{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T14:54:10Z","timestamp":1768402450638,"version":"3.49.0"},"publisher-location":"Cham","reference-count":44,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030589417","type":"print"},{"value":"9783030589424","type":"electronic"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-58942-4_25","type":"book-chapter","created":{"date-parts":[[2020,9,18]],"date-time":"2020-09-18T06:03:58Z","timestamp":1600409038000},"page":"381-398","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Multi-speed Gearbox Synthesis Using Global Search and Non-convex Optimization"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1747-9516","authenticated-orcid":false,"given":"Chiara","family":"Piacentini","sequence":"first","affiliation":[]},{"given":"Hyunmin","family":"Cheong","sequence":"additional","affiliation":[]},{"given":"Mehran","family":"Ebrahimi","sequence":"additional","affiliation":[]},{"given":"Adrian","family":"Butscher","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,19]]},"reference":[{"issue":"1","key":"25_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12532-018-0139-4","volume":"11","author":"JAE Andersson","year":"2019","unstructured":"Andersson, J.A.E., Gillis, J., Horn, G., Rawlings, J.B., Diehl, M.: CasADi: a software framework for nonlinear optimization and optimal control. Math. Program. Comput. 11(1), 1\u201336 (2019). https:\/\/doi.org\/10.1007\/s12532-018-0139-4","journal-title":"Math. Program. Comput."},{"key":"25_CR2","unstructured":"Berx, K., Gadeyne, K., Dhadamus, M., Pipeleers, G., Pinte, G.: Model-based gearbox synthesis. In: Mechatronics Forum International Conference, pp. 599\u2013605 (2014)"},{"key":"25_CR3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex Optimization","author":"S Boyd","year":"2004","unstructured":"Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)"},{"key":"25_CR4","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.advengsoft.2013.11.002","volume":"68","author":"O Buiga","year":"2014","unstructured":"Buiga, O., Tudose, L.: Optimal mass minimization design of a two-stage coaxial helical speed reducer with genetic algorithms. Adv. Eng. Softw. 68, 25\u201332 (2014)","journal-title":"Adv. Eng. Softw."},{"key":"25_CR5","unstructured":"Castro, M.P., Piacentini, C., Cire, A.A., Beck, J.C.: Relaxed decision diagrams for cost-optimal classical planning. In: Workshop HSDIP, ICAPS, pp. 50\u201358 (2018)"},{"issue":"2","key":"25_CR6","doi-asserted-by":"publisher","first-page":"021003","DOI":"10.1115\/1.3593409","volume":"11","author":"A Chakrabarti","year":"2011","unstructured":"Chakrabarti, A., et al.: Computer-based design synthesis research: an overview. J. Comput. Inf. Sci. Eng. 11(2), 021003 (2011)","journal-title":"J. Comput. Inf. Sci. Eng."},{"key":"25_CR7","doi-asserted-by":"crossref","unstructured":"Cheong, H., Ebrahimi, M., Butscher, A., Iorio, F.: Configuration design of mechanical assemblies using an estimation of distribution algorithm and constraint programming. In: 2019 IEEE Congress on Evolutionary Computation (CEC), pp. 2339\u20132346. IEEE (2019)","DOI":"10.1109\/CEC.2019.8789944"},{"key":"25_CR8","doi-asserted-by":"crossref","unstructured":"Chlamt\u00e1\u010d, E., Dinitz, M., Makarychev, Y.: Minimizing the union: tight approximations for small set bipartite vertex expansion. In: Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 881\u2013899. SIAM (2017)","DOI":"10.1137\/1.9781611974782.56"},{"key":"25_CR9","doi-asserted-by":"crossref","unstructured":"Chomsky, N., Lightfoot, D.W.: Syntactic structures. Walter de Gruyter (1957)","DOI":"10.1515\/9783112316009"},{"issue":"1","key":"25_CR10","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1299\/jsmec.44.291","volume":"44","author":"TH Chong","year":"2001","unstructured":"Chong, T.H., Bae, I., Kubo, A.: Multiobjective optimal design of cylindrical gear pairs for the reduction of gear size and meshing vibration. JSME Int J., Ser. C 44(1), 291\u2013298 (2001)","journal-title":"JSME Int J., Ser. C"},{"issue":"3","key":"25_CR11","doi-asserted-by":"publisher","first-page":"609","DOI":"10.1115\/1.1596242","volume":"125","author":"K Deb","year":"2003","unstructured":"Deb, K., Jain, S.: Multi-speed gearbox design using multi-objective evolutionary algorithms. J. Mech. Des. 125(3), 609\u2013619 (2003)","journal-title":"J. Mech. Des."