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Volumn 37, Issue 3, 2010, Pages 582-597

Decomposition, reformulation, and diving in university course timetabling

Author keywords

Decomposition; Diving; Heuristic; Integer programming; Metaheuristic; Reformulation; Soft constraints; University course timetabling

Indexed keywords

DIVING; HEURISTIC; METAHEURISTIC; REFORMULATION; SOFT CONSTRAINTS; UNIVERSITY COURSE TIMETABLING;

EID: 70349279898     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cor.2009.02.023     Document Type: Article
Times cited : (80)

References (73)
  • 1
    • 33846865758 scopus 로고    scopus 로고
    • Investigating Ahuja-Orlin's large neighbourhood search approach for examination timetabling
    • Abdullah S., Ahmadi S., Burke E.K., and Dror M. Investigating Ahuja-Orlin's large neighbourhood search approach for examination timetabling. OR Spectrum 29 2 (2007) 351-372
    • (2007) OR Spectrum , vol.29 , Issue.2 , pp. 351-372
    • Abdullah, S.1    Ahmadi, S.2    Burke, E.K.3    Dror, M.4
  • 2
    • 35348877211 scopus 로고    scopus 로고
    • A tabu-based large neighbourhood search methodology for the capacitated examination timetabling problem
    • Abdullah S., Ahmadi S., Burke E.K., Dror M., and McCollum B. A tabu-based large neighbourhood search methodology for the capacitated examination timetabling problem. J Oper Res Soc 58 (2006) 1494-1502
    • (2006) J Oper Res Soc , vol.58 , pp. 1494-1502
    • Abdullah, S.1    Ahmadi, S.2    Burke, E.K.3    Dror, M.4    McCollum, B.5
  • 3
    • 70349270943 scopus 로고    scopus 로고
    • Achterberg T. SCIP-A framework to integrate constraint and mixed integer programming. ZIB Technical Report TR-04-19; 2004.
    • Achterberg T. SCIP-A framework to integrate constraint and mixed integer programming. ZIB Technical Report TR-04-19; 2004.
  • 4
    • 84867980790 scopus 로고    scopus 로고
    • A survey of very large-scale neighborhood search techniques
    • Ahuja R.K., Ergun O., Orlin J.B., and Punnen A.P. A survey of very large-scale neighborhood search techniques. Discrete Appl Math 123 1-3 (2002) 75-102
    • (2002) Discrete Appl Math , vol.123 , Issue.1-3 , pp. 75-102
    • Ahuja, R.K.1    Ergun, O.2    Orlin, J.B.3    Punnen, A.P.4
  • 5
    • 33847014136 scopus 로고    scopus 로고
    • A mixed-integer programming approach to a class timetabling problem: a case study with gender policies and traffic considerations
    • Al-Yakoob S.M., and Sherali H.D. A mixed-integer programming approach to a class timetabling problem: a case study with gender policies and traffic considerations. Eur J Oper Res 180 3 (2007) 1028-1044
    • (2007) Eur J Oper Res , vol.180 , Issue.3 , pp. 1028-1044
    • Al-Yakoob, S.M.1    Sherali, H.D.2
  • 6
    • 36049033365 scopus 로고    scopus 로고
    • A computational study of local search algorithms for Italian high-school timetabling
    • Avella P., D'Auria B., Salerno S., and Vasil'Ev I. A computational study of local search algorithms for Italian high-school timetabling. J Heuristics 13 6 (2007) 543-556
    • (2007) J Heuristics , vol.13 , Issue.6 , pp. 543-556
    • Avella, P.1    D'Auria, B.2    Salerno, S.3    Vasil'Ev, I.4
  • 7
    • 26644466566 scopus 로고    scopus 로고
    • A computational study of a cutting plane algorithm for university course timetabling
    • Avella P., and Vasil'ev I. A computational study of a cutting plane algorithm for university course timetabling. J Scheduling 8 6 (2005) 497-514
    • (2005) J Scheduling , vol.8 , Issue.6 , pp. 497-514
    • Avella, P.1    Vasil'ev, I.2
  • 8
    • 84897565088 scopus 로고    scopus 로고
    • Computer-aided school and university timetabling: the new wave
    • Burke E.K., and Ross P. (Eds), Springer, Berlin
    • Bardadym V.A. Computer-aided school and university timetabling: the new wave. In: Burke E.K., and Ross P. (Eds). Practice and theory of automated timetabling. Lecture notes in computer science vol. 1153 (1996), Springer, Berlin 22-45
    • (1996) Practice and theory of automated timetabling. Lecture notes in computer science , vol.1153 , pp. 22-45
    • Bardadym, V.A.1
  • 9
    • 0027699082 scopus 로고
    • Formulating a mixed integer programming problem to improve solvability
    • Barnhart C., Johnson E.L., Nemhauser G.L., Sigismondi G., and Vance P. Formulating a mixed integer programming problem to improve solvability. Oper Res 41 6 (1993) 1013-1019
    • (1993) Oper Res , vol.41 , Issue.6 , pp. 1013-1019
    • Barnhart, C.1    Johnson, E.L.2    Nemhauser, G.L.3    Sigismondi, G.4    Vance, P.5
  • 10
    • 70349284808 scopus 로고    scopus 로고
    • Heuristics of the branch-cut-and-price-framework SCIP, TR-07-30, Berlin;
    • Berthold T. Heuristics of the branch-cut-and-price-framework SCIP. ZIB Technical Report TR-07-30, Berlin; 2007.
    • (2007) ZIB Technical Report
    • Berthold, T.1
  • 11
    • 70349270942 scopus 로고    scopus 로고
