Optimisation of Multiple Response Processes Using Different Modeling Techniques
Abstract
Purpose: This article aims to compare the impact on process optimisation with multiple responses of two different mathematical modelling methods: Ordinary Least Squares Method (OLS) and Symbolic Regression Method (SR).
Methodology/Approach: Data from the literature were selected from the design of experiments for a process with multiple responses. Using these data, models were obtained that represented each response as a function of independent variables using the OLS and SR techniques. Then, the Desirability method was applied together with the Generalized Reduced Gradient (GRG) in order to obtain the process adjustment that would lead to the optimisation of the responses.
Findings: The findings illustrate that the SR modelling technique yields models with superior predictive capabilities when contrasted with the OLS technique. Throughout the optimisation process, it becomes evident that the adjustments in the process diverge, even though the desirability function's value exhibits negligible variation.
Research Limitation/implication: This research considered only an SR algorithm and a process with two dependent variables and two independent variables.
Originality/Value of paper: No works were found in the literature that reported the use of the Age-Layered Population Structure (ALPS) algorithm in modelling processes that contain multiple responses. Furthermore, no comparison of this method with the OLS method was available.
Category: Research paper.
References
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Hornby, G.S. (2009) 'A Steady-State version of the Age-Layered Population Structure EA', in Springer eBooks, pp. 87–102. https://doi.org/10.1007/978-1-4419-1626-6_6.
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Kommenda, M., Burlacu, B., Kronberger, G. and Affenzeller, M. (2019), 'Parameter identification for symbolic regression using nonlinear least squares', Genetic Programming and Evolvable Machines, 21(3), pp. 471–501. doi: 10.1007/s10710-019-09371-3
Koza, J. R. (1992), Genetic Programming On the Programming of Computers by Means of Natural Selection, MIT Press.
Kuriger, G. W. and Grant, F. H. (2011), 'A lexicographic nelder–mead simulation optimisation method to solve multi-criteria problems', Computers & Industrial Engineering, 60(4), pp. 555–565. doi: 10.1016/j.cie.2010.12.013
Liu, H., Lin, H., Jiang, X., Mao, X., Liu, Q. and Li, B. (2019), 'Estimation of mass matrix in machine tool's weak components research by using symbolic regression', Computers & Industrial Engineering, 127, pp. 998–1011. doi: 10.1016/j.cie.2018.11.033
Mohammadzadeh S, D., Bolouri Bazaz, J., Vafaee Jani Yazd, S. H., and Alavi, A. H. (2016), 'Deriving an intelligent model for soil compression index utilising multi-gene genetic programming', Environmental Earth Sciences, 75(3), pp. 1-11. doi: 10.1007/s12665-015-4889-2.
Montgomery, D. C. (2017), Design and Analysis of Experiments, Wiley & Sons, Incorporated.
Niu, B., Wu, D. and Mu, Z. (2020), 'Product diversification decisions considering quality reliability and self-competition in a global supply chain', INFOR: Information Systems and Operational Research, 58(4), pp. 680–702. doi: 10.1080/03155986.2020.1746556
Ojha, V. K., Abraham, A. and Snášel, V. (2017), 'Metaheuristic design of feedforward neural networks: A review of two decades of research', Engineering Applications of Artificial Intelligence, 60, pp. 97–116. doi: 10.1016/j.engappai.2017.01.013
Ota, R.R. and Ojha, A.K. (2015) 'A comparative study on optimisation techniques for solving multi-objective geometric programming problems,' Applied Mathematical Sciences [Preprint]. https://doi.org/10.12988/ams.2015.4121029.
Patnaik, A. K., Agarwal, L. A., Panda, M. and Bhuyan, P. K. (2018), 'Entry capacity modelling of signalised roundabouts under heterogeneous traffic conditions', Transportation Letters, 12(2), pp. 100–112. doi: 10.1080/19427867.2018.1533160
Sandoval, C., Cuate, O., González, L. C., Trujillo, L. and Schütze, O. (2022), 'Towards fast approximations for the hypervolume indicator for multi-objective optimisation problems by genetic programming', Applied Soft Computing, 125, pp. 109103. doi: https://doi.org/10.1016/j.asoc.2022.109103
Searson, D. P. (2015), GPTIPS 2: An open-source software platform for symbolic data mining, in 'Handbook of Genetic Programming Applications', Springer International Publishing, pp. 551–573.
