{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,18]],"date-time":"2026-04-18T05:20:25Z","timestamp":1776489625431,"version":"3.51.2"},"reference-count":61,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2020,8,1]],"date-time":"2020-08-01T00:00:00Z","timestamp":1596240000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2020,8,1]],"date-time":"2020-08-01T00:00:00Z","timestamp":1596240000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T00:00:00Z","timestamp":1621296000000},"content-version":"am","delay-in-days":290,"URL":"http:\/\/www.elsevier.com\/open-access\/userlicense\/1.0\/"}],"funder":[{"DOI":"10.13039\/100014539","name":"Energy Institute, Texas A and M University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100014539","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100004378","name":"Shell","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100004378","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers & Chemical Engineering"],"published-print":{"date-parts":[[2020,8]]},"DOI":"10.1016\/j.compchemeng.2020.106902","type":"journal-article","created":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T22:57:44Z","timestamp":1589756264000},"page":"106902","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":37,"special_numbering":"C","title":["HY-POP: Hyperparameter optimization of machine learning models through parametric programming"],"prefix":"10.1016","volume":"139","author":[{"given":"William W.","family":"Tso","sequence":"first","affiliation":[]},{"given":"Baris","family":"Burnak","sequence":"additional","affiliation":[]},{"given":"Efstratios N.","family":"Pistikopoulos","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.compchemeng.2020.106902_bib0001","series-title":"Learning From Data","volume":"4","author":"Abu-Mostafa","year":"2012"},{"issue":"1","key":"10.1016\/j.compchemeng.2020.106902_bib0002","doi-asserted-by":"crossref","first-page":"10178","DOI":"10.1016\/j.ifacol.2017.08.1766","article-title":"A multiparametric mixed-integer bi-level optimization strategy for supply chain planning under demand uncertainty","volume":"50","author":"Avraamidou","year":"2017","journal-title":"IFAC-PapersOnLine"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0003","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.compchemeng.2018.07.007","article-title":"B-POP: Bi-level parametric optimization toolbox","volume":"122","author":"Avraamidou","year":"2019","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0004","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.compchemeng.2019.01.021","article-title":"A multi-parametric optimization approach for bilevel mixed-integer linear and quadratic programming problems","volume":"125","author":"Avraamidou","year":"2019","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0005","unstructured":"Barratt, S., Sharma, R., 2018. Optimizing for generalization in machine learning with cross-validation gradients. arXiv:1805.07072."},{"issue":"1","key":"10.1016\/j.compchemeng.2020.106902_bib0006","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0005-1098(01)00174-1","article-title":"The explicit linear quadratic regulator for constrained systems","volume":"38","author":"Bemporad","year":"2002","journal-title":"Automatica"},{"issue":"8","key":"10.1016\/j.compchemeng.2020.106902_bib0007","doi-asserted-by":"crossref","first-page":"1889","DOI":"10.1162\/089976600300015187","article-title":"Gradient-based optimization of hyperparameters","volume":"12","author":"Bengio","year":"2000","journal-title":"Neural Comput."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0008","series-title":"The 2006 IEEE International Joint Conference on Neural Network Proceedings","first-page":"1922","article-title":"Model selection via bilevel optimization","author":"Bennett","year":"2006"},{"issue":"Feb","key":"10.1016\/j.compchemeng.2020.106902_bib0009","first-page":"281","article-title":"Random search for hyper-parameter optimization","volume":"13","author":"Bergstra","year":"2012","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0010","series-title":"Advances in Neural Information Processing Systems","first-page":"2546","article-title":"Algorithms for hyper-parameter optimization","author":"Bergstra","year":"2011"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0011","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1016\/j.compchemeng.2018.02.017","article-title":"Optimal design of energy systems using constrained grey-box multi-objective optimization","volume":"116","author":"Beykal","year":"2018","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0012","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/j.compchemeng.2018.01.005","article-title":"Global optimization of grey-box computational systems using surrogate functions and application to highly constrained oil-field operations","volume":"114","author":"Beykal","year":"2018","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0013","series-title":"Proceedings