机器学习和元启发式算法优化混凝土配合比研究进展

陈云; 付前旺

机器学习和元启发式算法优化混凝土配合比研究进展

陈云^,,
付前旺

海南大学土木建筑工程学院, 海口 570228

基金项目: 国家自然科学基金:(52378504，51968020)；海南省重点研发计划项目(ZDYF2021 SHFZ070)

详细信息

通讯作者:
陈云，博士研究生，教授，博士生导师，研究方向为：高性能土木工程材料　E-mail: chenyunhappy@hainanu.edu.cn

中图分类号: TU528;TB332
计量
- 文章访问数: 60
- HTML全文浏览量: 60
- 被引次数: 0
出版历程
- 收稿日期: 2024-01-22
- 修回日期: 2024-02-29
- 录用日期: 2024-03-19
- 网络出版日期: 2024-04-16

Research progress on mixture optimization of concrete based on machine learning and metaheuristic algorithms

CHEN Yun^,,
FU Qian Wang

College of Civil Engineering and Architecture, Hainan University, Haikou 570228, China

Funds: National Natural Science Foundation of China (No. 52378504, 51968020); The Key Research and Development Program of Hainan Province (No. ZDYF2021 SHFZ070)

摘要

摘要: 混凝土配合比决定其成本、工作性能、力学性能和耐久性能，传统混凝土配合比优化方法是通过大量实验室试验，需要消耗大量时间、人力和资源。为了解决上述问题，利用机器学习和元启发式优化算法进行混凝土配合比优化已被证明是一种具有广阔前景的技术手段。本文全面回顾了有关混凝土配合比设计和优化方面的研究。首先，讨论了常用的机器学习和元启发式算法的基本工作原理和优势。然后，归纳总结了基于机器学习和元启发式算法在单一目标、多目标优化各种类型混凝土配合比方面的应用。最后，结合当前的技术水平，强调并讨论了推进混凝土配合比设计和优化领域的当前趋势和机遇，为机器学习技术在混凝土领域的更深层次的开发和应用提供了依据。
- 混凝土配合比 /
- 机器学习 /
- 元启发式算法 /
- 优化
Abstract: The concrete mix ratio determines its cost, workability, mechanical properties, and durability. The traditional method of concrete mix ratio optimization is through a large number of laboratory tests, which consumes a lot of time, labor, and resources. To solve the above problems, concrete proportion optimization using machine learning and meta-heuristic optimization algorithms has been proven to be a promising technical tool. Presents a comprehensive review of the research on concrete proportion design and optimization. First, the basic working principles and advantages of commonly used machine learning and meta-heuristic algorithms are discussed. Then, the applications of machine learning and meta-heuristic-based algorithms in single-objective and multi-objective optimization of various types of concrete proportions are summarized. Finally, current trends and opportunities in advancing the field of concrete proportion design and optimization are highlighted and discussed in the context of the current state of the art, providing a basis for deeper development and application of machine learning techniques in the field of concrete.
- Concrete mixture /
- Machine learning /
- Metaheuristic algorithm /
- Optimization

HTML全文

图 1 机器学习分类^[6]

Figure 1. Machine Learning Classification^[6]

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图 2 机器学习模型框架图^[7]

Figure 2. Schematic diagram of machine learning model^[7]

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图 3 GA流程图

Figure 3. GA Flowchart

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图 4 PSO算法示意图

Figure 4. Schematic diagram of the PSO algorithm

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图 5 天牛的觅食行为^[11]

Figure 5. The foraging behaviour of the beetle^[11]

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图 6 简化天牛模型^[11]

Figure 6. Simplified beetle model^[11]

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图 7 人工蜂群算法流程图^[12]

Figure 7. Flowchart of the Artificial Bee Colony algorithm^[12]

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图 8 数据驱动法预测水泥基复合材料力学性能和挖掘化学反应的流程图^[31]

Figure 8. Flowchart of the proposed data-driven approach to predict the mechanical properties and discover chemical reactions of cementitious composites^[31]

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图 9 硅灰混凝土多目标配合比优化GUI^[11]