Shin, S. and Cho, B. R. (2005), 'Bias-specified robust design optimisation and its analytical solutions', Computers & Industrial Engineering, 48(1), pp. 129–140. doi: 10.1016/j.cie.2004.07.011
Soori, M., Arezoo, B. and Dastres, R. (2023), 'Internet of things for smart factories in industry 4.0, a review', Internet of Things and Cyber-Physical Systems, 3, pp. 192–204. doi: 10.1016/j.iotcps.2023.04.006
Tesfamichael, S. G. and Ndlovu, A. (2018), 'Utility of ASTER and landsat for quantifying hydrochemical concentrations in abandoned gold mining', Science of The Total Environment, 618, pp. 1560–1571. doi: 10.1016/j.scitotenv.2017.09.335
Toledo, C. F. M., da Silva Arantes, M., Hossomi, M. Y. B. and Almada-Lobo, B. (2016), 'Mathematical programming-based approaches for multi-facility glass container production planning', Computers & Operations Research, 74, pp. 92–107. doi: 10.1016/j.cor.2016.02.019
Ward, E. J. (2008), 'A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools', Ecological Modelling, 211(1-2), pp. 1–10. doi: 10.1016/j.ecolmodel.2007.10.030
Yang, I.-T. (2005), 'Simulation-based estimation for correlated cost elements', International Journal of Project Management, 23(4), pp. 275–282. doi: 10.1016/j.ijproman.2004.12.002
Zhu, H., You, X. and Liu, S. (2019), 'Multiple ant colony optimisation based on pearson correlation coefficient', IEEE Access, 7, pp. 61628–61638. doi: 10.1109/ACCESS.2019.2915673
Akpa, O. M. and Unuabonah, E. I. (2011), 'Small-sample corrected Akaike information criterion: An appropriate statistical tool for ranking of adsorption isotherm models', Desalination, 272(1-3), pp. 20–26. doi: 10.1016/j.desal.2010.12.057
Ascencio, J. J., Philippini, R. R., Gomes, F. M., Pereira, F. M., da Silva, S. S., Kumar, V. and Chandel, A. K. (2021), 'Comparative highly efficient production of β-glucan by lasiodiplodia theobromae CCT 3966 and its multiscale characterisation', Fermentation, 7(3), pp. 108. doi: 10.3390/fermentation7030108
Bertrand, J. W. M. and Fransoo, J. C. (2002), 'Operations management research methodologies using quantitative modeling', International Journal of Operations & Production Management, 22(2), pp. 241–264. doi: 10.1108/01443570210414338
Bezerra, M. A., Ferreira, S. L. C., Novaes, C. G., dos Santos, A. M. P., Valasques, G. S., da Mata Cerqueira, U. M. F. and dos Santos Alves, J. P. (2019), 'Simultaneous optimisation of multiple responses and its application in analytical chemistry – a review', Talanta, 194, pp. 941–959. doi: 10.1016/j.talanta.2018.10.088
Burnham, K. P., Anderson, D. R. and Huyvaert, K. P. (2010), 'AIC model selection and multimodel inference in behavioral ecology: some background, observations, and comparisons', Behavioral Ecology and Sociobiology, 65(1), pp. 23–35. doi: 10.1007/s00265-010-1029-6
Dehuri, S. and Cho, S.-B. (2009), 'Multi-criterion Pareto based particle swarm optimised polynomial neural network for classification: A review and state-of-the-art', Computer Science Review, 3(1), pp. 19–40. doi: 10.1016/j.cosrev.2008.11.002
Derringer, G. and Suich, R. (1980), 'Simultaneous optimisation of several response variables', Journal of Quality Technology, 12(4), pp. 214–219. doi: 10.1080/00224065.1980.11980968
Frank, A. G., Dalenogare, L. S. and Ayala, N. F. (2019), 'Industry 4.0 technologies: Implementation patterns in manufacturing companies', International Journal of Production Economics, 210, pp. 15–26. doi: 10.1016/j.ijpe.2019.01.004
Fukuda, I. M., Pinto, C. F. F., dos Santos Moreira, C., Saviano, A. M. and Lourenço, F. R. (2018), 'Design of experiments (DoE) applied to pharmaceutical and analytical quality by design (QbD)', Brazilian Journal of Pharmaceutical Sciences, 54(spe). doi: 10.1590/s2175-97902018000001006