of the Fifth Annual Workshop on Computational Learning Theory","first-page":"144","article-title":"A training algorithm for optimal margin classifiers","author":"Boser","year":"1992"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0014","series-title":"ICML","first-page":"82","article-title":"Feature selection via concave minimization and support vector machines.","volume":"98","author":"Bradley","year":"1998"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0015","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.compchemeng.2019.03.004","article-title":"Integrated process design, scheduling, and control using multiparametric programming","volume":"125","author":"Burnak","year":"2019","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0016","unstructured":"Claesen, M., De Moor, B., 2015. Hyperparameter search in machine learning. arXiv:1502.02127."},{"issue":"1","key":"10.1016\/j.compchemeng.2020.106902_bib0017","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1007\/s10479-007-0176-2","article-title":"An overview of bilevel optimization","volume":"153","author":"Colson","year":"2007","journal-title":"Ann. Oper. Res."},{"issue":"7","key":"10.1016\/j.compchemeng.2020.106902_bib0018","doi-asserted-by":"crossref","first-page":"e16498","DOI":"10.1002\/aic.16498","article-title":"Sustainable ammonia production through process synthesis and global optimization","volume":"65","author":"Demirhan","year":"2019","journal-title":"AlChE J."},{"issue":"11","key":"10.1016\/j.compchemeng.2020.106902_bib0019","doi-asserted-by":"crossref","first-page":"4827","DOI":"10.1002\/aic.15825","article-title":"Process design and control optimization: asimultaneous approach by multi-parametric programming","volume":"63","author":"Diangelakis","year":"2017","journal-title":"AlChE J."},{"issue":"20","key":"10.1016\/j.compchemeng.2020.106902_bib0020","doi-asserted-by":"crossref","first-page":"400","DOI":"10.1016\/j.ifacol.2018.11.066","article-title":"On multiparametric\/explicit NMPC for quadratically constrained problems","volume":"51","author":"Diangelakis","year":"2018","journal-title":"IFAC-PapersOnLine"},{"issue":"4\/5","key":"10.1016\/j.compchemeng.2020.106902_sbref0019","doi-asserted-by":"crossref","DOI":"10.1147\/JRD.2017.2709578","article-title":"An effective algorithm for hyperparameter optimization of neural networks","volume":"61","author":"Diaz","year":"2017","journal-title":"IBM Journal of Research and Development"},{"issue":"12","key":"10.1016\/j.compchemeng.2020.106902_bib0022","doi-asserted-by":"crossref","first-page":"2097","DOI":"10.1016\/j.compchemeng.2010.07.032","article-title":"Multiparametric programming based algorithms for pure integer and mixed-integer bilevel programming problems","volume":"34","author":"Dom\u00ednguez","year":"2010","journal-title":"Comput. Chem. Eng."},{"issue":"2","key":"10.1016\/j.compchemeng.2020.106902_bib0023","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1214\/009053604000000067","article-title":"Least angle regression","volume":"32","author":"Efron","year":"2004","journal-title":"Ann. Stat."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0024","series-title":"NIPS workshop on Bayesian Optimization in Theory and Practice","first-page":"3","article-title":"Towards an empirical foundation for assessing Bayesian optimization of hyperparameters","volume":"10","author":"Eggensperger","year":"2013"},{"issue":"4","key":"10.1016\/j.compchemeng.2020.106902_bib0025","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/s10898-006-9100-6","article-title":"Parametric global optimisation for bilevel programming","volume":"38","author":"Fa\u00edsca","year":"2007","journal-title":"J. Glob. Optim."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0026","series-title":"Advances in Neural Information Processing Systems","first-page":"377","article-title":"Efficient multiple hyperparameter learning for log-linear models","author":"Foo","year":"2008"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0027","unstructured":"Franceschi, L., Frasconi, P., Salzo, S., Grazzi, R., Pontil, M., 2018. Bilevel programming for hyperparameter optimization and meta-learning. arXiv:1806.04910."},{"issue":"1","key":"10.1016\/j.compchemeng.2020.106902_bib0028","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v033.i01","article-title":"Regularization paths for generalized linear models via coordinate descent","volume":"33","author":"Friedman","year":"2010","journal-title":"J. Stat. Softw."},{"issue":"2","key":"10.1016\/j.compchemeng.2020.106902_bib0029","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.neunet.2009.07.001","article-title":"Sparse kernel learning with lasso and Bayesian inference algorithm","volume":"23","author":"Gao","year":"2010","journal-title":"Neural Netw."},{"issue":"5\u20136","key":"10.1016\/j.compchemeng.2020.106902_bib0030","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1016\/j.neunet.2005.06.044","article-title":"Bayesian approach to feature selection and parameter tuning for support vector machine classifiers","volume":"18","author":"Gold","year":"2005","journal-title":"Neural Netw."