{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T05:11:32Z","timestamp":1773205892359,"version":"3.50.1"},"reference-count":106,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T00:00:00Z","timestamp":1758240000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100011033","name":"Agencia Estatal de Investigaci\u00f3n","doi-asserted-by":"publisher","award":["PID2022-137818OB-I00"],"award-info":[{"award-number":["PID2022-137818OB-I00"]}],"id":[{"id":"10.13039\/501100011033","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computers &amp; Operations Research"],"published-print":{"date-parts":[[2026,1]]},"DOI":"10.1016\/j.cor.2025.107283","type":"journal-article","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T22:09:18Z","timestamp":1758578958000},"page":"107283","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A unified approach to extract interpretable rules from tree ensembles via Integer Programming"],"prefix":"10.1016","volume":"185","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7931-5755","authenticated-orcid":false,"given":"Lorenzo","family":"Bonasera","sequence":"first","affiliation":[]},{"given":"Emilio","family":"Carrizosa","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.cor.2025.107283_b1","doi-asserted-by":"crossref","unstructured":"Agrawal, R., Imieli\u0144ski, T., Swami, A., 1993. Mining association rules between sets of items in large databases. In: Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data. pp. 207\u2013216.","DOI":"10.1145\/170035.170072"},{"issue":"11","key":"10.1016\/j.cor.2025.107283_b2","doi-asserted-by":"crossref","first-page":"832","DOI":"10.1145\/182.358434","article-title":"Maintaining knowledge about temporal intervals","volume":"26","author":"Allen","year":"1983","journal-title":"Commun. ACM"},{"key":"10.1016\/j.cor.2025.107283_b3","article-title":"A comparison among interpretative proposals for random forests","volume":"6","author":"Aria","year":"2021","journal-title":"Mach. Learn. Appl."},{"issue":"8","key":"10.1016\/j.cor.2025.107283_b4","doi-asserted-by":"crossref","first-page":"990","DOI":"10.1016\/j.conengprac.2010.04.005","article-title":"Change point detection in time series data with random forests","volume":"18","author":"Auret","year":"2010","journal-title":"Control Eng. Pract."},{"issue":"6","key":"10.1016\/j.cor.2025.107283_b5","doi-asserted-by":"crossref","first-page":"623","DOI":"10.3233\/IDA-2010-0444","article-title":"Rules for contrast sets","volume":"14","author":"Azevedo","year":"2010","journal-title":"Intell. Data Anal."},{"issue":"4","key":"10.1016\/j.cor.2025.107283_b6","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1137\/1018115","article-title":"Set partitioning: A survey","volume":"18","author":"Balas","year":"1976","journal-title":"SIAM Rev."},{"key":"10.1016\/j.cor.2025.107283_b7","doi-asserted-by":"crossref","unstructured":"Bay, S.D., Pazzani, M.J., 1999. Detecting Change in Categorical Data: Mining Contrast Sets. In: Proceedings of the Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. pp. 302\u2013306.","DOI":"10.1145\/312129.312263"},{"key":"10.1016\/j.cor.2025.107283_b8","series-title":"International Conference on Artificial Intelligence and Statistics","first-page":"937","article-title":"Interpretable random forests via rule extraction","author":"B\u00e9nard","year":"2021"},{"key":"10.1016\/j.cor.2025.107283_b9","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1214\/20-EJS1792","article-title":"SIRUS: Stable and interpretable rule set for classification","volume":"15","author":"B\u00e9nard","year":"2021","journal-title":"Electron. J. Stat."},{"issue":"1","key":"10.1016\/j.cor.2025.107283_b10","first-page":"152","article-title":"Should we really use post-hoc tests based on mean-ranks?","volume":"17","author":"Benavoli","year":"2016","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.cor.2025.107283_b11","doi-asserted-by":"crossref","first-page":"1039","DOI":"10.1007\/s10994-017-5633-9","article-title":"Optimal classification trees","volume":"106","author":"Bertsimas","year":"2017","journal-title":"Mach. Learn."