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Comput."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>We consider the problem of computing optimal traffic light programs for urban road intersections using traffic flow conservation laws on networks. Based on a partial outer convexification approach, which has been successfully applied in the area of mixed-integer optimal control for systems of ordinary or differential algebraic equations, we develop a computationally tractable two-stage solution heuristic. The two-stage approach consists of the solution of a (smoothed) nonlinear programming problem with dynamic constraints and a reconstruction mixed-integer linear program without dynamic constraints. The two-stage approach is founded on a discrete approximation lemma for partial outer convexification, whose grid-independence properties for (smoothed) conservation laws are investigated. We use the two-stage approach to compute traffic light programs for two scenarios on different discretizations and demonstrate that the solution candidates cannot be improved in a reasonable amount of time by global state-of-the-art mixed-integer nonlinear programming solvers. The two-stage solution candidates are not only better than results obtained by global optimization of piecewise linearized traffic flow models but also can be computed at a faster rate.<\/jats:p>","DOI":"10.1137\/15m1048197","type":"journal-article","created":{"date-parts":[[2017,2,1]],"date-time":"2017-02-01T12:45:42Z","timestamp":1485953142000},"page":"B53-B75","source":"Crossref","is-referenced-by-count":21,"title":["Partial Outer Convexification for Traffic Light Optimization in Road Networks"],"prefix":"10.1137","volume":"39","author":[{"given":"Simone","family":"G\u00f6ttlich","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andreas","family":"Potschka","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ute","family":"Ziegler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,2,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1007\/s12532-008-0001-1"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1137\/0606047"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1080\/03605307908820117"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2010.2041976"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141004402683"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-007-0176-2"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/0-387-25570-2_6"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.trb.2011.04.001"},{"key":"atypb9","volume-title":"ZIB-Report (15-60)","author":"Gamreth G.","year":"2016"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1002\/oca.778"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1109\/TITS.2011.2141991"},{"key":"atypb12","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2014.10.001"},{"key":"atypb13","first-page":"2743251","author":"Gugat M.","year":"2016","journal-title":"Math. Probl. Eng."},{"key":"atypb14","volume-title":"Relaxation Methods for Hyperbolic PDE Mixed-Integer Optimal Control Problems, preprint","author":"Hante F. M.","year":"2015"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1007\/s10589-012-9518-3"},{"key":"atypb16","unstructured":"IBM Corporation,\n                      IBM ILOG CPLEX Optimization Studio\n                      ,http:\/\/www-03.ibm.com\/software\/products\/de\/ibmilogcpleoptistud\/(31 January 2017)."},{"key":"atypb17","unstructured":"M. Jung,\n                      Relaxations and Approximations for Mixed-Integer Optimal Control\n                      , Ph.D. thesis, University of Heidelberg, 2013."},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-38189-8_16"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1080\/10556788.2014.890196"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1002\/oca.892"},{"key":"atypb21","unstructured":"T. Koch,\n                      Rapid Mathematical Programming\n                      , Ph.D. thesis, TU Berlin, 2004."},{"key":"atypb22","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1955.0089"},{"key":"atypb23","first-page":"580546","author":"Ma D.","year":"2013","journal-title":"Math. Probl. Eng."},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1016\/0191-2615(93)90038-C"},{"key":"atypb25","doi-asserted-by":"publisher","DOI":"10.1287\/opre.4.1.42"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-010-0405-3"},{"key":"atypb27","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-011-0355-4"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21738-3"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-004-0559-y"},{"key":"atypb30","unstructured":"R. Wunderling,\n                      Paralleler und objektorientierter Simplex-Algorithmus\n                      , Ph.D. thesis, TU Berlin, 1996."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/15M1048197","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:23:20Z","timestamp":1787325800000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/15M1048197"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,1]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,1]]}},"alternative-id":["10.1137\/15M1048197"],"URL":"https:\/\/doi.org\/10.1137\/15m1048197","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,1]]}}}