{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T13:39:37Z","timestamp":1777729177780,"version":"3.51.4"},"reference-count":134,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,5]],"date-time":"2022-11-05T00:00:00Z","timestamp":1667606400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research, Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia","award":["GRANT 1864"],"award-info":[{"award-number":["GRANT 1864"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The conventional method for determining the Marshall Stability (MS) and Marshall Flow (MF) of asphalt pavements entails laborious, time-consuming, and expensive laboratory procedures. In order to develop new and advanced prediction models for MS and MF of asphalt pavements the current study applied three soft computing techniques: Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), and Multi Expression Programming (MEP). A comprehensive database of 343 data points was established for both MS and MF. The nine most significant and straightforwardly determinable geotechnical factors were chosen as the predictor variables. The root squared error (RSE), Nash\u2013Sutcliffe efficiency (NSE), mean absolute error (MAE), root mean square error (RMSE), relative root mean square error (RRMSE), coefficient of determination (R2), and correlation coefficient (R), were all used to evaluate the performance of models. The sensitivity analysis (SA) revealed the rising order of input significance of MS and MF. The results of parametric analysis (PA) were also found to be consistent with previous research findings. The findings of the comparison showed that ANN, ANFIS, and MEP are all reliable and effective methods for the estimation of MS and MF. The mathematical expressions derived from MEP represent the novelty of MEP and are relatively reliable and simple. Roverall values for MS and MF were in the order of MEP &gt; ANFIS &gt; ANN with all values over the permissible range of 0.80 for both MS and MF. Therefore, all the techniques showed higher performance, possessed high prediction and generalization capabilities, and assessed the relative significance of input parameters in the prediction of MS and MF. In terms of training, testing, and validation data sets and their closeness to the ideal fit, i.e., the slope of 1:1, MEP models outperformed the other two models. The findings of this study will contribute to the choice of an appropriate artificial intelligence strategy to quickly and precisely estimate the Marshall Parameters. Hence, the findings of this research study would assist in safer, faster, and more sustainable predictions of MS and MF, from the standpoint of time and resources required to perform the Marshall tests.<\/jats:p>","DOI":"10.3390\/sym14112324","type":"journal-article","created":{"date-parts":[[2022,11,7]],"date-time":"2022-11-07T03:10:46Z","timestamp":1667790646000},"page":"2324","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["Prediction of Marshall Stability and Marshall Flow of Asphalt Pavements Using Supervised Machine Learning Algorithms"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1333-5179","authenticated-orcid":false,"given":"Muhammad Aniq","family":"Gul","sequence":"first","affiliation":[{"name":"Department of Civil and Environmental Engineering, College of Engineering, King Faisal University (KFU), P.O. Box 380, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8329-5366","authenticated-orcid":false,"given":"Md Kamrul","family":"Islam","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, College of Engineering, King Faisal University (KFU), P.O. Box 380, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hamad Hassan","family":"Awan","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering (SCEE), H-12 Campus, National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Sohail","sequence":"additional","affiliation":[{"name":"School of Civil and Environmental Engineering (SCEE), H-12 Campus, National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7203-4814","authenticated-orcid":false,"given":"Abdulrahman Fahad","family":"Al Fuhaid","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, College of Engineering, King Faisal University (KFU), P.O. Box 380, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5069-0447","authenticated-orcid":false,"given":"Md","family":"Arifuzzaman","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, College of Engineering, King Faisal University (KFU), P.O. Box 380, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3621-9915","authenticated-orcid":false,"given":"Hisham Jahangir","family":"Qureshi","sequence":"additional","affiliation":[{"name":"Department of Civil and Environmental Engineering, College of Engineering, King Faisal University (KFU), P.O. Box 380, Al-Ahsa 31982, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Miani, M., Dunnhofer, M., Rondinella, F., Manthos, E., Valentin, J., Micheloni, C., and Baldo, N. (2021). Bituminous Mixtures Experimental Data Modeling Using a Hyperparameters-Optimized Machine Learning Approach. Appl. Sci., 11.","DOI":"10.3390\/app112411710"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1061\/(ASCE)0733-947X(2004)130:4(486)","article-title":"Verification and modeling of three-stage permanent deformation behavior of asphalt mixes","volume":"130","author":"Zhou","year":"2004","journal-title":"J. Transp. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"248","DOI":"10.1061\/(ASCE)MT.1943-5533.0000154","article-title":"Nonlinear genetic-based models for prediction of flow number of asphalt mixtures","volume":"23","author":"Gandomi","year":"2011","journal-title":"J. Mater. Civ. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1338","DOI":"10.1016\/j.conbuildmat.2010.09.010","article-title":"Formulation of flow number of asphalt mixes using a hybrid computational method","volume":"25","author":"Alavi","year":"2011","journal-title":"Constr. Build. Mater."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/j.conbuildmat.2014.09.110","article-title":"Mechanical performance of dry process fine crumb rubber asphalt mixtures placed on the Portuguese road network","volume":"73","author":"Dias","year":"2014","journal-title":"Constr. Build. Mater."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Liu, Q.T., and Wu, S.P. (2014). Effects of steel wool distribution on properties of porous asphalt concrete. Key Engineering Materials, Trans Tech Publications Ltd.","DOI":"10.4028\/www.scientific.net\/KEM.599.150"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Garc\u00eda, A., Norambuena-Contreras, J., Bueno, M., and Partl, M.N. (2014). Influence of Steel Wool Fibers on the Mechanical, Termal, and Healing Properties of Dense Asphalt Concrete, ASTM International.","DOI":"10.1520\/JTE20130197"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.conbuildmat.2014.10.035","article-title":"Overview of bituminous mixtures made with recycled concrete aggregates","volume":"74","year":"2015","journal-title":"Constr. Build. Mater."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"3493","DOI":"10.1016\/j.trpro.2016.05.315","article-title":"100% hot mix asphalt recycling: Challenges and benefits","volume":"14","author":"Zaumanis","year":"2016","journal-title":"Transp. Res. Procedia"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/14680629.2017.1329856","article-title":"Advances in pavement materials, design, characterisation, and simulation","volume":"18","author":"Wang","year":"2017","journal-title":"Road Mater. Pavement Des."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1061\/(ASCE)1532-3641(2002)2:3(305)","article-title":"3D finite element model for asphalt concrete response simulation","volume":"2","author":"Erkens","year":"2002","journal-title":"Int. J. Geomech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1163\/157361106776240761","article-title":"One-Dimensional Visco-Elastoplastic Constitutive Model for Asphalt Concrete","volume":"2","author":"Giunta","year":"2006","journal-title":"Multidiscip. Model. Mater. Struct."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"732","DOI":"10.1061\/(ASCE)EM.1943-7889.0000277","article-title":"Viscoelastoplastic continuum damage model for asphalt concrete in tension","volume":"137","author":"Underwood","year":"2011","journal-title":"J. Eng. Mech."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1007\/s12205-013-0352-7","article-title":"Viscoelastoplastic modeling of the behavior of hot mix asphalt in compression","volume":"17","author":"Yun","year":"2013","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"784","DOI":"10.1016\/j.conbuildmat.2015.07.054","article-title":"Computational analysis of the creep behaviour of bituminous mixtures","volume":"94","author":"Pasetto","year":"2015","journal-title":"Constr. Build. Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s11043-016-9305-0","article-title":"Anisotropy of bituminous mixture in the linear viscoelastic domain","volume":"20","year":"2016","journal-title":"Mech. Time Depend. Mater."},{"key":"ref_17","first-page":"390","article-title":"Numerical visco-elastoplastic constitutive modelization of creep recovery tests on hot mix asphalt","volume":"3","author":"Pasetto","year":"2016","journal-title":"J. Traffic Transp. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1016\/j.conbuildmat.2019.04.239","article-title":"Characterization and validation of the nonlinear viscoelastic-viscoplastic with hardening-relaxation constitutive relationship for asphalt mixtures","volume":"216","author":"Darabi","year":"2019","journal-title":"Constr. Build. Mater."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Anwar, M.K., Shah, S.A.R., Sadiq, A.N., Siddiq, M.U., Ahmad, H., Nawaz, S., Javead, A., Saeed, M.H., and Khan, A.R. (2020). Symmetric performance analysis for mechanical properties of sustainable asphalt materials under varying temperature conditions: An application of DT and NDT digital techniques. Symmetry, 12.","DOI":"10.3390\/sym12030433"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Arifuzzaman, M., Aniq Gul, M., Khan, K., and Hossain, S.Z. (2020). Application of artificial intelligence (ai) for sustainable highway and road system. Symmetry, 13.","DOI":"10.3390\/sym13010060"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF02823926","article-title":"Development of performance prediction models in flexible pavement using regression analysis method","volume":"10","author":"Kim","year":"2006","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"311","DOI":"10.3846\/13923730.2006.9636408","article-title":"Experimental research on the development of rutting in asphalt concrete pavements reinforced with geosynthetic materials","volume":"12","author":"Oginskas","year":"2006","journal-title":"J. Civ. Eng. Manag."