},{"key":"10.1016\/j.cor.2025.107283_b12","series-title":"Metaheuristics International Conference","first-page":"3","article-title":"Learning sparse-lets for interpretable classification of event-interval sequences","author":"Bonasera","year":"2024"},{"key":"10.1016\/j.cor.2025.107283_b13","doi-asserted-by":"crossref","DOI":"10.1016\/j.ejco.2024.100091","article-title":"Optimal shapelets tree for time series interpretable classification","author":"Bonasera","year":"2024","journal-title":"EURO J. Comput. Optim."},{"key":"10.1016\/j.cor.2025.107283_b14","series-title":"2007 IEEE 11th International Conference on Computer Vision","first-page":"1","article-title":"Image classification using random forests and ferns","author":"Bosch","year":"2007"},{"key":"10.1016\/j.cor.2025.107283_b15","series-title":"Data Warehousing and Knowledge Discovery: 16th International Conference, DaWaK 2014, Munich, Germany, September 2-4, 2014. Proceedings 16","first-page":"288","article-title":"Short text classification using semantic random forest","author":"Bouaziz","year":"2014"},{"key":"10.1016\/j.cor.2025.107283_b16","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1023\/A:1018054314350","article-title":"Bagging predictors","volume":"24","author":"Breiman","year":"1996","journal-title":"Mach. Learn."},{"key":"10.1016\/j.cor.2025.107283_b17","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."},{"key":"10.1016\/j.cor.2025.107283_b18","series-title":"Born Again Trees","first-page":"4","author":"Breiman","year":"1996"},{"key":"10.1016\/j.cor.2025.107283_b19","series-title":"European Conference on Logics in Artificial Intelligence","first-page":"778","article-title":"Interval temporal logic decision tree learning","author":"Brunello","year":"2019"},{"key":"10.1016\/j.cor.2025.107283_b20","doi-asserted-by":"crossref","DOI":"10.1016\/j.cor.2023.106180","article-title":"On clustering and interpreting with rules by means of mathematical optimization","volume":"154","author":"Carrizosa","year":"2023","journal-title":"Comput. Oper. Res."},{"issue":"1","key":"10.1016\/j.cor.2025.107283_b21","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s11750-021-00594-1","article-title":"Mathematical optimization in classification and regression trees","volume":"29","author":"Carrizosa","year":"2021","journal-title":"TOP"},{"issue":"1","key":"10.1016\/j.cor.2025.107283_b22","doi-asserted-by":"crossref","first-page":"150","DOI":"10.1016\/j.cor.2012.05.015","article-title":"Supervised classification and mathematical optimization","volume":"40","author":"Carrizosa","year":"2013","journal-title":"Comput. Oper. Res."},{"issue":"2","key":"10.1016\/j.cor.2025.107283_b23","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1111\/j.1541-0420.2005.00489.x","article-title":"Abundance-based similarity indices and their estimation when there are unseen species in samples","volume":"62","author":"Chao","year":"2006","journal-title":"Biometrics"},{"issue":"4","key":"10.1016\/j.cor.2025.107283_b24","first-page":"1","article-title":"Xgboost: extreme gradient boosting","volume":"1","author":"Chen","year":"2015","journal-title":"R Packag. Ver. 0.4-2"},{"issue":"2","key":"10.1016\/j.cor.2025.107283_b25","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1016\/j.dss.2005.03.005","article-title":"A new approach to classification based on association rule mining","volume":"42","author":"Chen","year":"2006","journal-title":"Decis. Support Syst."},{"key":"10.1016\/j.cor.2025.107283_b26","series-title":"2007 IEEE 23rd International Conference on Data Engineering","first-page":"716","article-title":"Discriminative frequent pattern analysis for effective classification","author":"Cheng","year":"2006"},{"key":"10.1016\/j.cor.2025.107283_b27","series-title":"Machine Learning\u2014EWSL-91: European Working Session on Learning Porto, Portugal, March 6\u20138, 1991 Proceedings 5","first-page":"151","article-title":"Rule induction with CN2: Some recent improvements","author":"Clark","year":"1991"},{"issue":"4","key":"10.1016\/j.cor.2025.107283_b28","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1023\/A:1022641700528","article-title":"The CN2 induction algorithm","volume":"3","author":"Clark","year":"1989","journal-title":"Mach. Learn."