{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T20:11:43Z","timestamp":1773864703659,"version":"3.50.1"},"publisher-location":"Cham","reference-count":26,"publisher":"Springer Nature Switzerland","isbn-type":[{"value":"9783032195814","type":"print"},{"value":"9783032195821","type":"electronic"}],"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.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026]]},"DOI":"10.1007\/978-3-032-19582-1_12","type":"book-chapter","created":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T12:37:44Z","timestamp":1773837464000},"page":"166-179","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Variable Neighborhood Search Heuristic for\u00a0Semi-supervised Minimum Sum-of-Squares Clustering"],"prefix":"10.1007","author":[{"given":"Mahuton Hugues","family":"Midingoyi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andr\u00e9","family":"Meneses","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9876-2921","authenticated-orcid":false,"given":"Daniel","family":"Aloise","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,19]]},"reference":[{"issue":"6","key":"12_CR1","doi-asserted-by":"publisher","first-page":"2688","DOI":"10.1016\/j.apm.2010.11.032","volume":"35","author":"A Alguwaizani","year":"2011","unstructured":"Alguwaizani, A., Hansen, P., Mladenovi\u0107, N., Ngai, E.: Variable neighborhood search for harmonic means clustering. Appl. Math. Model. 35(6), 2688\u20132694 (2011)","journal-title":"Appl. Math. Model."},{"key":"12_CR2","doi-asserted-by":"crossref","unstructured":"Aloise, D., Caporossi, G., Hansen, P., Liberti, L., Perron, S., Ruiz, M.: Modularity maximization in networks by variable neighborhood search. Graph Partitioning Graph Clustering 588(113) (2012)","DOI":"10.1090\/conm\/588\/11705"},{"issue":"2","key":"12_CR3","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1007\/s10994-009-5103-0","volume":"75","author":"D Aloise","year":"2009","unstructured":"Aloise, D., Deshpande, A., Hansen, P., Popat, P.: Np-hardness of euclidean sum-of-squares clustering. Mach. Learn. 75(2), 245\u2013248 (2009)","journal-title":"Mach. Learn."},{"key":"12_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1007\/978-3-319-07046-9_31","volume-title":"Integration of AI and OR Techniques in Constraint Programming","author":"B Babaki","year":"2014","unstructured":"Babaki, B., Guns, T., Nijssen, S.: Constrained clustering using column generation. In: Simonis, H. (ed.) CPAIOR 2014. LNCS, vol. 8451, pp. 438\u2013454. Springer, Cham (2014). https:\/\/doi.org\/10.1007\/978-3-319-07046-9_31"},{"key":"12_CR5","doi-asserted-by":"publisher","unstructured":"Baumann, P., Hochbaum, D.: An algorithm for clustering with confidence-based must-link and cannot-link constraints. INFORMS J. Comput. 37(4), 1044\u20131068 (2025). https:\/\/doi.org\/10.1287\/ijoc.2023.0419.cd","DOI":"10.1287\/ijoc.2023.0419.cd"},{"issue":"1","key":"12_CR6","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/s10479-017-2601-5","volume":"272","author":"J Brimberg","year":"2019","unstructured":"Brimberg, J., Mladenovi\u0107, N., Todosijevi\u0107, R., Uro\u0161evi\u0107, D.: Solving the capacitated clustering problem with variable neighborhood search. Ann. Oper. Res. 272(1), 289\u2013321 (2019)","journal-title":"Ann. Oper. Res."},{"issue":"6","key":"12_CR7","first-page":"2210","volume":"33","author":"J Cai","year":"2021","unstructured":"Cai, J., He, L., Hu, X., Jiang, M., Yu, P.S.: A review on semi-supervised clustering. IEEE Trans. Knowl. Data Eng. 33(6), 2210\u20132229 (2021)","journal-title":"IEEE Trans. Knowl. Data Eng."},{"issue":"2","key":"12_CR8","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1016\/j.ejor.2013.04.027","volume":"230","author":"E Carrizosa","year":"2013","unstructured":"Carrizosa, E., Mladenovi\u0107, N., Todosijevi\u0107, R.: Variable neighborhood search for minimum sum-of-squares clustering on networks. Eur. J. Oper. Res. 230(2), 356\u2013363 (2013)","journal-title":"Eur. J. Oper. Res."