ACS Publications. Most Trusted. Most Cited. Most Read
My Activity

Figure 1Loading Img

Genetic Programming for the Identification of Nonlinear Input−Output Models

View Author Information
Department of Process Engineering, University of Veszprém, P.O. Box 158, Veszprém 8201, Hungary
Cite this: Ind. Eng. Chem. Res. 2005, 44, 9, 3178–3186
Publication Date (Web):March 18, 2005
Copyright © 2005 American Chemical Society

    Article Views





    Other access options


    Linear-in-parameters models are quite widespread in process engineering, e.g., nonlinear additive autoregressive models, polynomial ARMA models, etc. This paper proposes a new method for the structure selection of these models. The method uses genetic programming to generate nonlinear input−output models of dynamical systems that are represented in a tree structure. The main idea of the paper is to apply the orthogonal least squares (OLS) algorithm to estimate the contribution of the branches of the tree to the accuracy of the model. This method results in more robust and interpretable models. The proposed approach has been implemented as a freely available MATLAB Toolbox, The simulation results show that the developed tool provides an efficient and fast method for determining the order and structure for nonlinear input−output models.

    Read this article

    To access this article, please review the available access options below.

    Get instant access

    Purchase Access

    Read this article for 48 hours. Check out below using your ACS ID or as a guest.


    Access through Your Institution

    You may have access to this article through your institution.

    Your institution does not have access to this content. You can change your affiliated institution below.


     To whom correspondence should be addressed. Tel.:  +36 88 622793. Fax:  +36 88 624171. E-mail:  [email protected].

    Cited By

    This article is cited by 140 publications.