},{"issue":"335\u2013342","key":"10.1016\/j.cor.2025.107283_b29","first-page":"3","article-title":"A simple, fast, and effective rule learner","volume":"99","author":"Cohen","year":"1999","journal-title":"AAAI\/IAAI"},{"key":"10.1016\/j.cor.2025.107283_b30","series-title":"Proceedings of the IASTED International Conference on Applied Informatics","first-page":"327","article-title":"Rule extraction from time series databases using classification trees","author":"Cotofrei","year":"2002"},{"key":"10.1016\/j.cor.2025.107283_b31","unstructured":"Das, G., Lin, K.-I., Mannila, H., Renganathan, G., Smyth, P., 1998. Rule Discovery from Time Series. In: Proceedings of the 4th International Conference on Knowledge Discovery and Data Mining. KDD 1998, pp. 16\u201322."},{"key":"10.1016\/j.cor.2025.107283_b32","series-title":"The UCR time series classification archive","author":"Dau","year":"2018"},{"key":"10.1016\/j.cor.2025.107283_b33","first-page":"1","article-title":"Statistical comparisons of classifiers over multiple data sets","volume":"7","author":"Dem\u0161ar","year":"2006","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.cor.2025.107283_b34","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/j.ins.2013.02.030","article-title":"A time series forest for classification and feature extraction","volume":"239","author":"Deng","year":"2013","journal-title":"Inform. Sci."},{"key":"10.1016\/j.cor.2025.107283_b35","doi-asserted-by":"crossref","DOI":"10.1016\/j.ejco.2024.100084","article-title":"Unboxing tree ensembles for interpretability: a hierarchical visualization tool and a multivariate optimal re-built tree","volume":"12","author":"Di Teodoro","year":"2024","journal-title":"EURO J. Comput. Optim."},{"key":"10.1016\/j.cor.2025.107283_b36","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1023\/A:1018006431188","article-title":"Unifying instance-based and rule-based induction","volume":"24","author":"Domingos","year":"1996","journal-title":"Mach. Learn."},{"key":"10.1016\/j.cor.2025.107283_b37","doi-asserted-by":"crossref","unstructured":"Dong, G., Li, J., 1999. Efficient Mining of Emerging Patterns: Discovering Trends and Differences. In: Proceedings of the Fifth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. pp. 43\u201352.","DOI":"10.1145\/312129.312191"},{"key":"10.1016\/j.cor.2025.107283_b38","series-title":"Intelligent Systems\u2019 2014: Proceedings of the 7th IEEE International Conference Intelligent Systems IS\u20192014, September 24-26, 2014, Warsaw, Poland, Volume 2: Tools, Architectures, Systems, Applications","first-page":"821","article-title":"Short-term load forecasting using random forests","author":"Dudek","year":"2015"},{"key":"10.1016\/j.cor.2025.107283_b39","series-title":"Proceedings of the 25th Annual Conference on Learning Theory","first-page":"17.1","article-title":"Learning DNF expressions from Fourier spectrum","author":"Feldman","year":"2012"},{"issue":"3","key":"10.1016\/j.cor.2025.107283_b40","article-title":"A cognitive load theory (CLT) analysis of machine learning explainability, transparency, interpretability, and shared interpretability.","volume":"6","author":"Fox","year":"2024","journal-title":"Mach. Learn. Knowl. Extr."},{"key":"10.1016\/j.cor.2025.107283_b41","first-page":"1189","article-title":"Greedy function approximation: a gradient boosting machine","author":"Friedman","year":"2001","journal-title":"Ann. Stat."},{"key":"10.1016\/j.cor.2025.107283_b42","first-page":"916","article-title":"Predictive learning via rule ensembles","author":"Friedman","year":"2008","journal-title":"Ann. Appl. Stat."},{"key":"10.1016\/j.cor.2025.107283_b43","series-title":"Foundations of Rule Learning","author":"F\u00fcrnkranz","year":"2012"},{"key":"10.1016\/j.cor.2025.107283_b44","series-title":"Advances in Knowledge Discovery and Data Mining: 14th Pacific-Asia Conference","first-page":"150","article-title":"A new emerging pattern mining algorithm and its application in supervised classification","author":"Garc\u00eda-Borroto","year":"2010"},{"key":"10.1016\/j.cor.2025.107283_b45","doi-asserted-by":"crossref","unstructured":"Gilpin, L.H., Bau, D., Yuan, B.Z., Bajwa, A., Specter, M., Kagal, L., 2018. Explaining Explanations: An Overview of Interpretability of Machine Learning. In: 2018 IEEE 5th International Conference on Data Science and Advanced Analytics. DSAA, pp. 80\u201389.","DOI":"10.1109\/DSAA.2018.00018"},{"key":"10.1016\/j.cor.2025.107283_b46","article-title":"Learning time-series shapelets","author":"Grabocka","year":"2014","journal-title":"Proc. ACM SIGKDD Int. Conf. Knowl. Discov. Data Min."