application of DDICs in different field
序号竞赛名称细节描述链接
1IEEE CEC’2019 Competition on Evolutionary Computation来自真实世界应用的7个基准多目标优化问题，其中评估成本很高https://github.com/HandingWang/DDMOP
2IEEE CEC’2020 Competition at IEEE world congress on computational intelligence来自气动优化和软件配置调整的2个现实应用程序的8个基准问题https://github.com/HandingWang/DDEOWCCI2020
3IEEE CEC’2021 Competition at IEEE congress on evolutionary computation不同场景下机器人群体模型参数优化的6个问题https://handingwang.github.io/DDEOCEC2021/
4IEEE CEC’2022 Competition on Heat Pipe-Constrained Component Layout Optimization设置了5个优化尺度不同的热管约束元件布局优化(HCLO)问题https://idrl-lab.github.io/CEC2022-HCLO/
5IEEE CEC’2023 Competition on Competition on Multiobjective Neural Architecture Search提供了端到端的流水线平台，称为EvoXBtch，用于生成NAS基准测试套件，涵盖了7种搜索空间、2种神经网络架构、2种广泛研究的数据集、6种硬件以及多达6种类型的优化目标https://www.emigroup.tech/index.php/news/ieee-cec2023-competition-on-multiobjective-neural-architecture-search/
6IEEE CEC’2023 Competition on Large-scale Continuous Optimization for Non-contact Measurement分别从多导体系统的非接触电压测量(NVM)和非接触电流测量(NIM)2个任务中精心选择了6个大规模优化问题https://github.com/ChengHust/IEEE-CEC-2023-Competition
7IEEE CEC’2024 Competition on "Super Large-scale Multiobjective Optimization for Status Assessment of Measuring Equipment"来自广域电力系统中仪表变压器的3个在线状态评估(即，ETT问题)，这3个大规模多目标优化问题的决策变量分别为
100万、1000万和1亿		https://github.com/ChengHust/IEEE-CEC-2024-Competition
Tab.5 Competitions based on practical application of EOPs in six recent years
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