Figure 9. Silica Fume Concrete Multi-Objective Proportion Optimization GUI^[11]

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图 10 共生生物搜索优化最小二乘支持向量机集成系统界面布局^[43]

Figure 10. Symbiotic organism search-optimized least squares support vector machine integrated system interface layout^[43]

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图 11 基于可解释的纤维增强超高性能混凝土逆向设计方法流程图^[47]

Figure 11. The flowchart of the reverse design method for ultrahigh performance fiber reinforced concrete based on interpretable grid search cross validation Catboost^[47]

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图 12 自动挖掘低碳经济型UHPC方法流程图^[58]

Figure 12. Flowchart of the proposed method for auto-discovery of low-carbon cost-effective UHPC^[58]

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图 13 多目标优化方法流程图^[88]

Figure 13. Flowchart of the proposed method for prediction and multi-objective optimization^[88]

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表 1 四种元启发式优化算法对比分析

Table 1. Comparative analysis of four meta-heuristic optimization algorithms

Algorithm	Author	Year	Inspiration	Class	Application area
Genetic Algorithm	Holland and Reitman	1978	The process of natural selection	Evolutionary-based	Power system, image reconstruction, scheduling, engineering, routing, feature selection, filtering recommender system, travelling salesman problem, electromagnetic optimization.
Particle swarm optimization	Eberhart and Kennedy	1995	The process of bird flock	Swarm-based	Feature selection, job scheduling, financial time series forecast, vapor-liquid equilibrium problem, engineering, economic dispatch problem, scheduling problem, medical diagnosis.
Beetle Antennae Search	Xiangyuan Jiang and Shuai Li	2017	The process of the searching behavior of longhorn beetles.	Individual-based	Power system, image reconstruction, feature selection, job scheduling, engineering, scheduling problem, electromagnetic optimization.
Artificial Bee Colony	Karaboga and Basturk	2007	The process of honey harvesting behavior of bee colony	Swarm-based	Scheduling, estimation of transportation energy demend, forecasting the blast-produced ground virbration, travelling salesman problem, engineering problem, clustering.

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表 2 应用机器学习(ML)优化普通混凝土配合比

Table 2. Optimal concrete mixture based on machine learning (ML)

