{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T07:35:57Z","timestamp":1769844957123,"version":"3.49.0"},"reference-count":36,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2015,11,12]],"date-time":"2015-11-12T00:00:00Z","timestamp":1447286400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Constraints"],"published-print":{"date-parts":[[2016,10]]},"DOI":"10.1007\/s10601-015-9234-6","type":"journal-article","created":{"date-parts":[[2015,11,12]],"date-time":"2015-11-12T08:01:19Z","timestamp":1447315279000},"page":"435-462","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A lagrangian propagator for artificial neural networks in constraint programming"],"prefix":"10.1007","volume":"21","author":[{"given":"Michele","family":"Lombardi","sequence":"first","affiliation":[]},{"given":"Stefano","family":"Gualandi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,12]]},"reference":[{"key":"9234_CR1","doi-asserted-by":"crossref","unstructured":"Audet, C. (2014). A survey on direct search methods for blackbox optimization and their applications. In Mathematics Without Boundaries (pp. 31\u201356): Springer.","DOI":"10.1007\/978-1-4939-1124-0_2"},{"key":"9234_CR2","doi-asserted-by":"crossref","unstructured":"Bartolini, A., Lombardi, M., Milano, M., & Benini, L. (2011). Neuron Constraints to Model Complex Real-World Problems. In Proc. of CP (pp. 115\u2013129).","DOI":"10.1007\/978-3-642-23786-7_11"},{"key":"9234_CR3","unstructured":"Bartolini, A., Lombardi, M., Milano, M., & Benini, L. (2012). Optimization and Controlled Systems: A Case Study on Thermal Aware Workload Dispatching. Proc. of AAAI."},{"issue":"1","key":"9234_CR4","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0167-7012(00)00201-3","volume":"43","author":"IA Basheer","year":"2000","unstructured":"Basheer, I.A., & Hajmeer, M. (2000). Artificial neural networks: fundamentals, computing, design, and application. Journal of Microbiological Methods, 43(1), 3\u201331.","journal-title":"Journal of Microbiological Methods"},{"key":"9234_CR5","unstructured":"Belew, R.K., McInerney, J., & Schraudolph, N.N. (1991). Evolving networks: Using the genetic algorithm with connectionist learning. Proc. of Artificial Life, 511\u2013547."},{"issue":"4-5","key":"9234_CR6","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1080\/10556780903087124","volume":"24","author":"P Belotti","year":"2009","unstructured":"Belotti, P., Lee, J., Liberti, L., Margot, F., & W\u00e4chter, A. (2009). Branching and bounds tightening techniques for non-convex MINLP. Optimization Methods and Software, 24(4-5), 597\u2013634.","journal-title":"Optimization Methods and Software"},{"issue":"3","key":"9234_CR7","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1007\/s10601-015-9193-y","volume":"20","author":"D Bergman","year":"2015","unstructured":"Bergman, D., Cir\u0117, A. A., & van Hoeve, W.-J. (2015). Lagrangian bounds from decision diagrams. Constraints, 20(3), 346\u2013361.","journal-title":"Constraints"},{"key":"9234_CR8","doi-asserted-by":"crossref","unstructured":"Bonfietti, A., & Lombardi, M. (2012). The weighted average constraint. In Proc. of CP (pp. 191\u2013206): Springer.","DOI":"10.1007\/978-3-642-33558-7_16"},{"key":"9234_CR9","doi-asserted-by":"crossref","unstructured":"Bonfietti, A., Lombardi, M., & Milano, M. (2015). Embedding decision trees and random forests in constraint programming. In Proc. of CPAIOR (pp. 74\u201390).","DOI":"10.1007\/978-3-319-18008-3_6"},{"issue":"3","key":"9234_CR10","doi-asserted-by":"crossref","first-page":"362","DOI":"10.1007\/s10601-015-9191-0","volume":"20","author":"H Cambazard","year":"2015","unstructured":"Cambazard, H., & Fages, J.