},{"issue":"3","key":"25_CR12","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1145\/3828.3830","volume":"32","author":"R Dechter","year":"1985","unstructured":"Dechter, R., Pearl, J.: Generalized best-first search strategies and the optimality of A. J. ACM (JACM) 32(3), 505\u2013536 (1985)","journal-title":"J. ACM (JACM)"},{"key":"25_CR13","volume-title":"Multicriteria Design Optimization: Procedures and Applications","author":"H Eschenauer","year":"2012","unstructured":"Eschenauer, H., Koski, J., Osyczka, A.: Multicriteria Design Optimization: Procedures and Applications. Springer, Heidelberg (2012)"},{"issue":"3","key":"25_CR14","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.swevo.2011.08.003","volume":"1","author":"M Hauschild","year":"2011","unstructured":"Hauschild, M., Pelikan, M.: An introduction and survey of estimation of distribution algorithms. Swarm Evol. Comput. 1(3), 111\u2013128 (2011)","journal-title":"Swarm Evol. Comput."},{"issue":"5","key":"25_CR15","doi-asserted-by":"publisher","first-page":"1080","DOI":"10.1007\/BF02984029","volume":"19","author":"HZ Huang","year":"2005","unstructured":"Huang, H.Z., Tian, Z.G., Zuo, M.J.: Multiobjective optimization of three-stage spur gear reduction units using interactive physical programming. J. Mech. Sci. Technol. 19(5), 1080\u20131086 (2005)","journal-title":"J. Mech. Sci. Technol."},{"issue":"1","key":"25_CR16","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1007\/BF00047572","volume":"12","author":"CR Hwang","year":"1988","unstructured":"Hwang, C.R.: Simulated annealing: theory and applications. Acta Applicandae Mathematicae 12(1), 108\u2013111 (1988)","journal-title":"Acta Applicandae Mathematicae"},{"issue":"3","key":"25_CR17","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0094-114X(90)90030-N","volume":"25","author":"P Jain","year":"1990","unstructured":"Jain, P., Agogino, A.M.: Theory of design: an optimization perspective. Mech. Mach. Theory 25(3), 287\u2013303 (1990)","journal-title":"Mech. Mach. Theory"},{"issue":"1","key":"25_CR18","doi-asserted-by":"publisher","first-page":"011102","DOI":"10.1115\/1.4031714","volume":"138","author":"C K\u00f6nigseder","year":"2016","unstructured":"K\u00f6nigseder, C., Shea, K.: Comparing strategies for topologic and parametric rule application in automated computational design synthesis. J. Mech. Des. 138(1), 011102 (2016)","journal-title":"J. Mech. Des."},{"issue":"3","key":"25_CR19","doi-asserted-by":"publisher","first-page":"497","DOI":"10.2307\/1910129","volume":"28","author":"A Land","year":"1960","unstructured":"Land, A., Doig, A.: An automatic method of solving discrete programming problems. Econometrica 28(3), 497\u2013520 (1960)","journal-title":"Econometrica"},{"issue":"5","key":"25_CR20","doi-asserted-by":"publisher","first-page":"895","DOI":"10.1115\/1.1767823","volume":"126","author":"X Li","year":"2004","unstructured":"Li, X., Schmidt, L.: Grammar-based designer assistance tool for epicyclic gear trains. J. Mech. Des. 126(5), 895\u2013902 (2004)","journal-title":"J. Mech. Des."},{"key":"25_CR21","doi-asserted-by":"crossref","unstructured":"Lin, Y.S., Shea, K., Johnson, A., Coultate, J., Pears, J.: A method and software tool for automated gearbox synthesis. In: ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, pp. 111\u2013121. American Society of Mechanical Engineers Digital Collection (2009)","DOI":"10.1115\/DETC2009-86935"},{"key":"25_CR22","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.jsc.2013.09.003","volume":"60","author":"BD McKay","year":"2014","unstructured":"McKay, B.D., Piperno, A.: Practical graph isomorphism, II. J. Symb. Comput. 60, 94\u2013112 (2014)","journal-title":"J. Symb. Comput."