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1080\/10298430701690462","article-title":"A re-visit to the development of fatigue and rutting equations used for asphalt pavement design","volume":"9","author":"Shukla","year":"2008","journal-title":"Int. J. Pavement Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1080\/10298436.2017.1380807","article-title":"Development of a nonlinear rutting model for asphalt concrete based on Weibull parameters","volume":"20","author":"Rahman","year":"2019","journal-title":"Int. J. Pavement Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1016\/j.gsf.2019.12.003","article-title":"State-of-the-art review of soft computing applications in underground excavations","volume":"11","author":"Zhang","year":"2020","journal-title":"Geosci. Front."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Dobrescu, C. (2020). Dynamic Response of the Newton Voigt\u2013Kelvin Modelled Linear Viscoelastic Systems at Harmonic Actions. Symmetry, 12.","DOI":"10.3390\/sym12091571"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1016\/j.jenvman.2019.03.057","article-title":"Evaluation of short-term strength development of cemented backfill with varying sulphide contents and the use of additives","volume":"239","author":"Li","year":"2019","journal-title":"J. Environ. Manag."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1007\/s10706-016-9990-0","article-title":"A comparative study of least square support vector machines and multiclass alternating decision trees for spatial prediction of rainfall-induced landslides in a tropical cyclones area","volume":"34","author":"Pham","year":"2016","journal-title":"Geotech. Geol. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1016\/j.advengsoft.2015.05.007","article-title":"Assessment of artificial neural network and genetic programming as predictive tools","volume":"88","author":"Gandomi","year":"2015","journal-title":"Adv. Eng. Softw."},{"key":"ref_30","first-page":"109","article-title":"Prediction of unconfined compressive strength of a stabilised expansive clay soil using ANN and regression analysis (SPSS)","volume":"7","author":"Sathyapriya","year":"2017","journal-title":"Asian J. Res. Soc. Sci. Humanit."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/j.cmpb.2018.05.029","article-title":"Estimating the refractive index of oxygenated and deoxygenated hemoglobin using genetic algorithm-support vector regression model","volume":"163","author":"Alade","year":"2018","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"121322","DOI":"10.1016\/j.jhazmat.2019.121322","article-title":"Prediction of mechanical properties of green concrete incorporating waste foundry sand based on gene expression programming","volume":"384","author":"Iqbal","year":"2020","journal-title":"J. Hazard. Mater."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Wu, Q., Wu, B., Hu, C., and Yan, X. (2021). Evolutionary Multilabel Classification Algorithm Based on Cultural Algorithm. Symmetry, 13.","DOI":"10.3390\/sym13020322"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Shahin, M.A. (2015). Genetic programming for modelling of geotechnical engineering systems. Handbook of Genetic Programming Applications, Springer.","DOI":"10.1007\/978-3-319-20883-1_2"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Li, L.-L., Liu, J.-Q., Zhao, W.-B., and Dong, L. (2021). Fault Diagnosis of High-Speed Brushless Permanent-Magnet DC Motor Based on Support Vector Machine Optimized by Modified Grey Wolf Optimization Algorithm. Symmetry, 13.","DOI":"10.3390\/sym13020163"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s00521-008-0208-0","article-title":"Prediction of compressive and tensile strength of Gaziantep basalts via neural networks and gene expression programming","volume":"18","year":"2009","journal-title":"Neural Comput. Appl."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1016\/j.jrmge.2013.05.006","article-title":"Estimating uniaxial compressive strength of rocks using genetic expression programming","volume":"5","author":"Ozbek","year":"2013","journal-title":"J. Rock Mech. Geotech. Eng."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"101635","DOI":"10.1016\/j.asej.2021.11.004","article-title":"Application of random forest for modelling of surface water salinity","volume":"13","author":"Khan","year":"2022","journal-title":"Ain Shams Eng. J."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1016\/B978-0-12-398296-4.00010-6","article-title":"10 Artificial neural networks in geotechnical engineering: Modeling and application issues","volume":"45","author":"Das","year":"2013","journal-title":"Metaheuristics Water Geotech Transp. Eng."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1016\/j.envsoft.2005.12.026","article-title":"A multi-model approach to analysis of environmental phenomena","volume":"22","author":"Giustolisi","year":"2007","journal-title":"Environ. Model. Softw."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"308239","DOI":"10.1155\/2009\/308239","article-title":"Recent advances and future challenges for artificial neural systems in geotechnical engineering applications","volume":"2009","author":"Shahin","year":"2009","journal-title":"Adv. Artif. Neural Syst."