},{"key":"12_CR9","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1016\/j.ins.2017.06.019","volume":"415","author":"LR Costa","year":"2017","unstructured":"Costa, L.R., Aloise, D., Mladenovi\u0107, N.: Less is more: basic variable neighborhood search heuristic for balanced minimum sum-of-squares clustering. Inf. Sci. 415, 247\u2013253 (2017)","journal-title":"Inf. Sci."},{"key":"12_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/978-3-642-40994-3_27","volume-title":"Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2013","author":"TBH Dao","year":"2013","unstructured":"Dao, T.B.H., Duong, K.C., Vrain, C.: A declarative framework for constrained clustering. In: Blockeel, H., Kersting, K., Nijssen, S., \u017delezn\u00fd, F. (eds.) Machine Learning and Knowledge Discovery in Databases: European Conference, ECML PKDD 2013. Lecture Notes in Computer Science, vol. 8190, pp. 419\u2013434. Springer, Berlin, Heidelberg (2013)"},{"issue":"4","key":"12_CR11","doi-asserted-by":"publisher","first-page":"1485","DOI":"10.1137\/S1064827597328327","volume":"21","author":"O Du Merle","year":"1999","unstructured":"Du Merle, O., Hansen, P., Jaumard, B., Mladenovic, N.: An interior point algorithm for minimum sum-of-squares clustering. SIAM J. Sci. Comput. 21(4), 1485\u20131505 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"12_CR12","unstructured":"Forgy, E.W.: Cluster analysis of multivariate data: efficiency versus interpretability of classifications. Biometrics 21, 768\u2013769 (1965)"},{"key":"12_CR13","doi-asserted-by":"crossref","unstructured":"Ganji, M., Bailey, J., Stuckey, P.J.: Lagrangian constrained clustering. In: Proceedings of the 2016 SIAM International Conference on Data Mining (SDM), pp. 288\u2013296. SIAM (2016)","DOI":"10.1137\/1.9781611974348.33"},{"key":"12_CR14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2020.104979","volume":"121","author":"G Gonz\u00e1lez-Almagro","year":"2020","unstructured":"Gonz\u00e1lez-Almagro, G., Luengo, J., Cano, J.R., Garc\u00eda, S.: Dils: constrained clustering through dual iterative local search. Comput. Operat. Res. 121, 104979 (2020)","journal-title":"Comput. Operat. Res."},{"issue":"3","key":"12_CR15","first-page":"364","volume":"21","author":"T Guns","year":"2016","unstructured":"Guns, T., Dao, T.B.H., Vrain, C., Duong, K.D.C.: Repetitive branch-and-bound using constraint programming for constrained minimum sum-of-squares clustering. Constraints 21(3), 364\u2013392 (2016)","journal-title":"Constraints"},{"issue":"12","key":"12_CR16","doi-asserted-by":"publisher","first-page":"4337","DOI":"10.1016\/j.patcog.2012.04.029","volume":"45","author":"P Hansen","year":"2012","unstructured":"Hansen, P., Ruiz, M., Aloise, D.: A vns heuristic for escaping local extrema entrapment in normalized cut clustering. Pattern Recogn. 45(12), 4337\u20134345 (2012)","journal-title":"Pattern Recogn."},{"key":"12_CR17","doi-asserted-by":"publisher","unstructured":"Huang, H., Cheng, Y., Zhao, R.: A semi-supervised clustering algorithm based on must-link set. In: Tang, C., Ling, C.X., Zhou, X., Cercone, N.J., Li, X. (eds.) ADMA 2008. LNCS (LNAI), vol. 5139, pp. 492\u2013499. Springer, Heidelberg (2008). https:\/\/doi.org\/10.1007\/978-3-540-88192-6_48","DOI":"10.1007\/978-3-540-88192-6_48"},{"issue":"2","key":"12_CR18","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","volume":"28","author":"SP Lloyd","year":"1982","unstructured":"Lloyd, S.P.: Least squares quantization in pcm. IEEE Trans. Inf. Theory 28(2), 129\u2013137 (1982)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"11","key":"12_CR19","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1016\/S0305-0548(97)00031-2","volume":"24","author":"N Mladenovi\u0107","year":"1997","unstructured":"Mladenovi\u0107, N., Hansen, P.: Variable neighborhood search. Comput. Oper. Res. 24(11), 1097\u20131100 (1997)","journal-title":"Comput. Oper. Res."