},{"issue":"37","key":"10.1016\/j.cor.2025.107283_b47","doi-asserted-by":"crossref","DOI":"10.1126\/scirobotics.aay7120","article-title":"XAI\u2014Explainable artificial intelligence","volume":"4","author":"Gunning","year":"2019","journal-title":"Sci. Robot."},{"key":"10.1016\/j.cor.2025.107283_b48","series-title":"SIAM Conference on Applied and Computational Discrete Algorithms","first-page":"88","article-title":"Fairmandering: A column generation heuristic for fairness-optimized political districting","author":"Gurnee","year":"2021"},{"key":"10.1016\/j.cor.2025.107283_b49","series-title":"Gurobi optimizer reference manual","author":"Gurobi Optimization","year":"2022"},{"key":"10.1016\/j.cor.2025.107283_b50","article-title":"Stop ordering machine learning algorithms by their explainability! a user-centered investigation of performance and explainability","volume":"69","author":"Herm","year":"2023","journal-title":"Int. J. Inf. Manage."},{"issue":"6","key":"10.1016\/j.cor.2025.107283_b51","doi-asserted-by":"crossref","DOI":"10.1007\/s11222-021-10057-z","article-title":"Unrestricted permutation forces extrapolation: variable importance requires at least one more model, or there is no free variable importance","volume":"31","author":"Hooker","year":"2021","journal-title":"Stat. Comput."},{"key":"10.1016\/j.cor.2025.107283_b52","series-title":"Interpretable clustering: A survey","author":"Hu","year":"2024"},{"issue":"489","key":"10.1016\/j.cor.2025.107283_b53","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1198\/jasa.2009.tm08622","article-title":"High-dimensional variable selection for survival data","volume":"105","author":"Ishwaran","year":"2010","journal-title":"J. Amer. Statist. Assoc."},{"issue":"4","key":"10.1016\/j.cor.2025.107283_b54","doi-asserted-by":"crossref","first-page":"917","DOI":"10.1007\/s10618-019-00619-1","article-title":"Deep learning for time series classification: a review","volume":"33","author":"Ismail Fawaz","year":"2019","journal-title":"Data Min. Knowl. Discov."},{"key":"10.1016\/j.cor.2025.107283_b55","doi-asserted-by":"crossref","DOI":"10.1016\/j.patcog.2022.108554","article-title":"Rule extraction with guarantees from regression models","volume":"126","author":"Johansson","year":"2022","journal-title":"Pattern Recognit."},{"key":"10.1016\/j.cor.2025.107283_b56","unstructured":"Kadous, M.W., 1999. Learning Comprehensible Descriptions of Multivariate Time Series. In: Proceedings of the Sixteenth International Conference on Machine Learning. vol. 454, p. 463."},{"key":"10.1016\/j.cor.2025.107283_b57","doi-asserted-by":"crossref","DOI":"10.1007\/s10618-016-0473-y","article-title":"Generalized random shapelet forests","volume":"30","author":"Karlsson","year":"2016","journal-title":"Data Min. Knowl. Discov."},{"key":"10.1016\/j.cor.2025.107283_b58","doi-asserted-by":"crossref","unstructured":"Klivans, A.R., Servedio, R., 2001. Learning DNF in time. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing. pp. 258\u2013265.","DOI":"10.1145\/380752.380809"},{"key":"10.1016\/j.cor.2025.107283_b59","series-title":"Artificial Intelligence in Medicine: 11th Conference on Artificial Intelligence in Medicine","first-page":"109","article-title":"Contrast set mining for distinguishing between similar diseases","author":"Kralj","year":"2007"},{"key":"10.1016\/j.cor.2025.107283_b60","doi-asserted-by":"crossref","unstructured":"Lakkaraju, H., Bach, S.H., Leskovec, J., 2016. Interpretable Decision Sets: A Joint Framework for Description and Prediction. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. pp. 1675\u20131684.","DOI":"10.1145\/2939672.2939874"},{"issue":"229","key":"10.1016\/j.cor.2025.107283_b61","first-page":"1","article-title":"Interpretable and fair boolean rule sets via column generation","volume":"24","author":"Lawless","year":"2023","journal-title":"J. Mach. Learn. Res."},{"issue":"3","key":"10.1016\/j.cor.2025.107283_b62","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1214\/15-AOAS848","article-title":"Interpretable classifiers using rules and Bayesian analysis: Building a better stroke prediction model","volume":"9","author":"Letham","year":"2015","journal-title":"Ann. Appl. Stat."