Gleeson, J. P., Murphy, T. B., O'Brien, J. D., Friel, N., Bargary, N. and O'Sullivan, D. J. P. (2021), 'Calibrating COVID-19 susceptible-exposed-infected-removed models with timevarying effective contact rates', Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 380(2214). doi: 10.1098/rsta.2021.0120
Gomes, F. M., Pereira, F. M., Marins, F. A. S. and Silva, M. B. (2017), 'Comparative study between the generalised reduced gradient and genetic algorithm in multiple response optimisation', Revista Produção Online, 17(2), pp. 592–619. doi: 10.14488/1676-1901.v17i2.2566
Gomes, F. M., Pereira, F. M., Marins, F. A. S. and Silva, M. B. (2019-a), 'Comparative study between different methods of agglutination in multiple response optimisation', Revista Gestão da Produção Operações e Sistemas, 14(1), pp. 95–113. doi: 10.15675/gepros.v14i1.2080
Gomes, F. M., Pereira, F. M., Silva, A. F. and Silva, M. B. (2019), 'Multiple response optimisation: Analysis of genetic programming for symbolic regression and assessment of desirability functions', Knowledge-Based Systems, 179, pp. 21–33. doi: 10.1016/j.knosys.2019.05.002
Gopalan, S. P., Kawamura, A., Takasaki, T., Amaguchi, H. and Azhikodan, G. (2018), 'An effective storage function model for an urban watershed in terms of hydrograph reproducibility and Akaike information criterion', Journal of Hydrology, 563, pp. 657–668. doi: 10.1016/j.jhydrol.2018.06.035
Halsey, L. G. (2019), 'The reign of the p-value is over: what alternative analyses could we employ to fill the power vacuum?', Biology Letters, 15(5), pp. 20190174. doi: 10.1098/rsbl.2019.0174
Han, Y., Ma, Y., Ouyang, L., Wang, J. and Tu, Y. (2019), 'Integrated multiresponse parameter and tolerance design with model parameter uncertainty', Quality and Reliability Engineering International, 36(1), pp. 414–433. doi: 10.1002/qre.2589
Hornby, G.S. (2006) 'ALPS the age-layered population structure for reducing the problem of premature convergence,' ‘Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation’ [Preprint]. https://doi.org/10.1145/1143997.1144142
Hornby, G.S. (2009) 'A Steady-State version of the Age-Layered Population Structure EA', in Springer eBooks, pp. 87–102. https://doi.org/10.1007/978-1-4419-1626-6_6.
Ingdal, M., Johnsen, R. and Harrington, D. A. (2019), 'The akaike information criterion in weighted regression of immittance data', Electrochimica Acta, 317, pp. 648–653. doi: 10.1016/j.electacta.2019.06.030
Keeler, B. L., Polasky, S., Brauman, K. A., Johnson, K. A., Finlay, J. C., O'Neill, A., Kovacs, K. and Dalzell, B. (2012), 'Linking water quality and well-being for improved assessment and valuation of ecosystem services', Proceedings of the National Academy of Sciences, 109(45), pp. 18619–18624. doi: 10.1073/pnas.1215991109
Kommenda, M., Burlacu, B., Kronberger, G. and Affenzeller, M. (2019), 'Parameter identification for symbolic regression using nonlinear least squares', Genetic Programming and Evolvable Machines, 21(3), pp. 471–501. doi: 10.1007/s10710-019-09371-3
Koza, J. R. (1992), Genetic Programming On the Programming of Computers by Means of Natural Selection, MIT Press.
Kuriger, G. W. and Grant, F. H. (2011), 'A lexicographic nelder–mead simulation optimisation method to solve multi-criteria problems', Computers & Industrial Engineering, 60(4), pp. 555–565. doi: 10.1016/j.cie.2010.12.013
Liu, H., Lin, H., Jiang, X., Mao, X., Liu, Q. and Li, B. (2019), 'Estimation of mass matrix in machine tool's weak components research by using symbolic regression', Computers & Industrial Engineering, 127, pp. 998–1011. doi: 10.1016/j.cie.2018.11.033
Mohammadzadeh S, D., Bolouri Bazaz, J., Vafaee Jani Yazd, S. H., and Alavi, A. H. (2016), 'Deriving an intelligent model for soil compression index utilising multi-gene genetic programming', Environmental Earth Sciences, 75(3), pp. 1-11. doi: 10.1007/s12665-015-4889-2.