},{"key":"12_CR20","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2022.105958","volume":"147","author":"V Piccialli","year":"2022","unstructured":"Piccialli, V., Russo, A., Sudoso, A.M.: An exact algorithm for semi-supervised minimum sum-of-squares clustering. Comput. Operat. Res. 147, 105958 (2022)","journal-title":"Comput. Operat. Res."},{"key":"12_CR21","doi-asserted-by":"crossref","unstructured":"Randel, R., Aloise, D., Mladenovi\u0107, N., Hansen, P.: On the k-medoids model for semi-supervised clustering. In: International Conference on Variable Neighborhood Search, pp. 13\u201327. Springer (2018)","DOI":"10.1007\/978-3-030-15843-9_2"},{"key":"12_CR22","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/978-3-642-24425-4_30","volume-title":"Rough Sets and Knowledge Technology","author":"T Rutayisire","year":"2011","unstructured":"Rutayisire, T., Yang, Y., Lin, C., Zhang, J.: A modified cop-Kmeans algorithm based on sequenced cannot-link set. In: Yao, J.T., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS (LNAI), vol. 6954, pp. 217\u2013225. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-24425-4_30"},{"key":"12_CR23","doi-asserted-by":"crossref","unstructured":"Tan, W., Yang, Y., Li, T.: An improved cop-kmeans algorithm for solving constraint violation. In: Computational Intelligence: Foundations and Applications. World Scientific Proceedings Series on Computer Engineering and Information Science, vol.\u00a04, pp. 690\u2013696. World Scientific Publishing (2010)","DOI":"10.1142\/9789814324700_0104"},{"key":"12_CR24","unstructured":"Wagstaff, K., Cardie, C., Rogers, S., Schr\u00f6dl, S.: Constrained k-means clustering with background knowledge. In: Proc. 18th Int. Conf. Mach. Learn. (ICML), pp. 577\u2013584. Morgan Kaufmann, San Francisco (2001)"},{"key":"12_CR25","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1016\/j.patcog.2019.01.042","volume":"90","author":"Y Xiao","year":"2019","unstructured":"Xiao, Y., Huang, C., Huang, J., Kaku, I., Xu, Y.: Optimal mathematical programming and variable neighborhood search for k-modes categorical data clustering. Pattern Recogn. 90, 183\u2013195 (2019)","journal-title":"Pattern Recogn."},{"key":"12_CR26","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/j.knosys.2011.08.011","volume":"32","author":"Y Yang","year":"2012","unstructured":"Yang, Y., Tan, W., Li, T., Ruan, D.: Consensus clustering based on constrained self-organizing map and improved cop-kmeans ensemble in intelligent decision support systems. Knowl.-Based Syst. 32, 101\u2013115 (2012)","journal-title":"Knowl.-Based Syst."}],"container-title":["Lecture Notes in Computer Science","Variable Neighborhood Search"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-032-19582-1_12","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T12:37:52Z","timestamp":1773837472000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-032-19582-1_12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"ISBN":["9783032195814","9783032195821"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-032-19582-1_12","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]},"assertion":[{"value":"19 March 2026","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Disclosure of Interests"}},{"value":"ICVNS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Variable Neighborhood Search","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Montreal, QC","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2025","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 May 2025","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 May 2025","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"icvns2025","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/2025.icvns.com","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}