    1. Kevin C. Seavey, Adam T. Jones and Arthur K. Kordon, Guido F. Smits and . Hybrid Genetic Programming−First-Principles Approach To Process and Product Modeling. Industrial & Engineering Chemistry Research 2010, 49 (5) , 2273-2285.
    2. Raghuraj K. Rao, Kyaw Tun and S. Lakshminarayanan. Genetic Programming Based Variable Interaction Models for Classification of Process and Biological Systems. Industrial & Engineering Chemistry Research 2009, 48 (10) , 4899-4907.
    3. Tristen Brown, Magdy Alanani, Ahmed Elshaer, Anas Issa. Formulation of Separation Distance to Mitigate Wind-Induced Pounding of Tall Buildings. Buildings 2024, 14 (2) , 479.
    4. Dhruv Khandelwal, Maarten Schoukens, Roland Tóth. Automated multi-objective system identification using grammar-based genetic programming. Automatica 2023, 154 , 111017.
    5. Zitong Wen, Lu Zhuo, Qin Wang, Jiao Wang, Ying Liu, Sichan Du, Ahmed Abdelhalim, Dawei Han. Data Fusion for Estimating High-Resolution Urban Heatwave Air Temperature. Remote Sensing 2023, 15 (16) , 3921.
    6. Gebrail Bekdaş, Celal Cakiroglu, Sanghun Kim, Zong Woo Geem. Optimal Dimensions of Post-Tensioned Concrete Cylindrical Walls Using Harmony Search and Ensemble Learning with SHAP. Sustainability 2023, 15 (10) , 7890.
    7. Daniele Pinton, Alberto Canestrelli, Sheng Zhuo Xu. Managing dyke retreat: Importance of century‐scale channel network evolution on storm surge modification over salt marshes under rising sea levels. Earth Surface Processes and Landforms 2023, 48 (4) , 830-849.
    8. Davut Ari, Baris Baykant Alagoz. DEHypGpOls: a genetic programming with evolutionary hyperparameter optimization and its application for stock market trend prediction. Soft Computing 2023, 27 (5) , 2553-2574.
    9. Davut Ari, Baris Baykant Alagoz. A differential evolutionary chromosomal gene expression programming technique for electronic nose applications. Applied Soft Computing 2023, 136 , 110093.
    10. Jingli Ren, Haiyan Wang. Ordinary differential equations. 2023, 129-172.
    11. . Bibliography. 2023, 229-240.
    12. Daniele Pinton, Alberto Canestrelli, Robert Moon, Benjamin Wilkinson. Estimating Ground Elevation in Coastal Dunes from High-Resolution UAV-LIDAR Point Clouds and Photogrammetry. Remote Sensing 2023, 15 (1) , 226.
    13. Maciej Ławryńczuk. Input convex neural networks in nonlinear predictive control: A multi-model approach. Neurocomputing 2022, 513 , 273-293.
    14. Behzad Bahrami Joo, Ali Jamali, Nader Nariman-zadeh. Multi-objective robust design approach usage in integration of bond graph and genetic programming. International Journal of Modelling and Simulation 2022, 42 (5) , 743-759.
    15. Khouloud Gaaloul, Claudio Menghi, Shiva Nejati, Lionel C. Briand, Yago Isasi Parache. Combining Genetic Programming and Model Checking to Generate Environment Assumptions. IEEE Transactions on Software Engineering 2022, 48 (9) , 3664-3685.
    16. Davut Ari, Baris Baykant Alagoz. An effective integrated genetic programming and neural network model for electronic nose calibration of air pollution monitoring application. Neural Computing and Applications 2022, 34 (15) , 12633-12652.
    17. M. W. Gray, D. Pinton, A. Canestrelli, N. Dix, P. Marcum, D. Kimbro, R. Grizzle. Beyond Residence Time: Quantifying Factors that Drive the Spatially Explicit Filtration Services of an Abundant Native Oyster Population. Estuaries and Coasts 2022, 45 (5) , 1343-1360.
    18. Huijing Yu, Xinjie Wang, Feifei Shen, Jian Long, Wenli Du. Novel automatic model construction method for the rapid characterization of petroleum properties from near-infrared spectroscopy. Fuel 2022, 316 , 123101.
    19. Baris Baykant Alagoz, Ozlem Imik Simsek, Davut Ari, Aleksei Tepljakov, Eduard Petlenkov, Hossein Alimohammadi. An Evolutionary Field Theorem: Evolutionary Field Optimization in Training of Power-Weighted Multiplicative Neurons for Nitrogen Oxides-Sensitive Electronic Nose Applications. Sensors 2022, 22 (10) , 3836.
    20. Mirosław Wojnicki, Jan Lubaś, Mateusz Gawroński, Sławomir Szuflita, Jerzy Kuśnierczyk, Marcin Warnecki. An Experimental Investigation of WAG Injection in a Carbonate Reservoir and Prediction of the Recovery Factor Using Genetic Programming. Energies 2022, 15 (6) , 2127.