},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Mohammadzadeh, S.D., Kazemi, S.-F., Mosavi, A., Nasseralshariati, E., and Tah, J.H. (2019). Prediction of compression index of fine-grained soils using a gene expression programming model. Infrastructures, 4.","DOI":"10.3390\/infrastructures4020026"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"1863","DOI":"10.1007\/s10462-020-09894-7","article-title":"Genetic programming in civil engineering: Advent, applications and future trends","volume":"54","author":"Zhang","year":"2021","journal-title":"Artif. Intell. Rev."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Awan, H.H., Hussain, A., Javed, M.F., Qiu, Y., Alrowais, R., Mohamed, A.M., Fathi, D., and Alzahrani, A.M. (2022). Predicting Marshall Flow and Marshall Stability of Asphalt Pavements Using Multi Expression Programming. Buildings, 12.","DOI":"10.3390\/buildings12030314"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1007\/BF02478259","article-title":"A logical calculus of the ideas immanent in nervous activity","volume":"5","author":"McCulloch","year":"1943","journal-title":"Bull. Math. Biophys."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Zacarias-Morales, N., Pancardo, P., Hern\u00e1ndez-Nolasco, J.A., and Garcia-Constantino, M. (2021). Attention-inspired artificial neural networks for speech processing: A systematic review. Symmetry, 13.","DOI":"10.3390\/sym13020214"},{"key":"ref_47","first-page":"49","article-title":"Artificial neural network applications in geotechnical engineering","volume":"36","author":"Shahin","year":"2001","journal-title":"Aust. Geomech."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"523","DOI":"10.1016\/j.aej.2017.04.007","article-title":"Predicting the ingredients of self compacting concrete using artificial neural network","volume":"56","author":"Yaman","year":"2017","journal-title":"Alex. Eng. J."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1109\/21.256541","article-title":"ANFIS: Adaptive-network-based fuzzy inference system","volume":"23","author":"Jang","year":"1993","journal-title":"IEEE Trans. Syst. Man Cybern."},{"key":"ref_50","unstructured":"Sugeno, M. (1985). Industrial Applications of Fuzzy Control, Elsevier Science Inc."},{"key":"ref_51","first-page":"448","article-title":"Prediction of pavement roughness using a hybrid gene expression programming-neural network technique","volume":"3","author":"Mazari","year":"2016","journal-title":"J. Traffic Transp. Eng."},{"key":"ref_52","unstructured":"Oltean, M., and Dumitrescu, D. (2002). Multi expression programming. J. Genet. Program. Evolvable Mach., Available online: https:\/\/www.researchgate.net\/publication\/2918165_Multi_Expression_Programming."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.eswa.2007.06.006","article-title":"Prediction of compressive and tensile strength of limestone via genetic programming","volume":"35","year":"2008","journal-title":"Expert Syst. Appl."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s00366-009-0140-7","article-title":"Multi expression programming: A new approach to formulation of soil classification","volume":"26","author":"Alavi","year":"2010","journal-title":"Eng. Comput."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1108\/02644401211206043","article-title":"Formulation of secant and reloading soil deformation moduli using multi expression programming","volume":"29","author":"Alavi","year":"2012","journal-title":"Eng. Comput."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1884","DOI":"10.1016\/j.cageo.2008.10.015","article-title":"Genetic programming-based attenuation relationship: An application of recent earthquakes in turkey","volume":"35","author":"Cabalar","year":"2009","journal-title":"Comput. Geosci."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"4660","DOI":"10.1016\/j.eswa.2009.12.042","article-title":"Prediction of Marshall test results for polypropylene modified dense bituminous mixtures using neural networks","volume":"37","year":"2010","journal-title":"Expert Syst. Appl."},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Nguyen, H.-L., Le, T.-H., Pham, C.-T., Le, T.-T., Ho, L.S., Le, V.M., Pham, B.T., and Ly, H.-B. (2019). Development of hybrid artificial intelligence approaches and a support vector machine algorithm for predicting the marshall parameters of stone matrix asphalt. Appl. Sci., 9.","DOI":"10.3390\/app9153172"},{"key":"ref_59","first-page":"98","article-title":"Effect of asphalt content on the marshall stability of asphalt concrete using artificial neural networks","volume":"16","author":"Saffarzadeh","year":"2009","journal-title":"Sci. Iran."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"6025","DOI":"10.1016\/j.eswa.2010.11.018","article-title":"Artificial neural network based modelling of the Marshall Stability of asphalt concrete","volume":"38","author":"Ozgan","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Baldo, N., Manthos, E., and Miani, M. (2019). Stiffness modulus and marshall parameters of hot mix asphalts: Laboratory data modeling by artificial neural networks characterized by cross-validation. Appl. Sci., 9.","DOI":"10.3390\/app9173502"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"120756","DOI":"10.1016\/j.conbuildmat.2020.120756","article-title":"Marshall stability and flow analysis of asphalt concrete under progressive temperature conditions: An application of advance decision-making approach","volume":"262","author":"Shah","year":"2020","journal-title":"Constr. Build. Mater."