Montgomery, D. C. (2017), Design and Analysis of Experiments, Wiley & Sons, Incorporated.
Niu, B., Wu, D. and Mu, Z. (2020), 'Product diversification decisions considering quality reliability and self-competition in a global supply chain', INFOR: Information Systems and Operational Research, 58(4), pp. 680–702. doi: 10.1080/03155986.2020.1746556
Ojha, V. K., Abraham, A. and Snášel, V. (2017), 'Metaheuristic design of feedforward neural networks: A review of two decades of research', Engineering Applications of Artificial Intelligence, 60, pp. 97–116. doi: 10.1016/j.engappai.2017.01.013
Ota, R.R. and Ojha, A.K. (2015) 'A comparative study on optimisation techniques for solving multi-objective geometric programming problems,' Applied Mathematical Sciences [Preprint]. https://doi.org/10.12988/ams.2015.4121029.
Patnaik, A. K., Agarwal, L. A., Panda, M. and Bhuyan, P. K. (2018), 'Entry capacity modelling of signalised roundabouts under heterogeneous traffic conditions', Transportation Letters, 12(2), pp. 100–112. doi: 10.1080/19427867.2018.1533160
Sandoval, C., Cuate, O., González, L. C., Trujillo, L. and Schütze, O. (2022), 'Towards fast approximations for the hypervolume indicator for multi-objective optimisation problems by genetic programming', Applied Soft Computing, 125, pp. 109103. doi: https://doi.org/10.1016/j.asoc.2022.109103
Searson, D. P. (2015), GPTIPS 2: An open-source software platform for symbolic data mining, in 'Handbook of Genetic Programming Applications', Springer International Publishing, pp. 551–573.
Shin, S. and Cho, B. R. (2005), 'Bias-specified robust design optimisation and its analytical solutions', Computers & Industrial Engineering, 48(1), pp. 129–140. doi: 10.1016/j.cie.2004.07.011
Soori, M., Arezoo, B. and Dastres, R. (2023), 'Internet of things for smart factories in industry 4.0, a review', Internet of Things and Cyber-Physical Systems, 3, pp. 192–204. doi: 10.1016/j.iotcps.2023.04.006
Tesfamichael, S. G. and Ndlovu, A. (2018), 'Utility of ASTER and landsat for quantifying hydrochemical concentrations in abandoned gold mining', Science of The Total Environment, 618, pp. 1560–1571. doi: 10.1016/j.scitotenv.2017.09.335
Toledo, C. F. M., da Silva Arantes, M., Hossomi, M. Y. B. and Almada-Lobo, B. (2016), 'Mathematical programming-based approaches for multi-facility glass container production planning', Computers & Operations Research, 74, pp. 92–107. doi: 10.1016/j.cor.2016.02.019
Ward, E. J. (2008), 'A review and comparison of four commonly used Bayesian and maximum likelihood model selection tools', Ecological Modelling, 211(1-2), pp. 1–10. doi: 10.1016/j.ecolmodel.2007.10.030
Yang, I.-T. (2005), 'Simulation-based estimation for correlated cost elements', International Journal of Project Management, 23(4), pp. 275–282. doi: 10.1016/j.ijproman.2004.12.002
Zhu, H., You, X. and Liu, S. (2019), 'Multiple ant colony optimisation based on pearson correlation coefficient', IEEE Access, 7, pp. 61628–61638. doi: 10.1109/ACCESS.2019.2915673
Authors
Maciel Gomes, F., Imamura, C. S., de Souza Sampaio, N. A., Monteiro Pereira, F., de Souza Andrade, H., & Borges Silva, M. (2023). Optimisation of Multiple Response Processes Using Different Modeling Techniques. Quality Innovation Prosperity, 27(3), 18–36. https://doi.org/10.12776/qip.v27i3.1899
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