    21. Selami Beyhan. Fuzzy Emulated Symbolic Regression for Modelling and Control of Markov Jump Systems With Unknown Transition Rates. IEEE Transactions on Circuits and Systems II: Express Briefs 2022, 69 (3) , 1352-1356.
    22. Dhruv Khandelwal. Preliminaries—Evolutionary Algorithms. 2022, 55-71.
    23. Tom Kusznir, Jaroslaw Smoczek. Multi-Gene Genetic Programming-Based Identification of a Dynamic Prediction Model of an Overhead Traveling Crane. Sensors 2022, 22 (1) , 339.
    24. Gyula Dorgo, Tibor Kulcsar, Janos Abonyi. Genetic programming-based symbolic regression for goal-oriented dimension reduction. Chemical Engineering Science 2021, 244 , 116769.
    25. Daniele Pinton, Alberto Canestrelli, Benjamin Wilkinson, Peter Ifju, Andrew Ortega. Estimating Ground Elevation and Vegetation Characteristics in Coastal Salt Marshes Using UAV-Based LiDAR and Digital Aerial Photogrammetry. Remote Sensing 2021, 13 (22) , 4506.
    26. Hatice Citakoglu. Comparison of multiple learning artificial intelligence models for estimation of long-term monthly temperatures in Turkey. Arabian Journal of Geosciences 2021, 14 (20)
    27. Malik Braik. A Hybrid Multi-gene Genetic Programming with Capuchin Search Algorithm for Modeling a Nonlinear Challenge Problem: Modeling Industrial Winding Process, Case Study. Neural Processing Letters 2021, 53 (4) , 2873-2916.
    28. Davut Ari, Baris Baykant Alagoz. A Genetic Programming Based Pollutant Concentration Predictor Design for Urban Pollution Monitoring Based on Multi-Sensor Electronic Nose. 2021, 168-172.
    29. Davut Ari, Baris Baykant Alagoz. Modeling Daily Financial Market Data by Using Tree-Based Genetic Programming. 2021, 382-386.
    30. Yu Yang, Xin Zhao, Min Huang, Xin Wang, Qibing Zhu. Multispectral image based germination detection of potato by using supervised multiple threshold segmentation model and Canny edge detector. Computers and Electronics in Agriculture 2021, 182 , 106041.
    31. Ge He, Tao Luo, Yagu Dang, Li Zhou, Yiyang Dai, Xu Ji. Combined mechanistic and genetic programming approach to modeling pilot NBR production: influence of feed compositions on rubber Mooney viscosity. RSC Advances 2021, 11 (2) , 817-829.
    32. Mohammed el Amin Bourouis, Abdeldjalil Zadjaoui, Abdelkader Djedid. Contribution of two artificial intelligence techniques in predicting the secondary compression index of fine-grained soils. Innovative Infrastructure Solutions 2020, 5 (3)
    33. Daniele Pinton, Alberto Canestrelli, Benjamin Wilkinson, Peter Ifju, Andrew Ortega. A new algorithm for estimating ground elevation and vegetation characteristics in coastal salt marshes from high‐resolution UAV‐based LiDAR point clouds. Earth Surface Processes and Landforms 2020, 45 (14) , 3687-3701.
    34. Kit Yan Chan, C.K. Kwong, Gül E. Kremer. Predicting customer satisfaction based on online reviews and hybrid ensemble genetic programming algorithms. Engineering Applications of Artificial Intelligence 2020, 95 , 103902.
    35. Rebecca Goebel, Tobias Glaser, Mirko Skiborowski. Machine-based learning of predictive models in organic solvent nanofiltration: Solute rejection in pure and mixed solvents. Separation and Purification Technology 2020, 248 , 117046.
    36. Seung-Seop Jin. Compositional kernel learning using tree-based genetic programming for Gaussian process regression. Structural and Multidisciplinary Optimization 2020, 62 (3) , 1313-1351.
    37. Dhruv Khandelwal, Maarten Schoukens, Roland Tóth. A Tree Adjoining Grammar representation for models of stochastic dynamical systems. Automatica 2020, 119 , 109099.
    38. . Genetic Programing for Modeling of Industrial Reactors. 2020, 259-282.
    39. Yufang Wang, Haiyan Wang, Shuhua Zhang. Prediction of daily PM2.5 concentration in China using data-driven ordinary differential equations. Applied Mathematics and Computation 2020, 375 , 125088.
    40. Faizal Hafiz, Akshya Swain, Eduardo Mendes. Multi-objective evolutionary framework for non-linear system identification: A comprehensive investigation. Neurocomputing 2020, 386 , 257-280.