Algorithms	Input variables	Output variables	Optimization objectives	Evaluation metrics	Datasets	Year	Authors
BPNN	Cement, fine/coarse aggregate, water, superplasticizer	Compressive strength, slump, permeability coefficient, elastic modulus	/	/	117	2003	Liu et al^[21]
ANN	Weathered sand, soil, cement, water, superplasticizer	Compressive strength, tangent modulus	/	/	10	2004	Li et al^[22]
ANN	Cement, fly ash, fine and coarse aggregates, water, superplasticizer, reducing-water ratio of superplasticizer	Strength, slump	/	Average sum-squared error	18	2006	Ji et al^[23]
BPNN, GA	Cement, fine/coarse aggregate, fly ash, superplasticizer	Compressive strength, slump	/	Average relative error	150	2007	Chen et al^[24]
NN, GA	Cement, fly ash, slag, water, superplasticizer, fine and coarse aggregates, binder, water/cement, water/binder water/solid, superplasticizer /binder, fly ash/binder, slag/binder, pozzolans/binder aggregate/binder, fine aggregate /aggregate	Strength, slump	/	RMSE	103	2007	Yeh^[25]
GA, ANN, BPNN	Cement, fly ash, fine aggregate, coarse aggregate, admixture, water-binder ratio.	Slump	/	RMSE, MAPE, R	560	2015	Chandwani et al^[26]
BBP, Regression	Cement, water, silica fume, coarse aggregate, fine aggregate, superplasticizer, the maximum size of aggregate and concrete age	Compressive strength	/	RMSE	1030	2019	Golafshani et al^[27]
DNN	Cement, water, fine-grained aggregate, coarse aggregate, water-cement ratio	Compressive strength	/	MAE, MSE, RMSE	741	2021	Ziolkowski et al^[28]
ExGBT, LGBT, GAM, KDP, Anomaly detection algorithm, K-means algorithm	Water, cement, fly ash, water-reducing admixture, air-entraining admixture, coarse/fine aggregate, fresh air	Fire-induced spalling, chloride penetration, strength	/	Area under the ROC curve, Log loss error	10000	2022	Naser^[30]
DL, GP, ANN, BO	Mixture proportions, chemical composition, particle size distribution, type of specimen, curing time	Compressive strength	/	RMSE, MAE, MAD, R²	760	2023	Mahjoubi et al^[31]
LR, NN, BT, RF, SVM	Water/cement, cement, fly ash contents, water-reducing admixture, air-entraining admixture contents, coarse/fine aggregate contents, fresh air content	Compressive strength	Compressive strength, cost, embodied CO₂	RMSE, R², MAPE	1031/ 9994	2019	Young et al^[32]
WCA, SLC, GA, ANN, SVM, Regression	Age, cement, water, superplasticizer, coarse aggregate, fine aggregate, the ratios of water to binder, superplasticizer to binder, fine aggregate to total aggregate, coarse aggregate to binder	Compressive strength	Compressive strength, cost, CO₂ emission, energy, resource consumptions	MAE, R, R², MSE, RMSE	232	2020	Naseri et al^[34]
BPNN, BAS, SVM, LR, DT, MLR, KNN, RF, NSGA-II, MOEA, MOPSO	Ordinary Portland cement, silica fume, water, coarse/fine aggregate, maximum size of coarse aggregate, superplasticizer, curing age	Strength	Strength, cost, embodied CO₂	RMSE, R	1030	2021	Zhang et al^[11]
RF, DT, SVM, BAS	Cement, water, blast furnace slag, coarse/fine aggregate, superplasticizer	Uniaxial compressive strength	Uniaxial compressive strength, cost	RMSE, R	102	2022	Zhu et al^[35]
COP, WCP, DL	Age, water, cement, fine/coarse aggregate, superplasticizer, supplementary cementing materials, weight ratios of water to binder, supplementary cementing materials to binder, coarse aggregate to binder, fine aggregate to total aggregate, superplasticizer to binder	Compressive strength	Compressive strength, cost, emission-CO₂, energy consumption, material consumption	R, MSE, MAE, R², RMSE	1200	2023	Naseri et al^[36]
Elastic net, Extremely randomized tree, Lasso/Ridge /amma regression, RF, DT, AdaBoost, GB, ExGBT, LightGBM, CatBoost, NSGA-III, C-TAEA	Water, cement, mineral admixture, fine/coarse aggregate, chemical admixture, performance parameter	Compressive strength, binder intensity	Compressive strength, binder intensity, cost	R², RMSE, MAE, MGD	610	2023	Zheng et al^[37]
Notes: DNN - Deep neural network, ExGBT - Extreme gradient boosted tree, LGBT - Light gradient boosted tree, GAM - Generalized additive model, KDP - Keras deep residual neural network, DL - Deep learning, GP - Gaussian processes, BO - Bayesian optimization, LR – Linear regression, BT – Boosted tree, WCA - Water cycle algorithm, SLC - Soccer league competition, RMSE - Root mean square error, MAPE - Mean absolute percentage error, MAE - Mean absolute error, MSE - Mean square error, ROC - Receiver operating characteristic, MAD - Median absolute deviation, DT - Decision tree, MLR - Multivariable linear regression, KNN - K-nearest neighbours, MOEA-, MOPSO - Multi-objective particle swarm optimization, COP - Coyote optimization programming, WCP - Water cycle programming, GB - Gradient boosting, C-TAEA - Constrained-targeted adaptive evolutionary algorithm, MGD - Mean gamma deviance.