},{"issue":"Oct","key":"10.1016\/j.compchemeng.2020.106902_bib0031","first-page":"1391","article-title":"The entire regularization path for the support vector machine","volume":"5","author":"Hastie","year":"2004","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0032","series-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction","author":"Hastie","year":"2009"},{"issue":"4","key":"10.1016\/j.compchemeng.2020.106902_bib0033","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s13218-015-0381-0","article-title":"Beyond manual tuning of hyperparameters","volume":"29","author":"Hutter","year":"2015","journal-title":"KI-K\u00fcnstliche Intell."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0034","series-title":"An Introduction to Statistical Learning","volume":"112","author":"James","year":"2013"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0035","series-title":"Advances in Neural Information Processing Systems","first-page":"673","article-title":"An efficient method for gradient-based adaptation of hyperparameters in SVM models","author":"Keerthi","year":"2007"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0036","series-title":"Computer Vision Winter Workshop (CVWW)","first-page":"39","article-title":"Continuous hyper-parameter learning for support vector machines","author":"Klatzer","year":"2015"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0037","series-title":"Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining","first-page":"443","article-title":"Autotune: a derivative-free optimization framework for hyperparameter tuning","author":"Koch","year":"2018"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0038","series-title":"Intelligent Control and Automation","first-page":"712","article-title":"Optimizing the hyper-parameters for SVM by combining evolution strategies with a grid search","author":"Liu","year":"2006"},{"issue":"1","key":"10.1016\/j.compchemeng.2020.106902_bib0039","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1007\/s13721-016-0125-6","article-title":"A review of automatic selection methods for machine learning algorithms and hyper-parameter values","volume":"5","author":"Luo","year":"2016","journal-title":"Netw. Model. Anal. Health Inform. Bioinform."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0040","unstructured":"MacKay, M., Vicol, P., Lorraine, J., Duvenaud, D., Grosse, R., 2019. Self-tuning networks: bilevel optimization of hyperparameters using structured best-response functions. arXiv:1903.03088."},{"issue":"3","key":"10.1016\/j.compchemeng.2020.106902_bib0041","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1007\/s10898-016-0463-z","article-title":"On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory","volume":"69","author":"Oberdieck","year":"2017","journal-title":"J. Glob. Optim."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0042","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.cherd.2016.09.034","article-title":"On multi-parametric programming and its applications in process systems engineering","volume":"116","author":"Oberdieck","year":"2016","journal-title":"Chem. Eng. Res. Des."},{"issue":"33","key":"10.1016\/j.compchemeng.2020.106902_bib0043","doi-asserted-by":"crossref","first-page":"8979","DOI":"10.1021\/acs.iecr.6b01913","article-title":"Pop\u2013parametric optimization toolbox","volume":"55","author":"Oberdieck","year":"2016","journal-title":"Ind. Eng. Chem. Res."},{"issue":"10","key":"10.1016\/j.compchemeng.2020.106902_bib0044","doi-asserted-by":"crossref","first-page":"e16680","DOI":"10.1002\/aic.16680","article-title":"Parametric optimization and control toward the design of a smart metal hydride refueling system","volume":"65","author":"Ogumerem","year":"2019","journal-title":"AlChE J."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0045","article-title":"Integrated data-driven process monitoring and explicit fault-tolerant multiparametric control","author":"Onel","year":"2019","journal-title":"Ind. Eng. Chem. Res."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0046","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.compchemeng.2018.03.025","article-title":"Big data approach to batch process monitoring: simultaneous fault detection and diagnosis using nonlinear support vector machine-based feature selection","volume":"115","author":"Onel","year":"2018","journal-title":"Comput. Chem. Eng."},{"issue":"3","key":"10.1016\/j.compchemeng.2020.106902_bib0047","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1002\/aic.16497","article-title":"A nonlinear support vector machine-based feature selection approach for fault detection and diagnosis: application to the tennessee eastman process","volume":"65","author":"Onel","year":"2019","journal-title":"AlChE J."