    41. Rebecca Goebel, Mirko Skiborowski. Machine-based learning of predictive models in organic solvent nanofiltration: Pure and mixed solvent flux. Separation and Purification Technology 2020, 237 , 116363.
    42. Kuai Xu, Feng Wang, Haiyan Wang, Yufang Wang, Ying Zhang. Mitigating the Impact of Data Sampling on Social Media Analysis and Mining. IEEE Transactions on Computational Social Systems 2020, 7 (2) , 546-555.
    43. Akhil Garg, Su Shaosen, Liang Gao, Xiongbin Peng, Prashant Baredar. Aging model development based on multidisciplinary parameters for lithium‐ion batteries. International Journal of Energy Research 2020, 44 (4) , 2801-2818.
    44. Helon Vicente Hultmann Ayala, Didace Habineza, Micky Rakotondrabe, Leandro dos Santos Coelho. Nonlinear black-box system identification through coevolutionary algorithms and radial basis function artificial neural networks. Applied Soft Computing 2020, 87 , 105990.
    45. Mahsa Shokri Varniab, Chih-Cheng Hung, Vahid Khalilzad Sharghi. Data mining and image analysis using genetic programming. ACM SIGAPP Applied Computing Review 2020, 19 (4) , 40-49.
    46. Hamid Khayyam, Ali Jamali, Hirad Assimi, Reza N. Jazar. Genetic Programming Approaches in Design and Optimization of Mechanical Engineering Applications. 2020, 367-402.
    47. Alex Kummer, Tamás Varga, János Abonyi. Genetic programming-based development of thermal runaway criteria. Computers & Chemical Engineering 2019, 131 , 106582.
    48. Faizal Hafiz, Akshya Swain, Eduardo M.A.M. Mendes. Two-Dimensional (2D) particle swarms for structure selection of nonlinear systems. Neurocomputing 2019, 367 , 114-129.
    49. Saad M. Darwish, Tamer A. Shendi, Ahmed Younes. Chemometrics approach for the prediction of chemical compounds’ toxicity degree based on quantum inspired optimization with applications in drug discovery. Chemometrics and Intelligent Laboratory Systems 2019, 193 , 103826.
    50. Mahsa Shokri Varniab, Chih-Cheng Hung, Vahid Khalilzad Sharghi. Classification of multiclass datasets using genetic programming. 2019, 76-82.
    51. Zhengfeng Zhang, Yan Zhou. A Linear-in-Parameters Genetic Programming Method for Chemical Kinetics System Identification. 2019, 169-173.
    52. Saad M. Darwish, Tamer A. Shendi, Ahmed Younes. Quantum‐inspired genetic programming model with application to predict toxicity degree for chemical compounds. Expert Systems 2019, 36 (4)
    53. Yu Zhang, Miguel Martinez-Garcia, Jose R. Serrano-Cruz, Anthony Latimer. Multi-region System Modelling by using Genetic Programming to Extract Rule Consequent Functions in a TSK Fuzzy System. 2019, 987-992.
    54. Dhruv Khandelwal, Maarten Schoukens, Roland Toth. Data-driven Modelling of Dynamical Systems Using Tree Adjoining Grammar and Genetic Programming. 2019, 2673-2680.
    55. Dhruv Khandelwal, Maarten Schoukens, Roland Toth. Grammar-based Representation and Identification of Dynamical Systems. 2019, 1318-1323.
    56. Abbasali TaghaviGhalesari, Carlos M. Chang-Albitres. Sustainable Design of Rigid Pavements Using a Hybrid GP and OLS Method. 2019, 317-325.
    57. Jose Roberto Ayala Solares, Hua-Liang Wei, Stephen A. Billings. A novel logistic-NARX model as a classifier for dynamic binary classification. Neural Computing and Applications 2019, 31 (1) , 11-25.
    58. Baoshan Ma, Xiangtian Jiao, Fanyu Meng, Fengping Xu, Yao Geng, Rubin Gao, Wei Wang, Yeqing Sun. Identification of Gene Regulatory Networks by Integrating Genetic Programming With Particle Filtering. IEEE Access 2019, 7 , 113760-113770.
    59. Lei Jiang, Ding Liu, Jing Zhang, Weifeng Duan. Nonlinear System Identification of CZ Silicon Crystal Growth between Pulling Speed and Diameter. 2018, 1686-1691.
    60. J. Wen, M. Raison, S. Achiche. Using a cost function based on kinematics and electromyographic data to quantify muscle forces. Journal of Biomechanics 2018, 80 , 151-158.
    61. Daniel Feseker, Mats Kinell, Matthias Neef. Experimental Study on Pressure Losses in Circular Orifices With Inlet Cross Flow. Journal of Turbomachinery 2018, 140 (7)
    62. Yong Yan, Lijuan Wang, Tao Wang, Xue Wang, Yonghui Hu, Quansheng Duan. Application of soft computing techniques to multiphase flow measurement: A review. Flow Measurement and Instrumentation 2018, 60 , 30-43.