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表 3 应用ML优化UHPC/HPC/HSC配合比

Table 3. Optimal UHPC/HPC/HSC mixture based on machine learning

Algorithms	Input variables	Output variables	Optimization objectives	Evaluation metrics	Datasets	Year	Authors
ANN	Cement, fly ash, blast furnace slag, water, superplasticizer, coarse/fine aggregate, water/cement ratio, water/cementitious ratio, superplasticizer/cementitious ratio, fly ash/cementitious ratio, slag/cementitious ratio (fly ash+ slag)/cementitious ratio	Compressive strength, slump	/	R²	695/ 120	1999	Yeh^[33]
GA	Water to binder ratio, water, fine aggregate ratio, fly ash replacement ratio, silica fume replacement ratio, air-entraining agent, superplasticizer	Compressive strength, slump	/	R²	189	2004	Lim et al^[38]
Elitist GA	Cement, fly ash, fine/coarse aggregates, water, superplasticizer, water / cement, water / (cement + fly ash), fly ash / cement, fly ash / (cement +fly ash)	Compressive strength	/	MSE	350	2009	Jayaram et al^[39]
Harmony search algorithm, NN, GA	Cement, fly ash, silica fume, fine/coarse aggregates, water, superplasticizer, fine aggregate ratio, water / binder	Compressive strength, slump	/	Probability	189	2012	Lee et al^[40]
GA, ESVM	Cement; fly ash; blast furnace slag; water; superplasticizer; coarse/fine aggregate, age of testing	Compressive strength	/	RMSE, MAE	1030	2014	Cheng^[41]
GP	Cement, blast furnace slag, fly ash, water, superplasticizer, coarse/fine aggregate	Strength	/	RMSE, Pearson correlation coefficient	453	2021	Ke et al^[42]
SOS, LSSVM, BPNN, ESIM, SVM	Fine/coarse aggregate, fly ash, silica fume, cement, blast furnace slag, water, superplasticizer, age of testing	Compressive strength, slump, electrical resistivity	Compressive strength, slump, electrical resistivity, cost	R, RMSE, MAPE, MAE	597/ 282/ 264	2023	Cheng et al^[43]
BPNN, GA	Cement，water/cement，silica fume，superplasticizer，fine/coarse aggregate，steel fiber content	Compressive strength	/	/	50	2020	Chen et al^[44]
GA, ANN	Cement, silica fume, limestone powder, river sand; water/cementitious materials ratio, superplasticizer/cementitious materials ratio	Packing density	Workability, packing density, compressive strength, pore structure, economy, ecology	R², RDP, RMSE, MAPE	26	2020	Fan et al^[45]
GA, ANN, LR	Cement, limestone powder, silica fume, river sand	Compressive strength, packing density	/	R², RDP, RMSE	80	2021	Fan et al^[46]
AdaBoost, LightGBM, XGBoost, CatBoost, RF	Cement, silica fume, quartz sand, steel fiber, superplasticizer, water, concrete age	Compressive strength	/	RMSE, R², MAE	400	2023	Zou et al^[47]
RF, CART	Cement, silica fume, supplementary cementing materials, quartz powder, water, superplasticizer proportion, siliceous micro sand, maximum size of the sand’s particle, water to binder, mixture’s total fiber volume, total fiber reinforcement index	Energy absorption capacity, strain at peak stress	/	R²	600	2023	Garcia et al^[48]
ANN	Fly ash, silica fume, superplasticizer, water/cement, water to binder	Compressive strength	/	/	9	2004	Wang et al^[49]
ANN, GA	Water to binder ratio, sand ratio, the amount of cement per cubic meter of concrete, the ratio of fly ash/slag/silica fume mass to cementitious materials mass	Slump, compressive strength, tensile strength, elastic modulus, shrinkage, creep coefficient, cracking risk coefficient	Slump, compressive strength, tensile strength, elastic modulus, shrinkage, creep coefficient, cracking risk coefficient	MAE, MSE, RMSE, R²	25	2020	Li et al^[50]