},{"issue":"2","key":"10.1016\/j.cor.2025.107283_b63","doi-asserted-by":"crossref","first-page":"498","DOI":"10.2307\/2273574","article-title":"Michael R. \u03a0Garey and David S. Johnson. Computers and intractability. A guide to the theory of NP-completeness. WH Freeman and Company, San Francisco1979, x+ 338 pp","volume":"48","author":"Lewis","year":"1983","journal-title":"J. Symb. Log."},{"key":"10.1016\/j.cor.2025.107283_b64","doi-asserted-by":"crossref","first-page":"66538","DOI":"10.1109\/ACCESS.2020.2984024","article-title":"Generic SAO similarity measure via extended S\u00f8rensen-Dice index","volume":"8","author":"Li","year":"2020","journal-title":"IEEE Access"},{"key":"10.1016\/j.cor.2025.107283_b65","doi-asserted-by":"crossref","unstructured":"Liu, B., Mazumder, R., 2023. Fire: An optimization approach for fast interpretable rule extraction. In: Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. pp. 1396\u20131405.","DOI":"10.1145\/3580305.3599353"},{"key":"10.1016\/j.cor.2025.107283_b66","series-title":"1998 ACM SIGMOD Workshop on Research Issues on Data Mining and Knowledge Discovery, Seattle, WA, USA","article-title":"Stock movement prediction and n-dimensional inter-transaction association rules","author":"Lu","year":"1998"},{"issue":"3","key":"10.1016\/j.cor.2025.107283_b67","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/s10618-019-00617-3","article-title":"Proximity forest: an effective and scalable distance-based classifier for time series","volume":"33","author":"Lucas","year":"2019","journal-title":"Data Min. Knowl. Discov."},{"key":"10.1016\/j.cor.2025.107283_b68","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.eswa.2016.06.009","article-title":"What makes classification trees comprehensible?","volume":"62","author":"Lu\u0161trek","year":"2016","journal-title":"Expert Syst. Appl."},{"key":"10.1016\/j.cor.2025.107283_b69","series-title":"2018 IEEE 3rd International Conference on Cloud Computing and Big Data Analysis","first-page":"346","article-title":"Image classification based on improved random forest algorithm","author":"Man","year":"2018"},{"key":"10.1016\/j.cor.2025.107283_b70","first-page":"2049","article-title":"Node harvest","author":"Meinshausen","year":"2010","journal-title":"Ann. Appl. Stat."},{"key":"10.1016\/j.cor.2025.107283_b71","series-title":"2019 10th International Conference on Information, Intelligence, Systems and Applications","first-page":"1","article-title":"Model-agnostic interpretability with Shapley values","author":"Messalas","year":"2019"},{"key":"10.1016\/j.cor.2025.107283_b72","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.inffus.2022.08.021","article-title":"Rulecosi+: Rule extraction for interpreting classification tree ensembles","volume":"89","author":"Obregon","year":"2023","journal-title":"Inf. Fusion"},{"key":"10.1016\/j.cor.2025.107283_b73","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/j.eswa.2019.02.012","article-title":"RuleCOSI: Combination and simplification of production rules from boosted decision trees for imbalanced classification","volume":"126","author":"Obregon","year":"2019","journal-title":"Expert Syst. Appl."},{"key":"10.1016\/j.cor.2025.107283_b74","series-title":"Proceedings 14th International Conference on Data Engineering","first-page":"412","article-title":"Cyclic association rules","author":"Ozden","year":"1998"},{"key":"10.1016\/j.cor.2025.107283_b75","first-page":"2825","article-title":"Scikit-learn: Machine learning in python","volume":"12","author":"Pedregosa","year":"2011","journal-title":"J. Mach. Learn. Res."},{"issue":"2019","key":"10.1016\/j.cor.2025.107283_b76","first-page":"9","article-title":"The pairwise multiple comparison of mean ranks package (PMCMR)","volume":"27","author":"Pohlert","year":"2014","journal-title":"R Packag."},{"issue":"3","key":"10.1016\/j.cor.2025.107283_b77","doi-asserted-by":"crossref","first-page":"245","DOI":"10.3233\/IDA-2001-5305","article-title":"Boosting interval based literals","volume":"5","author":"Rodr\u00edguez","year":"2001","journal-title":"Intell. Data Anal."