Modeling of compressive strength of HPC mixes using a combined algorithm of genetic programming and orthogonal least squares

  • Mousavi, S.M. (Department of Civil Engineering, Sharif University of Technology) ;
  • Gandomi, A.H. (Department of Civil Engineering, Tafresh University) ;
  • Alavi, A.H. (School of Civil Engineering, Iran University of Science and Technology) ;
  • Vesalimahmood, M. (School of Mathematics, Iran University of Science and Technology)
  • Received : 2009.12.02
  • Accepted : 2010.06.17
  • Published : 2010.09.30


In this study, a hybrid search algorithm combining genetic programming with orthogonal least squares (GP/OLS) is utilized to generate prediction models for compressive strength of high performance concrete (HPC) mixes. The GP/OLS models are developed based on a comprehensive database containing 1133 experimental test results obtained from previously published papers. A multiple least squares regression (LSR) analysis is performed to benchmark the GP/OLS models. A subsequent parametric study is carried out to verify the validity of the models. The results indicate that the proposed models are effectively capable of evaluating the compressive strength of HPC mixes. The derived formulas are very simple, straightforward and provide an analysis tool accessible to practicing engineers.



  1. Alavi, A.H., Gandomi, A.H., Sahab, M.G. and Gandomi, M. (2010), "Multi expression programming: a new approach to formulation of soil classification", Eng. Comput., 26(2), 111-118.
  2. Banzhaf, W., Nordin, P., Keller, R. and Francone, F. (1998), Genetic Programming - An Introduction. on the Automatic Evolution of Computer Programs and Its Application, San Francisco: (The Morgan Kaufmann Series in Artificial Intelligence), Morgan Kaufmann Publishers, Heidelberg.
  3. Basma, A.A., Barakat, S. and Oraimi, S.A. (1999), "Prediction of cement degree of hydration using artificial neural networks", Mater. J., 96(2), 166-172.
  4. Billings, S., Korenberg, M. and Chen, S. (1988), "Identification of nonlinear outputaffine systems using an orthogonal least-squares algorithm", Int. J. Syst. Sci., 19(8), 1559-1568.
  5. Cao, H., Yu, J., Kang, L. and Chen, Y. (1999), "The kinetic evolutionary modelling of complex systems of chemical reactions", Comput. Chem. Eng., 23(1), 143-151.
  6. Chen, L. (2003), "A study of applying macroevolutionary genetic programming to concrete strength estimation", Expert. Syst. Appl., 17(4), 290-294.
  7. Chen, L. and Wang, T. (2010), "Modeling strength of high-performance concrete using an improved grammatical evolution combined with macro genetic algorithm", J. Comput. Civil Eng., 24(3), 281-288.
  8. Chen, S., Billings, S. and Luo, W. (1989), "Orthogonal least squares methods and their application to non-linear system identification", Int. J. Control, 50(5), 1873-1896.
  9. Domone, P. and Soutsos, M. (1994), "An approach to the proportioning of high-strength concrete mixes", Concrete Int., 16(10), 26-31.
  10. Gandomi, A.H., Alavi, A.H. and Sahab, M.G. (2010a), "New formulation for compressive strength of CFRP Confined concrete cylinders using linear genetic programming", Mater. Struct., 43(7), 963-983.
  11. Gandomi, A.H., Alavi, A.H., Mirzahosseini, M.R. and Moghadas Nejad, F. (2010b), "Nonlinear genetic-based models for prediction of flow number of asphalt mixtures", J. Mater. Civil Eng. (ASCE), DOI: 10.1061/(ASCE)MT.1943-5533.0000154 (in press).
  12. Gandomi, A.H. and Alavi, A.H. (2010c), "Hybridizing genetic programming with orthogonal least squares for modeling of soil liquefaction", Computational Collective Intelligence and Hybrid Systems Concepts and Applications, IGI Global Publishing (in press).
  13. Gandomi, A.H., Alavi, A.H. and Arjmandi, P. (2010a), "Genetic programming and orthogonal least squares: a hybrid approach to modeling of compressive strength of CFRP-confined concrete cylinders" J. Mech. Mater. Struct. (in press).
  14. Gandomi, A.H., Alavi, A.H., Sahab, M.G. and Arjmandi, P. (2010b), "Formulation of elastic modulus of concrete using linear genetic programming", J. Mech. Sci. Tech., 24(6), 1011-1017.
  15. Goodspeed, C.H., Vanikar, S. and Cook, R. (1996), "High-performance concrete (HPC) defined for highway structures", Concrete Int., 18(2), 62-67.
  16. Jepsen, M.T. (2002), "Predicting concrete durability by using artificial neural network", Published in a Special NCR-publication, ID. 5268.
  17. Ji, T., Lin, T. and Lin, X. (2006), "A concrete mix proportion design algorithm based on artificial neural networks", Cement Concrete Res., 36(7), 1399-1408.
  18. Johari, A., Habibagahi, G. and Ghahramani, A. (2006), "Prediction of soil-water characteristic curve using genetic programming", J. Geotech. Geoenviron. Eng., 132(5), 661-665.
  19. Kasperkiewicz, J., Racz, J. and Dubrawski, A. (1995), "HPC strength prediction using artificial neural network", J. Comput. Civil Eng., 9(4), 279-284.
  20. Koza, J.R. (1992), Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, Cambridge.
  21. Madar, J., Abonyi, J. and Szeifert, F. (2005a), "Genetic programming for the identification of nonlinear inputoutput models", Indian Eng. Chem. Res., 44(9), 3178-3186.
  22. Madar, J., Abonyi, J. and Szeifert, F. (2005b), "Genetic programming for the identification of nonlinear inputoutput models", White Paper.
  23. Madar, J., Abonyi, J. and Szeifert, F. (2004), "Genetic programming for system identification", Proceedings of the Intelligent Systems Design and Applications (ISDA 2004) Conference, Budapest, Hungary.
  24. Maravall, A. and Gomez, V. (2004), EViews Software, Ver. 5, Quantitative Micro Software, LLC, Irvine CA.
  25. Pearson, R.K. (2003), "Selecting nonlinear model structures for computer control", J. Process Contr., 13(1), 1-26.
  26. Raghu Prasad, B.K., Eskandari, H. and Venkatarama Reddy, B.V. (2009), "Prediction of compressive strength of SCC and HPC with high volume fly ash using ANN", Constr. Build. Mater., 23(1), 117-128.
  27. Rajasekaran, S. and Amalraj, R. (2002), "Predictions of design parameters in civil engineering problems using SLNN with a single hidden RBF neuron", Comput. Struct., 80(31), 2495-2505.
  28. Rajasekaran, S. and Lavanya, S. (2007), "Hybridization of genetic algorithm with immune system for optimization problems in structural engineering", Struct. Multidiscip. O., 34(5), 415-429.
  29. Rajasekaran, S., Suresh, D. and Pai, G.A.V. (2002), "Application of sequential learning neural networks to civil engineering modeling problems", Eng. Comput., 18, 138-147.
  30. Reeves, C.R. (1997), "Genetic algorithm for the operations research", Inf. J. Comput., 9, 231-250.
  31. Ryan, T.P. (1997), Modern Regression Methods, Wiley, New York.
  32. Salajegheh, E. and Ali, H. (2005), "Optimum design of structures against earthquake by wavelet neural network and filter banks", Earthq. Eng. Struct. D., 34(1), 67-82.
  33. Yeh, I. and Lien, L. (2009), "Knowledge discovery of concrete material using genetic operation trees", Expert. Syst. Appl., 36, 5807-5812.
  34. Yeh, I.C. (1998), "Modeling of strength of high-performance concrete using artificial neural networks", Cement Concrete Res., 28(12), 1797-808.
  35. Yeh, I.C. (1998), "Modeling of strength of high-performance concrete using artificial neural networks", Cement Concrete Res., 28(12), 1797-1808.
  36. Yeh, I.C. (2006a), "Exploring concrete slump model using artificial neural networks", J. Comput. Civil Eng., 20(3), 217-221.
  37. Yeh, I.C. (2006b), "Analysis of strength of concrete using design of experiments and neural networks", J. Mater. Civil Eng., 18(4), 597-604.
  38. Yeh, I.C. (2006c), "Generalization of strength versus water-cementations ratio relationship to age", Cement Concrete Res., 36(10), 1865-1873.
  39. Yeh, I.C. (2007), "Modeling slump flow of concrete using second-order regressions and artificial neural networks", Cement Concrete Comp., 29, 474-480.