BPNN, SVR, RT, RF, KNN, LR, MLR, PSO	Cement, blast furnace slag, fly ash, water, fine/coarse aggregate, bentonite, silty clay, superplasticizer, curing age	Strength, slump	Strength, slump, cost	RMSE, R	1030	2020	Zhang et al^[51]
RF, NSGA-II	Water to binder, cement, fine/coarse aggregate, fly ash, silica fume, superplasticizer	Compressive strength, chloride ion permeability coefficient	Compressive strength, chloride ion permeability coefficient, cost	RMSE, R²	71	2022	Wu et al^[52]
RF, AEPSO	Cement, blast furnace slag, fly ash, water, fine/coarse aggregate, superplasticizer, age	Compressive strength	Compressive strength, cost, emission-CO₂	RMSE, R, MAE	1133	2022	Ren et al^[53]
RF, NSGA-II, BPNN, SVM, GBDT	Cement, fine/coarse aggregate, superplasticizer, fly ash, water-binder ratio	Relative dynamic elastic modulus, chloride ion permeability coefficient, cost	Relative dynamic elastic modulus, chloride ion permeability coefficient, cost	RMSE, R², MAPE	92	2023	Chen et al^[54]
RF, RFE, BO, LSSVM, NSGA-III, BPNN, WNN	Fly ash, cement, fine/coarse aggregate, water, composite superplasticizer, water-binder ratio, average particle size, sand ratio, mud, needle-like particles, water absorption	Chloride ion permeability coefficient, relative dynamic elastic modulus, strength	Chloride ion permeability coefficient, relative dynamic elastic modulus, strength, cost	RMSE, R²	100	2023	Yang et al^[55]
MLR, MLPNN, GPR, PSO	Cement, silica fume, quartz flour, siliceous sand, water, polycarboxylate ether-based superplasticizers, steel microfibers	Strength, slump	Strength, slump, cost	RMSE, R, MAE	53	2022	Sadrossadat et al^[56]
GP, BBO, LR, RF, XGBoost, GA-ANN	Cement, water, sand, admixture, quartz powder, steel fiber, silica fume, fly ash	Compressive strength	Compressive strength, workability, embodied-CO₂, packing density, cost	MSE, R²	110	2022	Saleh et al^[57]
Ridge, MLP, SVM, Partial least squares, RF, BO, LightGBM, AGE-MOEA, XGBoost, Extra trees, C-TAEA, NSGA-II, UNSGA-III	Portland cement, fly ash, slag, silica fume, metakaolin, nano silica, limestone powder, quartz powder, fine sand, tap water, superplasticizer, steel fiber	Compressive strength, flexural strength, mini-slump spread, porosity	Compressive strength, flexural strength, mini-slump spread, porosity, life-cycle carbon footprint, embodied energy, material cost	MAE, MAPE, MAD, R²	785	2023	Mahjoubi et al^[58]
XGBoost, SVR, GBR, RFR, GA, NSGA-II	Cement, fly ash, blast furnace slag, superplasticizer, water, coarse/fine aggregate, age	Compressive strength	Compressive strength, cost, CO₂ emission	R², RMSE, MAE	1342+1133	2023	Tipu et al^[59]
Notes: ESVM - Evolutionary support vector machine, SOS - Symbiotic organism search, LSSVM - Least squares support vector machine, ESIM - Evolutionary support vector machine inference model, CART - Classification and regression tree, RT – Regression tree, AEPSO - Adaptive evolutionary particle swarm optimization, GBDT - Gradient boosting decision tree, RFE - Recursive feature elimination, WNN - Wavelet neural network, MLPNN - Multi-layer perceptron neural network, GPR - Gaussian processing regression, BBO - Batch bayesian optimization, MLP - Multilayer perceptron, AGE-MOEA - Adaptive geometry estimation-based many-objective evolutionary algorithm, GBR - Gradient boosting regression, RFR – Random forest regression, RDP - Relative percent deviation.