},{"issue":"3","key":"10.1016\/j.cor.2025.107283_b78","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1016\/j.ejor.2013.08.036","article-title":"All-integer column generation for set partitioning: Basic principles and extensions","volume":"233","author":"R\u00f6nnberg","year":"2014","journal-title":"European J. Oper. Res."},{"issue":"5","key":"10.1016\/j.cor.2025.107283_b79","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1038\/s42256-019-0048-x","article-title":"Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead","volume":"1","author":"Rudin","year":"2019","journal-title":"Nat. Mach. Intell."},{"key":"10.1016\/j.cor.2025.107283_b80","series-title":"27th International Symposium on Temporal Representation and Reasoning","article-title":"Knowledge extraction with interval temporal logic decision trees","author":"Sciavicco","year":"2020"},{"key":"10.1016\/j.cor.2025.107283_b81","series-title":"International Work-Conference on the Interplay Between Natural and Artificial Computation","first-page":"3","article-title":"Towards a general method for logical rule extraction from time series","author":"Sciavicco","year":"2019"},{"issue":"19","key":"10.1016\/j.cor.2025.107283_b82","doi-asserted-by":"crossref","first-page":"3663","DOI":"10.1093\/bioinformatics\/btz149","article-title":"Surrogate minimal depth as an importance measure for variables in random forests","volume":"35","author":"Seifert","year":"2019","journal-title":"Bioinformatics"},{"issue":"2","key":"10.1016\/j.cor.2025.107283_b83","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1016\/j.ejor.2017.02.020","article-title":"Optimization approaches to supervised classification","volume":"261","author":"Silva","year":"2017","journal-title":"European J. Oper. Res."},{"key":"10.1016\/j.cor.2025.107283_b84","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1471-2105-9-307","article-title":"Conditional variable importance for random forests","volume":"9","author":"Strobl","year":"2008","journal-title":"BMC Bioinformatics"},{"key":"10.1016\/j.cor.2025.107283_b85","series-title":"2016 IEEE 26th International Workshop on Machine Learning for Signal Processing","first-page":"1","article-title":"Learning sparse two-level boolean rules","author":"Su","year":"2016"},{"key":"10.1016\/j.cor.2025.107283_b86","series-title":"2020 3rd International Conference on Advanced Electronic Materials, Computers and Software Engineering","first-page":"370","article-title":"Application research of text classification based on random forest algorithm","author":"Sun","year":"2020"},{"issue":"5","key":"10.1016\/j.cor.2025.107283_b87","doi-asserted-by":"crossref","first-page":"713","DOI":"10.1007\/s13676-019-00145-6","article-title":"Integral column generation for the set partitioning problem","volume":"8","author":"Tahir","year":"2019","journal-title":"EURO J. Transp. Logist."},{"issue":"5","key":"10.1016\/j.cor.2025.107283_b88","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1017\/S1471068424000401","article-title":"Generating global and local explanations for tree-ensemble learning methods by answer set programming","volume":"24","author":"Takemura","year":"2024","journal-title":"Theory Pract. Log. Program."},{"issue":"118","key":"10.1016\/j.cor.2025.107283_b89","first-page":"1","article-title":"Tslearn, a machine learning toolkit for time series data","volume":"21","author":"Tavenard","year":"2020","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.cor.2025.107283_b90","doi-asserted-by":"crossref","first-page":"100700","DOI":"10.1109\/ACCESS.2022.3207765","article-title":"Explainable AI for time series classification: a review, taxonomy and research directions","volume":"10","author":"Theissler","year":"2022","journal-title":"IEEE Access"},{"issue":"2","key":"10.1016\/j.cor.2025.107283_b91","first-page":"117","article-title":"Knowledge extraction from time series and its application to surface roughness simulation","volume":"5","author":"Ullah","year":"2006","journal-title":"Inf. Knowl. Syst. Manag."},{"issue":"11","key":"10.1016\/j.cor.2025.107283_b92","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1145\/1968.1972","article-title":"A theory of the learnable","volume":"27","author":"Valiant","year":"1984","journal-title":"Commun. ACM"},{"issue":"2","key":"10.1016\/j.cor.2025.107283_b93","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1145\/2641190.2641198","article-title":"Openml: networked science in machine learning","volume":"15","author":"Vanschoren","year":"2014","journal-title":"ACM SIGKDD Explor. Newsl."