},{"key":"25_CR23","unstructured":"Mittal, S., Frayman, F.: Towards a generic model of configuraton tasks. In: IJCAI, vol. 89, pp. 1395\u20131401. Citeseer (1989)"},{"issue":"3","key":"25_CR24","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/BF01578994","volume":"2","author":"S Mullins","year":"1991","unstructured":"Mullins, S., Rinderle, J.R.: Grammatical approaches to engineering design, part i: an introduction and commentary. Res. Eng. Design 2(3), 121\u2013135 (1991)","journal-title":"Res. Eng. Design"},{"key":"25_CR25","unstructured":"Murthy, S.S., Addanki, S.: PROMPT: an innovative design tool. IBM Thomas J, Watson Research Division (1987)"},{"issue":"3","key":"25_CR26","first-page":"137","volume":"5","author":"BA Nadel","year":"1991","unstructured":"Nadel, B.A., Lin, J.: Automobile transmission design as a constraint satisfaction problem: modelling the kinematic level. AI EDAM 5(3), 137\u2013171 (1991)","journal-title":"AI EDAM"},{"issue":"3","key":"25_CR27","doi-asserted-by":"publisher","first-page":"309","DOI":"10.1016\/0045-7825(78)90046-4","volume":"15","author":"A Osyczka","year":"1978","unstructured":"Osyczka, A.: An approach to multicriterion optimization problems for engineering design. Comput. Methods Appl. Mech. Eng. 15(3), 309\u2013333 (1978)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"issue":"3","key":"25_CR28","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1115\/1.2826695","volume":"117","author":"L Pomrehn","year":"1995","unstructured":"Pomrehn, L., Papalambros, P.: Discrete optimal design formulations with application to gear train design. J. Mech. Des. 117(3), 419\u2013424 (1995)","journal-title":"J. Mech. Des."},{"issue":"2","key":"25_CR29","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/0010-4485(88)90053-X","volume":"20","author":"S Prayoonrat","year":"1988","unstructured":"Prayoonrat, S., Walton, D.: Practical approach to optimum gear train design. Comput. Aided Des. 20(2), 83\u201392 (1988)","journal-title":"Comput. Aided Des."},{"key":"25_CR30","doi-asserted-by":"publisher","first-page":"718","DOI":"10.1016\/j.procs.2018.07.127","volume":"133","author":"P Rai","year":"2018","unstructured":"Rai, P., Agrawal, A., Saini, M.L., Jodder, C., Barman, A.G.: Volume optimization of helical gear with profile shift using real coded genetic algorithm. Procedia Comput. Sci. 133, 718\u2013724 (2018)","journal-title":"Procedia Comput. Sci."},{"issue":"3","key":"25_CR31","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1016\/j.mechmachtheory.2009.10.010","volume":"45","author":"V Savsani","year":"2010","unstructured":"Savsani, V., Rao, R., Vakharia, D.: Optimal weight design of a gear train using particle swarm optimization and simulated annealing algorithms. Mech. Mach. Theory 45(3), 531\u2013541 (2010)","journal-title":"Mech. Mach. Theory"},{"issue":"4","key":"25_CR32","doi-asserted-by":"publisher","first-page":"371","DOI":"10.1115\/1.1315299","volume":"122","author":"LC Schmidt","year":"1999","unstructured":"Schmidt, L.C., Shetty, H., Chase, S.C.: A graph grammar approach for structure synthesis of mechanisms. J. Mech. Des. 122(4), 371\u2013376 (1999)","journal-title":"J. Mech. Des."},{"issue":"1","key":"25_CR33","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01197554","volume":"14","author":"J Sobieszczanski-Sobieski","year":"1997","unstructured":"Sobieszczanski-Sobieski, J., Haftka, R.T.: Multidisciplinary aerospace design optimization: survey of recent developments. Struct. Optim. 14(1), 1\u201323 (1997)","journal-title":"Struct. Optim."},{"issue":"11","key":"25_CR34","doi-asserted-by":"publisher","first-page":"1351","DOI":"10.1080\/0305215X.2011.646264","volume":"44","author":"A Swantner","year":"2012","unstructured":"Swantner, A., Campbell, M.I.: Topological and parametric optimization of gear trains. Eng. Optim. 44(11), 1351\u20131368 (2012)","journal-title":"Eng. Optim."