Cited by

  1. Predictive modeling of concrete compressive strength based on cement strength class vol.11, pp.6, 2013,
  2. Virtual teaching and learning environments: Automatic evaluation with symbolic regression vol.31, pp.4, 2016,
  3. Robust attenuation relations for peak time-domain parameters of strong ground motions vol.67, pp.1, 2012,
  4. New prediction models for concrete ultimate strength under true-triaxial stress states: An evolutionary approach vol.110, 2017,
  5. A data mining approach to compressive strength of CFRP-confined concrete cylinders vol.36, pp.6, 2010,
  6. A new predictive model for compressive strength of HPC using gene expression programming vol.45, pp.1, 2012,
  7. A new multi-gene genetic programming approach to nonlinear system modeling. Part I: materials and structural engineering problems vol.21, pp.1, 2012,
  8. Prediction of compressive strength of concrete using multiple regression model vol.45, pp.6, 2010,
  9. Prediction of concrete compressive strength using non-destructive test results vol.21, pp.4, 2010,
  10. New machine learning prediction models for compressive strength of concrete modified with glass cullet vol.36, pp.3, 2019,
  11. Non-Tuned Machine Learning Approach for Predicting the Compressive Strength of High-Performance Concrete vol.13, pp.5, 2010,
  12. Applications of Gene Expression Programming and Regression Techniques for Estimating Compressive Strength of Bagasse Ash based Concrete vol.10, pp.9, 2010,
  13. Machine Learning-Based Modeling with Optimization Algorithm for Predicting Mechanical Properties of Sustainable Concrete vol.2021, pp.None, 2010,
  14. Performance Evaluation of Soft Computing for Modeling the Strength Properties of Waste Substitute Green Concrete vol.13, pp.5, 2010,
  15. Multigene Expression Programming Based Forecasting the Hardened Properties of Sustainable Bagasse Ash Concrete vol.14, pp.19, 2021,