},{"key":"10.1016\/j.cor.2025.107283_b94","series-title":"Intelligent Information Systems","first-page":"64","article-title":"Evaluating fidelity of explainable methods for predictive process analytics","author":"Velmurugan","year":"2021"},{"key":"10.1016\/j.cor.2025.107283_b95","first-page":"1","article-title":"Through the looking glass: evaluating post hoc explanations using transparent models","author":"Velmurugan","year":"2023","journal-title":"Int. J. Data Sci. Anal."},{"key":"10.1016\/j.cor.2025.107283_b96","series-title":"International Conference on Machine Learning","first-page":"9743","article-title":"Born-again tree ensembles","author":"Vidal","year":"2020"},{"key":"10.1016\/j.cor.2025.107283_b97","series-title":"Learning optimized Or\u2019s of And\u2019s","author":"Wang","year":"2015"},{"key":"10.1016\/j.cor.2025.107283_b98","series-title":"International Conference on Machine Learning","first-page":"6687","article-title":"Generalized linear rule models","author":"Wei","year":"2019"},{"key":"10.1016\/j.cor.2025.107283_b99","series-title":"Reoptimization Techniques in MIP Solvers","author":"Witzig","year":"2014"},{"key":"10.1016\/j.cor.2025.107283_b100","series-title":"2012 IEEE International Conference on Information and Automation","first-page":"795","article-title":"An improved random forest classifier for image classification","author":"Xu","year":"2012"},{"key":"10.1016\/j.cor.2025.107283_b101","series-title":"International Conference on Machine Learning","first-page":"3921","article-title":"Scalable Bayesian rule lists","author":"Yang","year":"2017"},{"key":"10.1016\/j.cor.2025.107283_b102","series-title":"Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining","first-page":"947","article-title":"Time series shapelets: A new primitive for data mining","author":"Ye","year":"2009"},{"issue":"2","key":"10.1016\/j.cor.2025.107283_b103","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/BF02944803","article-title":"Rule extraction: Using neural networks or for neural networks?","volume":"19","author":"Zhou","year":"2004","journal-title":"J. Comput. Sci. Tech."},{"issue":"5","key":"10.1016\/j.cor.2025.107283_b104","doi-asserted-by":"crossref","first-page":"593","DOI":"10.3390\/electronics10050593","article-title":"Evaluating the quality of machine learning explanations: A survey on methods and metrics","volume":"10","author":"Zhou","year":"2021","journal-title":"Electronics"},{"issue":"2","key":"10.1016\/j.cor.2025.107283_b105","first-page":"1","article-title":"Unbiased measurement of feature importance in tree-based methods","volume":"15","author":"Zhou","year":"2021","journal-title":"ACM Trans. Knowl. Discov. Data (TKDD)"},{"key":"10.1016\/j.cor.2025.107283_b106","series-title":"International Conference on Web Information Systems Engineering","first-page":"367","article-title":"TERM: Tree ensemble models for interpretable rule mining","author":"Zhu","year":"2024"}],"container-title":["Computers &amp; Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0305054825003120?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0305054825003120?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T07:31:52Z","timestamp":1773127912000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0305054825003120"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1]]},"references-count":106,"alternative-id":["S0305054825003120"],"URL":"https:\/\/doi.org\/10.1016\/j.cor.2025.107283","relation":{},"ISSN":["0305-0548"],"issn-type":[{"value":"0305-0548","type":"print"}],"subject":[],"published":{"date-parts":[[2026,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A unified approach to extract interpretable rules from tree ensembles via Integer Programming","name":"articletitle","label":"Article Title"},{"value":"Computers & Operations Research","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cor.2025.107283","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2025 The Authors. Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"107283"}}