-G. (2015). New filtering for atmostnvalue and its weighted variant: A lagrangian approach. Constraints, 20(3), 362\u2013380.","journal-title":"Constraints"},{"issue":"1","key":"9234_CR11","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/S0378-7788(01)00085-8","volume":"34","author":"TT Chow","year":"2002","unstructured":"Chow, T.T., Zhang, G.Q., Lin, Z., & Song, C.L. (2002). Global optimization of absorption chiller system by genetic algorithm and neural network. Energy and Buildings, 34(1), 103\u2013109.","journal-title":"Energy and Buildings"},{"key":"9234_CR12","doi-asserted-by":"crossref","unstructured":"Conn, A.R., Scheinberg, K., & Vicente, L.N. (2009). Introduction To Derivative-free Optimization, volume 8. Siam.","DOI":"10.1137\/1.9780898718768"},{"issue":"1","key":"9234_CR13","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1137\/080718814","volume":"20","author":"G d\u2019Antonio","year":"2009","unstructured":"d\u2019Antonio, G., & Frangioni, A. (2009). Convergence analysis of deflected conditional approximate subgradient methods. SIAM Journal on Optimization, 20(1), 357\u2013386.","journal-title":"SIAM Journal on Optimization"},{"key":"9234_CR14","doi-asserted-by":"crossref","unstructured":"Focacci, F., Lodi, A., & Milano, M. (1999). Cost-based domain filtering.","DOI":"10.1007\/978-3-540-48085-3_14"},{"key":"9234_CR15","unstructured":"Ge, S.S., Hang, C.C., Lee, T.H., & Zhang, T. (2010). Stable adaptive neural network control. Springer Publishing Company, Incorporated."},{"key":"9234_CR16","unstructured":"Gent, I.P., Kotthoff, L., Miguel, I., & Nightingale, P. (2010). Machine learning for constraint solver design \u2013 A case study for the alldifferent constraint. CoRR, abs\/1008.4326."},{"key":"9234_CR17","doi-asserted-by":"crossref","unstructured":"Glover, F., Kelly, J.P., & Laguna, M. (1999). New Advances for Wedding optimization and simulation. In Proc. of WSC. IEEE (pp. 255\u2013260).","DOI":"10.1145\/324138.324223"},{"issue":"6","key":"9234_CR18","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1061\/(ASCE)TE.1943-5436.0000128","volume":"136","author":"K Gopalakrishnan","year":"2009","unstructured":"Gopalakrishnan, K., & Asce, A.M. (2009). Neural Network Swarm Intelligence Hybrid Nonlinear Optimization Algorithm for Pavement Moduli Back-Calculation. Journal of Transportation Engineering, 136(6), 528\u2013536.","journal-title":"Journal of Transportation Engineering"},{"key":"9234_CR19","doi-asserted-by":"crossref","unstructured":"Gualandi, S., & Malucelli, F. (2012). Resource constrained shortest paths with a super additive objective function. In Proc. of CP (pp. 299\u2013315): Springer.","DOI":"10.1007\/978-3-642-33558-7_24"},{"issue":"1","key":"9234_CR20","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/JSSC.2010.2079450","volume":"46","author":"J Howard","year":"2011","unstructured":"Howard, J., Dighe, S., Vangal, S.R., Ruhl, G., Borkar, N., Jain, S., Erraguntla, V., Konow, M., Riepen, M., Gries, M., & et al. (2011). A 48-core ia-32 processor in 45 nm cmos using on-die message-passing and dvfs for performance and power scaling. IEEE Journal of Solid-State Circuits, 46(1), 173\u2013183.","journal-title":"IEEE Journal of Solid-State Circuits"},{"issue":"5","key":"9234_CR21","doi-asserted-by":"crossref","first-page":"501","DOI":"10.1109\/TVLSI.2006.876103","volume":"14","author":"W Huang","year":"2006","unstructured":"Huang, W., Ghosh, S., & Velusamy, S. (2006). HotSpot: A compact thermal modeling methodology for early-stage VLSI design. IEEE Transactions on VLSI, 14 (5), 501\u2013513.","journal-title":"IEEE Transactions on VLSI"},{"key":"9234_CR22","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1613\/jair.2861","volume":"36","author":"F Hutter","year":"2009","unstructured":"Hutter, F., Hoos, H. H., Leyton-Brown, K., & Stu\u0307tzle, T. (2009). Paramils: An automatic algorithm configuration framework. Journal of Artificial Intelligence Research, 36, 267\u2013306.","journal-title":"Journal of Artificial Intelligence Research"},{"key":"9234_CR23","doi-asserted-by":"crossref","unstructured":"Jayaseelan, R., & Mitra, T. (2009). A hybrid local-global approach for multi-core thermal management. In Proc. of ICCAD (pp. 314\u2013320): ACM Press.","DOI":"10.1145\/1687399.1687459"},{"issue":"10","key":"9234_CR24","doi-asserted-by":"crossref","first-page":"1448","DOI":"10.1016\/j.neunet.2009.05.013","volume":"22","author":"S Kiranyaz","year":"2009","unstructured":"Kiranyaz, S., Ince, T., Yildirim, A., & Gabbouj, M. (2009). Evolutionary artificial neural networks by multi-dimensional particle swarm optimization. Neural Networks, 22(10), 1448\u20131462.","journal-title":"Neural Networks"},{"key":"9234_CR25","unstructured":"Lemar\u00e9chal, C. (2001). Lagrangian relaxation. In Computational Combinatorial Optimization (pp. 112\u2013156): Springer."