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Morova, N., Sargin, \u015e., Terzi, S., Saltan, M., and Serin, S. (2012, January 2\u20134). Modeling Marshall Stability of light asphalt concretes fabricated using expanded clay aggregate with Artificial Neural Networks. Proceedings of the 2012 International Symposium on Innovations in Intelligent Systems and Applications, Trabzon, Turkey.","DOI":"10.1109\/INISTA.2012.6246946"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Morova, N., Eriskin, E., Terzi, S., Karahancer, S., Serin, S., Saltan, M., and Usta, P. (2017, January 3\u20135). Modelling Marshall Stability of fiber reinforced asphalt mixtures with ANFIS. Proceedings of the 2017 IEEE International Conference on INnovations in Intelligent SysTems and Applications (INISTA), Gdynia, Poland.","DOI":"10.1109\/INISTA.2017.8001152"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Serin, S., Morova, N., Sarg\u0131n, \u015e., Terzi, S., and Saltan, M. (2013, January 23\u201325). Modeling Marshall stability of lightweight asphalt concretes fabricated using expanded clay aggregate with anfis. Proceedings of the BCCCE\u2014International Balkans Conference on Challenges of Civil Engineering, Epoka, Albania.","DOI":"10.1109\/INISTA.2012.6246946"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"209","DOI":"10.7764\/rdlc.19.2.209-219","article-title":"Predicting Marshall stability and flow of bituminous mix containing waste fillers by the adaptive neuro-fuzzy inference system","volume":"19","author":"Mistry","year":"2020","journal-title":"Rev. Construcci\u00f3n"},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"111915","DOI":"10.1016\/j.jenvman.2020.111915","article-title":"Producing non-traditional flour from watermelon rind pomace: Artificial neural network (ANN) modeling of the drying process","volume":"281","author":"Fabani","year":"2021","journal-title":"J. Environ. Manag."},{"key":"ref_68","first-page":"243","article-title":"ANN and neuro-fuzzy modeling for shear strength characterization of soils","volume":"92","author":"Venkatesh","year":"2020","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"131364","DOI":"10.1016\/j.jclepro.2022.131364","article-title":"New prediction models for the compressive strength and dry-thermal conductivity of bio-composites using novel machine learning algorithms","volume":"350","author":"Khan","year":"2022","journal-title":"J. Clean. Prod."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"e06136","DOI":"10.1016\/j.heliyon.2021.e06136","article-title":"Evaluation of ANN and ANFIS modeling ability in the prediction of AISI 1050 steel machining performance","volume":"7","author":"Sada","year":"2021","journal-title":"Heliyon"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.jenvman.2015.02.034","article-title":"Statistical analysis and ANN modeling for predicting hydrological extremes under climate change scenarios: The example of a small Mediterranean agro-watershed","volume":"154","author":"Kourgialas","year":"2015","journal-title":"J. Environ. Manag."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"621163","DOI":"10.3389\/fmats.2021.621163","article-title":"Geopolymer concrete compressive strength via artificial neural network, adaptive neuro fuzzy interface system, and gene expression programming with K-fold cross validation","volume":"8","author":"Khan","year":"2021","journal-title":"Front. Mater."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"113977","DOI":"10.1016\/j.eswa.2020.113977","article-title":"New activation functions for single layer feedforward neural network","volume":"164","year":"2021","journal-title":"Expert Syst. Appl."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"721367","DOI":"10.1155\/2015\/721367","article-title":"Deep neural networks with multistate activation functions","volume":"2015","author":"Cai","year":"2015","journal-title":"Comput. Intell. Neurosci."},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Tang, C., Luktarhan, N., and Zhao, Y. (2020). SAAE-DNN: Deep Learning Method on Intrusion Detection. Symmetry, 12.","DOI":"10.3390\/sym12101695"},{"key":"ref_76","unstructured":"Ramachandran, P., Zoph, B., and Le, Q. (2017). Searching for Activation Functions. arXiv."},{"key":"ref_77","unstructured":"Xu, B., Huang, R., and Li, M. (2016). Revise saturated activation functions. arXiv."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1080\/03772063.2016.1240633","article-title":"New algebraic activation function for multi-layered feed forward neural networks","volume":"63","author":"Edla","year":"2017","journal-title":"IETE J. Res."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1016\/S0927-0256(01)00160-4","article-title":"Modelling the correlation between processing parameters and properties in titanium alloys using artificial neural network","volume":"21","author":"Malinov","year":"2001","journal-title":"Comput. Mater. Sci."},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1016\/j.icheatmasstransfer.2016.06.003","article-title":"Experimental evaluation and ANN modeling of thermal conductivity of graphene oxide nanoplatelets\/deionized water nanofluid","volume":"76","author":"Tahani","year":"2016","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_81","unstructured":"Tang, Y.