},{"issue":"1","key":"10.1016\/j.compchemeng.2020.106902_bib0048","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1186\/s12885-017-3877-1","article-title":"Using Resistin, glucose, age and BMI to predict the presence of breast cancer","volume":"18","author":"Patr\u00edcio","year":"2018","journal-title":"BMC Cancer"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0049","unstructured":"Pedregosa, F., 2016. Hyperparameter optimization with approximate gradient. arXiv:1602.02355."},{"issue":"8","key":"10.1016\/j.compchemeng.2020.106902_bib0050","doi-asserted-by":"crossref","first-page":"1918","DOI":"10.1002\/aic.11965","article-title":"Perspectives in multiparametric programming and explicit model predictive control","volume":"55","author":"Pistikopoulos","year":"2009","journal-title":"AlChE J."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0051","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.compchemeng.2012.06.031","article-title":"From multi-parametric programming theory to MPC-on-a-chip multi-scale systems applications","volume":"47","author":"Pistikopoulos","year":"2012","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0052","doi-asserted-by":"crossref","unstructured":"Pistikopoulos, E. N., Diangelakis, N. A., Oberdieck, R., 2020. Multi-Parametric Optimization and Control. Vol.\u00a0 1.","DOI":"10.1002\/9781119265245"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0053","series-title":"Multi-Parametric Programming: Theory, Algorithms, and Applications","volume":"1","author":"Pistikopoulos","year":"2011"},{"issue":"3","key":"10.1016\/j.compchemeng.2020.106902_bib0054","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1007\/s10898-012-9951-y","article-title":"Derivative-free optimization: a review of algorithms and comparison of software implementations","volume":"56","author":"Rios","year":"2013","journal-title":"J. Glob. Optim."},{"issue":"2","key":"10.1016\/j.compchemeng.2020.106902_bib0055","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TEVC.2017.2712906","article-title":"A review on bilevel optimization: from classical to evolutionary approaches and applications","volume":"22","author":"Sinha","year":"2017","journal-title":"IEEE Trans. Evol. Comput."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0056","series-title":"Advances in Neural Information Processing Systems","first-page":"2951","article-title":"Practical Bayesian optimization of machine learning algorithms","author":"Snoek","year":"2012"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0057","doi-asserted-by":"crossref","first-page":"106675","DOI":"10.1016\/j.compchemeng.2019.106675","article-title":"A systematic framework for the synthesis of operable process intensification systems\u2013reactive separation systems","volume":"134","author":"Tian","year":"2020","journal-title":"Comput. Chem. Eng."},{"issue":"1","key":"10.1016\/j.compchemeng.2020.106902_bib0058","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression shrinkage and selection via the lasso","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Stat. Soc."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0059","series-title":"Computer Aided Chemical Engineering","doi-asserted-by":"crossref","first-page":"1705","DOI":"10.1016\/B978-0-444-64241-7.50279-2","article-title":"Toward optimal synthesis of renewable ammonia and methanol processes (RAMP)","volume":"44","author":"Tso","year":"2018"},{"key":"10.1016\/j.compchemeng.2020.106902_bib0060","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1016\/j.compchemeng.2017.02.010","article-title":"The ALAMO approach to machine learning","volume":"106","author":"Wilson","year":"2017","journal-title":"Comput. Chem. Eng."},{"key":"10.1016\/j.compchemeng.2020.106902_bib0061","series-title":"Advances in Neural Information Processing Systems","first-page":"49","article-title":"1-norm support vector machines","author":"Zhu","year":"2004"}],"container-title":["Computers & Chemical Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0098135420300715?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0098135420300715?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T17:51:23Z","timestamp":1758822683000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0098135420300715"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8]]},"references-count":61,"alternative-id":["S0098135420300715"],"URL":"https:\/\/doi.org\/10.1016\/j.compchemeng.2020.106902","relation":{},"ISSN":["0098-1354"],"issn-type":[{"value":"0098-1354","type":"print"}],"subject":[],"published":{"date-parts":[[2020,8]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"HY-POP: Hyperparameter optimization of machine learning models through parametric programming","name":"articletitle","label":"Article Title"},{"value":"Computers & Chemical Engineering","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.compchemeng.2020.106902","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2020 Elsevier Ltd. All rights reserved.","name":"copyright","label":"Copyright"}],"article-number":"106902"}}