},{"key":"9234_CR26","doi-asserted-by":"crossref","unstructured":"Ljung, L. (1999). System identification. Wiley Online Library.","DOI":"10.1002\/047134608X.W1046"},{"key":"9234_CR27","doi-asserted-by":"crossref","unstructured":"Lombardi, M., & Gualandi, S. (2013). A new propagator for two-layer neural networks in empirical model learning. In Proc. of CP (pp. 448\u2013463).","DOI":"10.1007\/978-3-642-40627-0_35"},{"key":"9234_CR28","unstructured":"Montana, D.J., & Davis, L. (1989). Training feedforward neural networks using genetic algorithms. In Proc. of IJCAI (pp. 762\u2013767)."},{"key":"9234_CR29","doi-asserted-by":"crossref","unstructured":"Moore, J., Chase, J.S., & Ranganathan, P. (2006). Weatherman: Automated, Online and Predictive Thermal Mapping and Management for Data Centers. In Proc. of ICAC. IEEE (pp. 155\u2013164).","DOI":"10.1109\/ICAC.2006.1662394"},{"key":"9234_CR30","unstructured":"Mor\u00e9, J.J. (1978). The Levenberg-Marquardt algorithm: implementation and theory. In Numerical analysis (pp. 105\u2013116): Springer."},{"issue":"1","key":"9234_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.paerosci.2005.02.001","volume":"41","author":"NV Queipo","year":"2005","unstructured":"Queipo, N.V., Haftka, R.T., Shyy, W., Goel, T., Vaidyanathan, R., & Tucker, P.K. (2005). Surrogate-based analysis and optimization. Progress In Aerospace Sciences, 41(1), 1\u201328.","journal-title":"Progress In Aerospace Sciences"},{"key":"9234_CR32","doi-asserted-by":"crossref","unstructured":"Sellmann, M. (2004). Theoretical foundations of cp-based lagrangian relaxation. In Proc. of CP (pp. 634\u2013647): Springer.","DOI":"10.1007\/978-3-540-30201-8_46"},{"issue":"1\u20134","key":"9234_CR33","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1023\/A:1021845304798","volume":"118","author":"M Sellmann","year":"2003","unstructured":"Sellmann, M., & Fahle, T. (2003). Constraint programming based lagrangian relaxation for the automatic recording problem. Annals of Operations Research, 118 (1\u20134), 17\u201333.","journal-title":"Annals of Operations Research"},{"key":"9234_CR34","doi-asserted-by":"crossref","unstructured":"Slusky, M.R., & van Hoeve, W.J. (2013). A lagrangian relaxation for golomb rulers. In Proc. of CPAIOR (pp. 251\u2013267): Springer.","DOI":"10.1007\/978-3-642-38171-3_17"},{"key":"9234_CR35","doi-asserted-by":"crossref","unstructured":"Van Cauwelaert, S., Lombardi, M., & Schaus, P. (2015). Understanding the potential of propagators. In Proc. of CPAIOR (pp. 427\u2013436).","DOI":"10.1007\/978-3-319-18008-3_29"},{"issue":"1","key":"9234_CR36","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0169-2070(97)00044-7","volume":"14","author":"G Zhang","year":"1998","unstructured":"Zhang, G., Patuwo, B.E., & Hu, M.Y. (1998). Forecasting with artificial neural networks: The state of the art. International Journal of Forecasting, 14(1), 35\u201362.","journal-title":"International Journal of Forecasting"}],"container-title":["Constraints"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10601-015-9234-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10601-015-9234-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10601-015-9234-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10601-015-9234-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T13:18:00Z","timestamp":1567343880000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10601-015-9234-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,12]]},"references-count":36,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["9234"],"URL":"https:\/\/doi.org\/10.1007\/s10601-015-9234-6","relation":{},"ISSN":["1383-7133","1572-9354"],"issn-type":[{"value":"1383-7133","type":"print"},{"value":"1572-9354","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,12]]}}}