    63. Rebecca Goebel, Tobias Glaser, Ilka Niederkleine, Mirko Skiborowski. Towards predictive models for organic solvent nanofiltration. 2018, 115-120.
    64. Yuhao Huang, Liang Gao, Zhang Yi, Kang Tai, P. Kalita, Paweena Prapainainar, Akhil Garg. An application of evolutionary system identification algorithm in modelling of energy production system. Measurement 2018, 114 , 122-131.
    65. Kit Yan Chan, Hak-Keung Lam, Cedric Ka Fai Yiu, Tharam S. Dillon. A Flexible Fuzzy Regression Method for Addressing Nonlinear Uncertainty on Aesthetic Quality Assessments. IEEE Transactions on Systems, Man, and Cybernetics: Systems 2017, 47 (8) , 2363-2377.
    66. Lijuan Wang, Jinyu Liu, Yong Yan, Xue Wang, Tao Wang. Gas-Liquid Two-Phase Flow Measurement Using Coriolis Flowmeters Incorporating Artificial Neural Network, Support Vector Machine, and Genetic Programming Algorithms. IEEE Transactions on Instrumentation and Measurement 2017, 66 (5) , 852-868.
    67. A. Ramírez-Hernández, A. Aparicio-Saguilán, G. Reynoso-Meza, J. Carrillo-Ahumada. Multi-objective optimization of process conditions in the manufacturing of banana (Musa paradisiaca L.) starch/natural rubber films. Carbohydrate Polymers 2017, 157 , 1125-1133.
    68. A. Garg, K. Tai, B. N. Panda. System Identification: Survey on Modeling Methods and Models. 2017, 607-615.
    69. Abdelfeteh Sadok, Rachid Zentar, Nor-Eddine Abriak. Genetic programming for granular compactness modelling. European Journal of Environmental and Civil Engineering 2016, 20 (10) , 1249-1261.
    70. Jose Roberto Ayala Solares, Hua-Liang Wei, R. J. Boynton, Simon N. Walker, Stephen A. Billings. Modeling and prediction of global magnetic disturbance in near-Earth space: A case study for K p index using NARX models. Space Weather 2016, 14 (10) , 899-916.
    71. Changik Han, Jiyang Wang, Mingguo Zheng, Ende Wang, Jianming Xia, GwangSu Li, Sunchol Choe. New variogram modeling method using MGGP and SVR. Earth Science Informatics 2016, 9 (2) , 197-213.
    72. Kit Yan Chan, Sai Ho Ling. A forward selection based fuzzy regression for new product development that correlates engineering characteristics with consumer preferences. Journal of Intelligent & Fuzzy Systems 2016, 30 (3) , 1869-1880.
    73. Helon Vicente Hultmann Ayala, Leandro dos Santos Coelho. Cascaded evolutionary algorithm for nonlinear system identification based on correlation functions and radial basis functions neural networks. Mechanical Systems and Signal Processing 2016, 68-69 , 378-393.
    74. Ke-Lin Du, M. N. S. Swamy. Genetic Programming. 2016, 71-82.
    75. Suhas B. Ghugare, Sanjeev S. Tambe. Development of genetic programming based softsensor model for styrene polymerization process and its application in model based control. 2016, 238-244.
    76. J. R. Ayala Solares, Hua-Liang Wei. Nonlinear model structure detection and parameter estimation using a novel bagging method based on distance correlation metric. Nonlinear Dynamics 2015, 82 (1-2) , 201-215.
    77. Ali Khazaei, Akbar Shojaei. Modeling and optimization of friction materials based on genetic programming and experimental frictional data. Journal of Reinforced Plastics and Composites 2015, 34 (7) , 581-590.
    78. Dazi Li, Qianwen Xie, Qibing Jin. Quasi-Linear Extreme Learning Machine Model Based Nonlinear System Identification. 2015, 121-130.
    79. Saeed K. Babanajad. Application of Genetic Programming for Uniaxial and Multiaxial Modeling of Concrete. 2015, 399-430.
    80. Renu Vyas, Purva Goel, Sanjeev S. Tambe. Genetic Programming Applications in Chemical Sciences and Engineering. 2015, 99-140.
    81. D. Moreno-Salinas, E. Besada-Portas, J.A. López-Orozco, D. Chaos, J.M. de la Cruz, J. Aranda. Symbolic Regression for Marine Vehicles Identification∗∗The authors wish to thank the “Ministerio de Economáıa y Com-petitividad” of Spain for support under projects DPI2013-46665-C2- 1-R and DPI2013-46665-C2-2-R. The authors wish to thank also the National University Distance Education (UNED) for support unde project 2014-012-UNED-PROY.. IFAC-PapersOnLine 2015, 48 (16) , 210-216.