-J., Zhang, Q.-Y., and Lin, W. (2010, January 23\u201325). Artificial neural network based spectrum sensing method for cognitive radio. Proceedings of the 2010 6th International Conference on Wireless Communications Networking and Mobile Computing (WiCOM), Shenzhen, China."},{"key":"ref_82","first-page":"39","article-title":"Comparison of artificial neural network transfer functions abilities to simulate extreme runoff data","volume":"33","author":"Dorofki","year":"2012","journal-title":"Int. Proc. Chem. Biol. Environ. Eng."},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"100358","DOI":"10.1016\/j.trgeo.2020.100358","article-title":"Using artificial neural network and genetics algorithm to estimate the resilient modulus for stabilized subgrade and propose new empirical formula","volume":"24","author":"Hanandeh","year":"2020","journal-title":"Transp. Geotech."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"242","DOI":"10.1108\/02644401111118132","article-title":"A robust data mining approach for formulation of geotechnical engineering systems","volume":"28","author":"Alavi","year":"2011","journal-title":"Eng. Comput."},{"key":"ref_85","doi-asserted-by":"crossref","unstructured":"Nosratabadi, S., Mosavi, A., Duan, P., Ghamisi, P., Filip, F., Band, S.S., Reuter, U., Gama, J., and Gandomi, A.H. (2020). Data science in economics: Comprehensive review of advanced machine learning and deep learning methods. Mathematics, 8.","DOI":"10.35542\/osf.io\/5dwrt"},{"key":"ref_86","doi-asserted-by":"crossref","unstructured":"Shahin, M.A. (2013). Artificial intelligence in geotechnical engineering: Applications, modeling aspects, and future directions. Metaheuristics in Water, Geotechnical and Transport Engineering, Elsevier.","DOI":"10.1016\/B978-0-12-398296-4.00008-8"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1016\/j.jenvman.2017.07.044","article-title":"Reviewing Bayesian Networks potentials for climate change impacts assessment and management: A multi-risk perspective","volume":"202","author":"Sperotto","year":"2017","journal-title":"J. Environ. Manag."},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Khan, K., Ashfaq, M., Iqbal, M., Khan, M.A., Amin, M.N., Shalabi, F.I., Faraz, M.I., and Jalal, F.E. (2022). Multi Expression Programming Model for Strength Prediction of Fly-Ash-Treated Alkali-Contaminated Soils. Materials, 15.","DOI":"10.3390\/ma15114025"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1007\/s42452-019-0883-8","article-title":"The effect of data size of ANFIS and MLR models on prediction of unconfined compression strength of clayey soils","volume":"1","author":"Akan","year":"2019","journal-title":"SN Appl. Sci."},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"117266","DOI":"10.1016\/j.conbuildmat.2019.117266","article-title":"Predicting the compressive strength of normal and High-Performance Concretes using ANN and ANFIS hybridized with Grey Wolf Optimizer","volume":"232","author":"Golafshani","year":"2020","journal-title":"Constr. Build. Mater."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"342","DOI":"10.1016\/j.jenvman.2018.11.047","article-title":"Adsorptive removal of Pb (II) by means of hydroxyapatite\/chitosan nanocomposite hybrid nanoadsorbent: ANFIS modeling and experimental study","volume":"232","author":"Sadeghizadeh","year":"2019","journal-title":"J. Environ. Manag."},{"key":"ref_92","doi-asserted-by":"crossref","unstructured":"Khan, K., Jalal, F.E., Khan, M.A., Salami, B.A., Amin, M.N., Alabdullah, A.A., Samiullah, Q., Arab, A.M.A., Faraz, M.I., and Iqbal, M. (2022). Prediction Models for Evaluating Resilient Modulus of Stabilized Aggregate Bases in Wet and Dry Alternating Environments: ANN and GEP Approaches. Materials, 15.","DOI":"10.3390\/ma15134386"},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1007\/s12665-018-7348-z","article-title":"Development of an intelligent system based on ANFIS model for predicting soil erosion","volume":"77","author":"Islam","year":"2018","journal-title":"Environ. Earth Sci."},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Khan, S., Ali Khan, M., Zafar, A., Javed, M.F., Aslam, F., Musarat, M.A., and Vatin, N.I. (2021). Predicting the ultimate axial capacity of uniaxially loaded cfst columns using multiphysics artificial intelligence. Materials, 15.","DOI":"10.3390\/ma15010039"},{"key":"ref_95","unstructured":"Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Longman Publishing Co., Inc."},{"key":"ref_96","unstructured":"Koza, J.R. (1992). Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press."},{"key":"ref_97","doi-asserted-by":"crossref","first-page":"6618407","DOI":"10.1155\/2021\/6618407","article-title":"Compressive strength of fly-ash-based geopolymer concrete by gene expression programming and random forest","volume":"2021","author":"Khan","year":"2021","journal-title":"Adv. Civ. Eng."