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表 4 应用ML优化RAC/RBAC配合比

Table 4. Optimal RAC/RBAC mixture based on machine learning

Algorithms	Input variables	Output variables	Optimization objectives	Evaluation metrics	Datasets	Year	Authors
GA	Water/binder, water, cement, sand, aggregate, admixture	Slump, compressive strength, final setting, specific gravity, elastic modulus, carbonation speed coefficient, price, CO₂ emission	Slump, compressive strength, final setting, specific gravity, elastic modulus, carbonation speed coefficient, price, CO₂ emission	Probability	6/4	2013	Park^[60]
NN	Cement, water/cement, crushed tile, crushed brick, natural aggregate	Compressive strength	/	MAE, RMSE, MAPE, R, E	147	2017	Šipoš^[61]
ICA, MLP, GA, PSO	Water, cement, recycled coarse aggregates, natural coarse/fine aggregates, water/cement	Compressive, tensile, flexural strengths, slump	/	MAE	1348	2021	Pajand et al^[62]
GBRT, PSO, RNN, GP	Water/cement, cement, sand, recycled aggregate, gavel, superplasticizer, silica fume, age, specimen type	Compressive strength	Compressive strength, cost, CO₂ emission	RMSE, MAE, R²	1134	2020	Nunez et al^[63]
FA, RF, BPNN, SVM	Cement, water, sand, natural coarse aggregates, superplasticizer, recycled coarse aggregates, maximum size, water absorption, density	Uniaxial compressive strength, splitting tensile strength	Uniaxial compressive strength, splitting tensile strength, cost, CO₂ emission	RMSE, R	344	2020	Zhang et al^[64]
BPNN, GWO, SVM, RF, ELM, XGBoost, GRNN, PSO	Cement, water/cement, crushed tile ratio, crushed brick ratio, natural aggregate ratio	Compressive strength	Compressive strength, cost, CO₂ emission	R, R², SD, RMSE	182	2023	Wang et al^[65]
BPNN, GPR, RF, BO, GBDT, NSGA-II	Cement，water, sand, fly ash, aggregate replacement ratio, aggregate water absorption, age, carbon dioxide volume fraction, ambient temperature, humidity, carbonation time	Electrical flux, carbonization depth	Electrical flux, carbonation depth, cost, strength	R², RMSE	200+500	2023	Liu et al^[66]
BPNN, GPR, CART, RF, BO, GBDT, XGBoost, CMOPSO	Water, cement, sand, coarse aggregates, fly ash, strength grade of cement, replacement ratio of recycled coarse aggregates, weighted water absorption of coarse aggregates, maximum particle size of coarse aggregates, curing time	Compressive strength	Compressive strength, materials cost, carbon footprint, energy intensity	R², RMSE, MAPE	1373	2023	Liu et al^[67]
Notes: ICA – Imperialist competitive algorithm, GBRT – Gradient boosting regression tree, RNN – Recurrent neural network, FA – Firefly algorithm, GWO – Gray wolf optimizer, ELM – Extreme learning machine, GRNN – Generalized regression neural network, CMOPSO - Competitive mechanism-based multi-objective particle swarm optimization, SD - Standard deviation.

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表 5 应用ML优化GPC/AAC配合比

Table 5. Optimal GPC/AAC mixture based on machine learning

Algorithms	Input variables	Output variables	Optimization objectives	Evaluation metrics	Datasets	Year	Authors
MARS	Fly ash, aggregates, alkaline activator, added water, NaOH molarity, solid% in Na₂SiO₃, heat curing	Compressive strength	/	R, RMSE, MAE	98	2018	Lokuge et al^[68]
ANN	Fly ash, coarse aggregate, fine aggregate, NaOH activator, Na₂SiO₃ activator, added water, SiO₂ % in Na₂SiO₃, Na₂O % in Na₂SiO₃, NaOH molarity, heat curing	Compressive strength, flexural strength, elastic modulus	/	MSE, R,	166	2021	Gunasekara et al^[69]
RF	Precursor, ground granulated blast furnace slag ratio, Na₂O, elastic modulus, water, fine/coarse aggregate	Compressive strength, slump, static/dynamic yield stress, plastic viscosity	Compressive strength, slump, static/dynamic yield stress, plastic viscosity, CO₂ emission	R², MAE, MAPE, RMSE	145+193	2023	Sun et al^[70]
ANN, GA	Total mass of SiO₂, Al₂O₃, Fe₂O₃, CaO, Na₂O, fine/coarse aggregates, superplasticizer, water, age, curing temperature, time, relative humidity	Compressive strength, slump	Transportation, CO₂ emission, cost	RMSE, MAE, R², R	1178	2022	Shobeiri et al^[71]
NSGA-II, BPNN, XGBoost	Fly ash chemical composition, superplasticizer; fly ash; fine/coarse aggregate; extra water; high temperature; high temperature curing; standard curing	Uniaxial compressive strength	Uniaxial compressive strength, cost, CO₂ emission	MSE, MAE, R²	896	2023	Dong et al^[72]
RFR, ETR, GBR, XGBR, BO, NSGA-II	Fly ash, blast furnace slag, sodium silicate, sodium hydroxide, water, coarse/fine aggregate, curing relative humidity, temperature, curing age, silica modulus, reactivity modulus, alumina modulus, lime modulus, hydraulic modulus	Uniaxial compressive strength	Uniaxial compressive strength, cost, CO₂ emission	R, MAE, RMSE	676	2023	Huang et al^[73]
RF, GB, BPNN, GPR, PSO	Slag, fly ash, coarse/fine aggregate, NaOH, sodium silicate, water, superplasticizer	Compressive strength	Compressive strength, cost, carbon emission	R², RMSE, MAPE	143	2023	Li et al^[74]
Notes: RFR – Random forest regression, ETR – Extremely randomized tree, XGBR – Extreme gradient boosting regression.