},{"key":"25_CR35","unstructured":"TREMEC: Tremec. http:\/\/www.tremec.com . Accessed 28 Nov 2019"},{"key":"25_CR36","doi-asserted-by":"crossref","unstructured":"Tsai, L.W., Maki, E., Liu, T., Kapil, N.: The categorization of planetary gear trains for automatic transmissions according to kinematic topology. Technical report, SAE Technical Paper (1988)","DOI":"10.4271\/885062"},{"issue":"3","key":"25_CR37","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1137\/0208032","volume":"8","author":"LG Valiant","year":"1979","unstructured":"Valiant, L.G.: The complexity of enumeration and reliability problems. SIAM J. Comput. 8(3), 410\u2013421 (1979)","journal-title":"SIAM J. Comput."},{"key":"25_CR38","unstructured":"Vinterbo, S.A.: A note on the hardness of the k-ambiguity problem. Technical Report DSG-T R-2002-006 (2002)"},{"issue":"1","key":"25_CR39","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/s10107-004-0559-y","volume":"106","author":"A W\u00e4chter","year":"2006","unstructured":"W\u00e4chter, A., Biegler, L.T.: On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25\u201357 (2006)","journal-title":"Math. Program."},{"issue":"4","key":"25_CR40","doi-asserted-by":"publisher","first-page":"370","DOI":"10.1115\/1.2429697","volume":"129","author":"GG Wang","year":"2006","unstructured":"Wang, G.G., Shan, S.: Review of metamodeling techniques in support of engineering design optimization. J. Mech. Des. 129(4), 370\u2013380 (2006)","journal-title":"J. Mech. Des."},{"issue":"7","key":"25_CR41","doi-asserted-by":"publisher","first-page":"1071","DOI":"10.1016\/0094-114X(94)90074-4","volume":"29","author":"H Wang","year":"1994","unstructured":"Wang, H., Wang, H.P.: Optimal engineering design of spur gear sets. Mech. Mach. Theory 29(7), 1071\u20131080 (1994)","journal-title":"Mech. Mach. Theory"},{"issue":"1","key":"25_CR42","first-page":"139","volume":"44","author":"J Wojnarowski","year":"2006","unstructured":"Wojnarowski, J., Kope\u0107, J., Zawi\u015blak, S.: Gears and graphs. J. Theor. Appl. Mech. 44(1), 139\u2013162 (2006)","journal-title":"J. Theor. Appl. Mech."},{"issue":"3\u20134","key":"25_CR43","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1016\/S0360-8352(98)00149-1","volume":"35","author":"T Yokota","year":"1998","unstructured":"Yokota, T., Taguchi, T., Gen, M.: A solution method for optimal weight design problem of the gear using genetic algorithms. Comput. Ind. Eng. 35(3\u20134), 523\u2013526 (1998)","journal-title":"Comput. Ind. Eng."},{"issue":"4","key":"25_CR44","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1016\/0010-4485(93)90055-S","volume":"25","author":"H Zarefar","year":"1993","unstructured":"Zarefar, H., Muthukrishnan, S.: Computer-aided optimal design via modified adaptive random-search algorithm. Comput. Aided Des. 25(4), 240\u2013248 (1993)","journal-title":"Comput. Aided Des."}],"container-title":["Lecture Notes in Computer Science","Integration of Constraint Programming, Artificial Intelligence, and Operations Research"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-58942-4_25","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,19]],"date-time":"2022-11-19T00:58:49Z","timestamp":1668819529000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-58942-4_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030589417","9783030589424"],"references-count":44,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-58942-4_25","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"19 September 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CPAIOR","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Vienna","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Austria","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 September 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24 September 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cpaior2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/cpaior2020.dbai.tuwien.ac.at\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"72","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"25","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"7","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"35% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.08","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.08","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}