},{"key":"ref_98","doi-asserted-by":"crossref","unstructured":"Javed, M.F., Farooq, F., Memon, S.A., Akbar, A., Khan, M.A., Aslam, F., Alyousef, R., Alabduljabbar, H., and Rehman, S.K.U. (2020). New prediction model for the ultimate axial capacity of concrete-filled steel tubes: An evolutionary approach. Crystals, 10.","DOI":"10.3390\/cryst10090741"},{"key":"ref_99","doi-asserted-by":"crossref","first-page":"1771","DOI":"10.1007\/s00521-012-1144-6","article-title":"Design equations for prediction of pressuremeter soil deformation moduli utilizing expression programming systems","volume":"23","author":"Alavi","year":"2013","journal-title":"Neural Comput. Appl."},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"105506","DOI":"10.1016\/j.enggeo.2020.105506","article-title":"Genetic programming model for estimating soil suction in shallow soil layers in the vicinity of a tree","volume":"268","author":"Cheng","year":"2020","journal-title":"Eng. Geol."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"105758","DOI":"10.1016\/j.enggeo.2020.105758","article-title":"High performance prediction of soil compaction parameters using multi expression programming","volume":"276","author":"Wang","year":"2020","journal-title":"Eng. Geol."},{"key":"ref_102","doi-asserted-by":"crossref","first-page":"3603","DOI":"10.1016\/j.asej.2021.03.018","article-title":"Sustainable use of fly-ash: Use of gene-expression programming (GEP) and multi-expression programming (MEP) for forecasting the compressive strength geopolymer concrete","volume":"12","author":"Chu","year":"2021","journal-title":"Ain Shams Eng. J."},{"key":"ref_103","doi-asserted-by":"crossref","unstructured":"Khan, M.A., Farooq, F., Javed, M.F., Zafar, A., Ostrowski, K.A., Aslam, F., Malazdrewicz, S., and Ma\u015blak, M. (2021). Simulation of depth of wear of eco-friendly concrete using machine learning based computational approaches. Materials, 15.","DOI":"10.3390\/ma15010058"},{"key":"ref_104","doi-asserted-by":"crossref","unstructured":"Aldrees, A., Khan, M.A., Tariq, M.A.U.R., Mustafa Mohamed, A., Ng, A.W.M., and Bakheit Taha, A.T. (2022). Multi-Expression Programming (MEP): Water Quality Assessment Using Water Quality Indices. Water, 14.","DOI":"10.3390\/w14060947"},{"key":"ref_105","doi-asserted-by":"crossref","first-page":"285","DOI":"10.25088\/ComplexSystems.14.4.285","article-title":"A comparison of several linear genetic programming techniques","volume":"14","author":"Oltean","year":"2003","journal-title":"Complex Syst."},{"key":"ref_106","first-page":"2167","article-title":"How to Rationally Compare the Performances of Different Machine Learning Models?","volume":"6","author":"Maeda","year":"2018","journal-title":"PeerJ Prepr."},{"key":"ref_107","doi-asserted-by":"crossref","first-page":"3368","DOI":"10.1007\/s11356-018-3749-5","article-title":"Leachate generation rate modeling using artificial intelligence algorithms aided by input optimization method for an MSW landfill","volume":"26","author":"Abunama","year":"2019","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_108","doi-asserted-by":"crossref","first-page":"13202","DOI":"10.1007\/s11356-020-11490-9","article-title":"Proposed formulation of surface water quality and modelling using gene expression, machine learning, and regression techniques","volume":"28","author":"Shah","year":"2021","journal-title":"Environ. Sci. Pollut. Res."},{"key":"ref_109","doi-asserted-by":"crossref","unstructured":"Papadimitriou, F. (2020). What is Spatial Complexity?. Spatial Complexity, Springer.","DOI":"10.1007\/978-3-030-59671-2"},{"key":"ref_110","doi-asserted-by":"crossref","unstructured":"Papadimitriou, F. (2020). The Probabilistic Basis of Spatial Complexity. Spatial Complexity, Springer.","DOI":"10.1007\/978-3-030-59671-2"},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1016\/j.ecoinf.2009.01.001","article-title":"Modelling spatial landscape complexity using the Levenshtein algorithm","volume":"4","author":"Papadimitriou","year":"2009","journal-title":"Ecol. Inform."},{"key":"ref_112","unstructured":"Rekha, M. (2022, June 11). MLmuse: Correlation and Collinearity\u2014How They Can Make or Break a Model. Correlation Analysis and Collinearity|Data Science|Multicollinearity|Clairvoyant Blog (clairvoyantsoft.com). Available online: https:\/\/blog.clairvoyantsoft.com\/correlation-and-collinearity-how-they-can-make-or-break-a-model-9135fbe6936a."},{"key":"ref_113","doi-asserted-by":"crossref","first-page":"39","DOI":"10.12691\/ajams-8-2-1","article-title":"Detecting multicollinearity in regression analysis","volume":"8","author":"Shrestha","year":"2020","journal-title":"Am. J. Appl. Math. Stat."},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"558","DOI":"10.4097\/kja.19087","article-title":"Multicollinearity and misleading statistical results","volume":"72","author":"Kim","year":"2019","journal-title":"Korean J. Anesthesiol."},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1016\/j.molliq.2018.12.144","article-title":"An intelligent approach for the modeling and experimental optimization of molecular hydrodesulfurization over AlMoCoBi catalyst","volume":"278","author":"Bagudu","year":"2019","journal-title":"J. Mol. Liq."},{"key":"ref_116","unstructured":"Alawi, M., and Rajab, M. (2005, January 11\u201313). Determination of optimum bitumen content and Marshall stability using neural networks for asphaltic concrete mixtures. Proceedings of the 9th WSEAS International Conference on Computers, World Scientific and Engineering Academy and Society (WSEAS), Athens, Greece."