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表 6 应用ML优化LWC配合比

Table 6. Optimal LWC mixture based on machine learning

Algorithms	Input variables	Output variables	Optimization objectives	Evaluation metrics	Datasets	Year	Authors
SVR, MLP, GBR, XGBoost	Cement, supplementary cementitious materials, light weight aggregates types, normal weight aggregates, superplasticizer, age of testing, oven dry densities of each light weight high strength concrete mix	Compressive strength, splitting tensile strength	/	R², RMSE, MAE, MAPE	403	2023	Sifan et al^[75]
SVM, ANN, DT, GPR, XGBoost	Cement, sand, water-to-cement ratio, lightweight aggregate, normal aggregate, density of lightweight aggregate, water absorption of lightweight aggregate, superplasticizer, curing time, fly ash, lightweight aggregate type	Compressive strength	/	RMSE, MAE, MSE, R²,	420	2023	Hussain et al^[76]
ANN, DNN, RBM, DBN, GA, NSGA-II	The percentage of lightweight expanded clay aggregate, water-to cement ratio, cement content, silica fume dosage	Compressive, tensile strength	Compressive strength, cost, Life cycle assessment	R², MAE, RMSE	240	2021	Dabbaghi et al^[77]
MOFA, SVR	Cement, water, natural fine aggregate, lightweight coarse aggregate, superplasticizer, the density of lightweight coarse aggregate, maximum size of coarse aggregate, age	Uniaxial compressive strength, density	Uniaxial compressive strength, density, cost	RMSE, MAE, MAPE, R	144	2021	Zhang et al^[78]
Notes: RBM – Restricted Boltzmann machine, MOFA – Multi-objective firefly algorithm.