    82. Helon Vicente Hultmann Ayala, Luciano F. da Cruz, Roberto Z. Freire, Leandro dos Santos Coelho. Cascaded free search differential evolution applied to nonlinear system identification based on correlation functions and neural networks. 2014, 1-7.
    83. Leandro dos Santos Coelho, Teodoro Cardoso Bora, Carlos Eduardo Klein. A genetic programming approach based on Lévy flight applied to nonlinear identification of a poppet valve. Applied Mathematical Modelling 2014, 38 (5-6) , 1729-1736.
    84. Akhil Garg, Ankit Garg, K. Tai. A multi-gene genetic programming model for estimating stress-dependent soil water retention curves. Computational Geosciences 2014, 18 (1) , 45-56.
    85. Tibor Kulcsar, Gabor Bereznai, Gabor Sarossy, Robert Auer, Janos Abonyi. Visualisation of High Dimensional Data by Use of Genetic Programming: Application to On-line Infrared Spectroscopy Based Process Monitoring. 2014, 223-231.
    86. . Bibliography. 2013, 115-125.
    87. Brijesh Kumar Giri, Jussi Hakanen, Kaisa Miettinen, Nirupam Chakraborti. Genetic programming through bi-objective genetic algorithms with a study of a simulated moving bed process involving multiple objectives. Applied Soft Computing 2013, 13 (5) , 2613-2623.
    88. Kit Yan Chan, C. K. Kwong. Modeling of epoxy dispensing process using a hybrid fuzzy regression approach. The International Journal of Advanced Manufacturing Technology 2013, 65 (1-4) , 589-600.
    89. Christian L. Dunis, Jason Laws, Andreas Karathanasopoulos. GP algorithm versus hybrid and mixed neural networks. The European Journal of Finance 2013, 19 (3) , 180-205.
    90. Seyyed Mohammad Mousavi, Amir Hossein Alavi, Ali Mollahasani, Amir Hossein Gandomi, Milad Arab Esmaeili. Formulation of soil angle of shearing resistance using a hybrid GP and OLS method. Engineering with Computers 2013, 29 (1) , 37-53.
    91. G. Hardier, C. Roos, C. Seren. Creating Sparse Rational Approximations for Linear Fractional Representations using Genetic Programming. IFAC Proceedings Volumes 2013, 46 (20) , 393-398.
    92. Robson S. Magalhães, Cristiano H. O. Fontes, Luiz A. L. de Almeida, Marcelo Embiruçu. Identification of Artificial Neural Network Models for Three-Dimensional Simulation of a Vibration-Acoustic Dynamic System. Open Journal of Acoustics 2013, 03 (01) , 14-24.
    93. H. Nayyeri, K. Khorasani. Modeling aircraft jet engine and system identification by using Genetic Programming. 2012, 1-4.
    94. Kit Yan Chan, Tharam S. Dillon, C. K. Kwong. Handling uncertainties in modelling manufacturing processes with hybrid swarm intelligence. International Journal of Production Research 2012, 50 (6) , 1714-1725.
    95. M. Rouhani, R. Abdoli. A comparison of different feature extraction methods for diagnosis of valvular heart diseases using PCG signals. Journal of Medical Engineering & Technology 2012, 36 (1) , 42-49.
    96. Kit Yan Chan, C. K. Kwong, Tharam S. Dillon. Integrated Product Design. 2012, 1-24.
    97. Kit Yan Chan, C. K. Kwong, Tharam S. Dillon. A Nonlinear Fuzzy Regression for Developing Manufacturing Process Models. 2012, 199-212.
    98. Kit Yan Chan, C. K. Kwong, Tharam S. Dillon. Development of Product Design Models Using Classical Evolutionary Programming. 2012, 95-109.
    99. Kit Yan Chan, C. K. Kwong, Tharam S. Dillon. Development of Product Design Models Using Fuzzy Regression Based Genetic Programming. 2012, 111-128.
    100. Amir Hossein Gandomi, Amir Hossein Alavi. Multi-stage genetic programming: A new strategy to nonlinear system modeling. Information Sciences 2011, 181 (23) , 5227-5239.
    Load all citations

    Pair your accounts.

    Export articles to Mendeley

    Get article recommendations from ACS based on references in your Mendeley library.

    Pair your accounts.

    Export articles to Mendeley

    Get article recommendations from ACS based on references in your Mendeley library.

    You’ve supercharged your research process with ACS and Mendeley!

    STEP 1:
    Click to create an ACS ID

    Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

    Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

    Please note: If you switch to a different device, you may be asked to login again with only your ACS ID.

    Your Mendeley pairing has expired. Please reconnect