},{"key":"ref_117","first-page":"106","article-title":"Modeling marshall stability and flow for hot mix asphalt using artificial intelligence techniques","volume":"11","author":"Kandil","year":"2013","journal-title":"Nat. Sci."},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1016\/j.trpro.2016.05.333","article-title":"Marshall stability and flow of lime-modified asphalt concrete","volume":"14","author":"Ogundipe","year":"2016","journal-title":"Transp. Res. Procedia"},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/j.compgeo.2015.05.021","article-title":"Prediction of unconfined compressive strength of geopolymer stabilized clayey soil using artificial neural network","volume":"69","author":"Mozumder","year":"2015","journal-title":"Comput. Geotech."},{"key":"ref_120","doi-asserted-by":"crossref","first-page":"117920","DOI":"10.1016\/j.conbuildmat.2019.117920","article-title":"RETRACTED: Strength and dynamic elasticity modulus of rubberized concrete designed with ANFIS modeling and ultrasonic technique","volume":"240","author":"Jalal","year":"2020","journal-title":"Constr. Build. Mater."},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.solener.2019.02.060","article-title":"Predicting the specific heat capacity of alumina\/ethylene glycol nanofluids using support vector regression model optimized with Bayesian algorithm","volume":"183","author":"Alade","year":"2019","journal-title":"Sol. Energy"},{"key":"ref_122","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.nanoso.2018.12.001","article-title":"Modeling and prediction of the specific heat capacity of Al2O3\/water nanofluids using hybrid genetic algorithm\/support vector regression model","volume":"17","author":"Alade","year":"2019","journal-title":"Nano Struct. Nano Objects"},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.cageo.2012.07.001","article-title":"Modeling rainfall-runoff process using soft computing techniques","volume":"51","author":"Kisi","year":"2013","journal-title":"Comput. Geosci."},{"key":"ref_124","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1080\/17486025.2014.921333","article-title":"Use of evolutionary computing for modelling some complex problems in geotechnical engineering","volume":"10","author":"Shahin","year":"2015","journal-title":"Geomech. Geoengin."},{"key":"ref_125","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1007\/s00521-016-2320-x","article-title":"Estimation of soil dispersivity using soft computing approaches","volume":"28","author":"Emamgholizadeh","year":"2017","journal-title":"Neural Comput. Appl."},{"key":"ref_126","doi-asserted-by":"crossref","first-page":"101593","DOI":"10.1016\/j.asej.2021.09.020","article-title":"Compressive strength prediction of rice husk ash using multiphysics genetic expression programming","volume":"13","author":"Aslam","year":"2022","journal-title":"Ain Shams Eng. J."},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1139\/T07-052","article-title":"Artificial neural networks approach for swell pressure versus soil suction behaviour","volume":"44","author":"Erzin","year":"2007","journal-title":"Can. Geotech. J."},{"key":"ref_128","unstructured":"Frank, I.E., and Todeschini, R. (1994). The Data Analysis Handbook, Elsevier."},{"key":"ref_129","doi-asserted-by":"crossref","unstructured":"Dao, D.V., Ly, H.-B., Trinh, S.H., Le, T.-T., and Pham, B.T. (2019). Artificial intelligence approaches for prediction of compressive strength of geopolymer concrete. Materials, 12.","DOI":"10.3390\/ma12060983"},{"key":"ref_130","doi-asserted-by":"crossref","first-page":"302","DOI":"10.1002\/qsar.200710043","article-title":"On some aspects of variable selection for partial least squares regression models","volume":"27","author":"Roy","year":"2008","journal-title":"QSAR Comb. Sci."},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"146524","DOI":"10.1016\/j.scitotenv.2021.146524","article-title":"Sustainable utilization of foundry waste: Forecasting mechanical properties of foundry sand based concrete using multi-expression programming","volume":"780","author":"Iqbal","year":"2021","journal-title":"Sci. Total Environ."},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"111456","DOI":"10.1016\/j.jenvman.2020.111456","article-title":"Surrogate based Global Sensitivity Analysis of ADM1-based Anaerobic Digestion Model","volume":"282","author":"Trucchia","year":"2021","journal-title":"J. Environ. Manag."},{"key":"ref_133","doi-asserted-by":"crossref","unstructured":"Derbel, M., Hachicha, W., and Aljuaid, A.M. (2021). Sensitivity Analysis of the Optimal Inventory-Pooling Strategies According to Multivariate Demand Dependence. Symmetry, 13.","DOI":"10.3390\/sym13020328"},{"key":"ref_134","doi-asserted-by":"crossref","unstructured":"Khan, M.A., Zafar, A., Akbar, A., Javed, M.F., and Mosavi, A. (2021). Application of Gene Expression Programming (GEP) for the prediction of compressive strength of geopolymer concrete. Materials, 14.","DOI":"10.31219\/osf.io\/bwm4k"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2324\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:11:05Z","timestamp":1760145065000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/11\/2324"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,5]]},"references-count":134,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["sym14112324"],"URL":"https:\/\/doi.org\/10.3390\/sym14112324","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,5]]}}}