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表 7 应用ML优化其它类型混凝土配合比

Table 7. Optimal other types concrete mixture based on machine learning

Concrete types	Algorithms	Input variables	Output variables	Optimization objectives	Evaluation metrics	Datasets	Year	Authors
Pozzolanic concrete	ANN, BPNN	Water, cement, ground granulated blast furnace slag, fly ash, coarse/fine aggregate, superplasticizer	Compressive strength, slump	/	R², SSE	482/ 295	2018	Kao et al^[79]
Cemented paste backfill	PSO, MR	Cement percentage, solid content, water contents	Strength, yield stress, cost	Strength, yield stress, cost	R²	16	2020	Sadrossadat et al^[80]
Wet-sprayed concrete	ANN, PSO, GA	Cement, water-cement ratio, water-reducing agent, sand/gravel ratio, age of maintenance	Compressive strength	/	R², MRE	32	2021	Han et al^[81]
Cement grouting material	AdaBoost	Water-cement ratio, expansion agent, water reducing agent, accelerating agent	Flexural, compressive strengths, fluidity, shrinkage rate	/	R²	16	2022	Ren et al^[82]
Steelmaking slag concrete	SVR, ANN, XGBoost, GPR	Cement, fine steel slag, coarse steel slag, fine/coarse aggregate; water, superplasticizer, pozzolanic admixtures, supplementary cementing materials, filler	Compressive strength	/	R², MAE, RMSE	406/ 146	2022	Penido et al^[83]
Cement-based grouting materials	SVR, DT, RF, AdaBoost, XGBoost, BO	Water-binder ratio, sand-binder ratio, silica fume, blast furnace slag, metakaolin, fly ash, hardening expansion agent, superplasticizer, plastic expansion agent, stabilizer, anti-foaming agent, early strength agent	Compressive strength, fluidity	/	R², RMSE	442/ 217	2023	Zhao et al^[84]
Aerogel-incorporated concrete	DT, SVR, MLP, RF, XGBoost, GBDT, LightGBM	Water-binder ratio, aerogel replacement rate, silica fume replacement rate, age, dry/saturated state	Compressive/ flexural strengths, thermal conductivity	/	R², MAE, RMSE, MAPE	660	2023	Han et al^[85]
Pervious concrete	SVR, BAS	Water-to-cement, coarse aggregate size, aggregate-to-cement ratio	Permeability coefficient, uniaxial compressive strength, splitting tensile strength	/	R, RMSE	90	2020	Zhang et al^[86]
Steel fibre reinforced concrete	SVR, FA	Cement, coarse/fine aggregate, superplasticiser, the volume fraction of steel fibre, the length, diameter of steel fibre	Uniaxial compressive strength, flexural strength	Uniaxial compressive strength, flexural strength, cost	R, MAE, RMSE, MAPE	299/ 269	2020	Huang et al^[87]
Strain-hardening cementitious composites	AdaBoost, SVM, XGBoost, NSGA-III, UNSGA-III, ANN, CART	Cement/fly ash/slag/rice husk/limestone/metakaolin/silica fume/sand/water -to-binder ratio, superplasticizer, fiber volume/length/diameter, fiber Young’s modulus	Compressive strength, tensile strength, ductility	Compressive strength, tensile strength, ductility, cost, CO₂ emission	R², ME, MAE, MSE, MAD	745	2021	Mahjoubi et al^[88]
Rubbercrete	M5 P, MGEP, GWO	cement, water, coarse/fine aggregate, silica fume, superplasticizer, waste coarse rubber, waste fine rubber, concrete age	Compressive strength	Compressive strength, cost, CO₂ emission, the amount waste rubber of consumption	R, MAE, RMSE	712	2021	Golafshani et al^[89]
Electrically conductive cementitious composites	SVR, BAS	Age, cement, graphite powder, ground granulated blast furnace slag, steel slag	Flexural strength, electrical conductivity	Flexural strength, electrical conductivity, Cost	R, MAPE, MAE, RMSE	252/ 336	2021	Sun et al^[90]
Graphite-based nanomaterials reinforced cementitious composites	KNN, SVR, RFR, XGBoost, BPNN, BO, NSGA-II	Cement, sand fitness modulus, sand, Graphite-based nanomaterials material/diameter/thickness/surface area of graphite-based nanomaterials, water, superplasticizer, ultrasonication, curing age, dry	Uniaxial compressive strength, electrical resistivity	Uniaxial compressive strength, electrical resistivity	R², MAE, MSE	379/416	2022	Dong et al^[4]
Green concrete	MLR, KNN, SVM, GP, RF, ANN, GBM, XGBM	Waste granite powder, waste marble powder, ground granulated blast furnace slag, fly ash, silica fume, cement, water, fine/coarse aggregates, superplasticizer, age	Compressive Strength	Compressive Strength, cost, global warming potential, acidification potential, fossil fuel depletion potential	MSE, MAPE, MBE, RMSE, MAE, R²	2644	2023	Shamsabadi et al^[91]
Notes: MR - Multiple regression, GBM - Gradient boosting machine, XGBM - Extreme gradient boosting machine, SSE – Sum of the squares error, MRE – Mean relative error, ME – Maximum error, MBE – Mean bias error.

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