    • RENS-relaxation enforced neighborhood search
    • TR-07-28, Berlin;
    • Berthold T. RENS-relaxation enforced neighborhood search. ZIB Technical Report TR-07-28, Berlin; 2007.
    • (2007) ZIB Technical Report
    • Berthold, T.1
  • 14
    • 0344236266 scopus 로고    scopus 로고
    • Metaheuristics in combinatorial optimization: overview and conceptual comparison
    • Blum C., and Roli A. Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35 3 (2003) 268-308
    • (2003) ACM Comput Surv , vol.35 , Issue.3 , pp. 268-308
    • Blum, C.1    Roli, A.2
  • 15
    • 27844501135 scopus 로고    scopus 로고
    • Equitable colorings of bounded treewidth graphs
    • Bodlaender H.L., and Fomin F.V. Equitable colorings of bounded treewidth graphs. Theor Comput Sci 349 1 (2005) 22-30
    • (2005) Theor Comput Sci , vol.349 , Issue.1 , pp. 22-30
    • Bodlaender, H.L.1    Fomin, F.V.2
  • 16
    • 0033114970 scopus 로고    scopus 로고
    • A multi-stage evolutionary algorithm for the timetable problem
    • Burke E., and Newall J. A multi-stage evolutionary algorithm for the timetable problem. IEEE Trans Evol Comput 13 1 (1999) 63-74
    • (1999) IEEE Trans Evol Comput , vol.13 , Issue.1 , pp. 63-74
    • Burke, E.1    Newall, J.2
  • 17
    • 3042756825 scopus 로고    scopus 로고
    • Applications to timetabling
    • Gross J.L., and Yellen J. (Eds), CRC, London, UK
    • Burke E.K., de Werra D., and Kingston J.H. Applications to timetabling. In: Gross J.L., and Yellen J. (Eds). Handbook of graph theory (2004), CRC, London, UK 445-474
    • (2004) Handbook of graph theory , pp. 445-474
    • Burke, E.K.1    de Werra, D.2    Kingston, J.H.3
  • 18
    • 0031368151 scopus 로고    scopus 로고
    • Automated university timetabling: the state of the art
    • Burke E.K., Jackson K., Kingston J.H., and Weare R.F. Automated university timetabling: the state of the art. Comput J 40 9 (1997) 565-571
    • (1997) Comput J , vol.40 , Issue.9 , pp. 565-571
    • Burke, E.K.1    Jackson, K.2    Kingston, J.H.3    Weare, R.F.4
  • 19
    • 70349287933 scopus 로고    scopus 로고
    • On a clique-based integer programming formulation of vertex colouring with applications in course timetabling
    • Technical Report NOTTCS-TR-2007-10, The University of Nottingham, Nottingham;, Also available at
    • Burke EK, Mareček J, Parkes AJ, Rudová H. On a clique-based integer programming formulation of vertex colouring with applications in course timetabling. Technical Report NOTTCS-TR-2007-10, The University of Nottingham, Nottingham; 2007. Also available at: 〈http://arxiv.org/abs/0710.3603〉.
    • (2007)
    • Burke, E.K.1    Mareček, J.2    Parkes, A.J.3    Rudová, H.4
  • 21
    • 70349300189 scopus 로고    scopus 로고
    • Penalising patterns in timetables: novel integer programming formulations
    • Nickel S., and Kalcsics J. (Eds), Springer, Berlin
    • Burke E.K., Mareček J., Parkes A.J., and Rudová H. Penalising patterns in timetables: novel integer programming formulations. In: Nickel S., and Kalcsics J. (Eds). Operations research proceedings 2007 (2008), Springer, Berlin 409-414
    • (2008) Operations research proceedings 2007 , pp. 409-414
    • Burke, E.K.1    Mareček, J.2    Parkes, A.J.3    Rudová, H.4
  • 22
    • 0037118761 scopus 로고    scopus 로고
    • Recent research directions in automated timetabling
    • Burke E.K., and Petrovic S. Recent research directions in automated timetabling. Eur J Oper Res 140 2 (2002) 266-280
    • (2002) Eur J Oper Res , vol.140 , Issue.2 , pp. 266-280
    • Burke, E.K.1    Petrovic, S.2
  • 23
    • 0344642507 scopus 로고    scopus 로고
    • A taxonomy of evolutionary algorithms in combinatorial optimization
    • Calégari P., Coray G., Hertz A., Kobler D., and Kuonen P. A taxonomy of evolutionary algorithms in combinatorial optimization. J Heuristics 5 2 (1999) 145-158
    • (1999) J Heuristics , vol.5 , Issue.2 , pp. 145-158
    • Calégari, P.1    Coray, G.2    Hertz, A.3    Kobler, D.4    Kuonen, P.5
  • 24
    • 17144420325 scopus 로고
    • A Lagrangian relaxation approach to the classroom assignment problem
    • Carter M.W. A Lagrangian relaxation approach to the classroom assignment problem. INFORMS J Comput 27 (1989) 230-245
    • (1989) INFORMS J Comput , vol.27 , pp. 230-245
    • Carter, M.W.1
  • 26
    • 32044469861 scopus 로고    scopus 로고
    • Vehicle routing problem with elementary shortest path based column generation
    • Chabrier A. Vehicle routing problem with elementary shortest path based column generation. Comput Oper Res 33 10 (2006) 2972-2990
    • (2006) Comput Oper Res , vol.33 , Issue.10 , pp. 2972-2990
    • Chabrier, A.1
  • 27
    • 12344255882 scopus 로고    scopus 로고
    • Exploring relaxation induced neighborhoods to improve MIP solutions
    • Danna E., Rothberg E., and Pape C.L. Exploring relaxation induced neighborhoods to improve MIP solutions. Math Program 102 1 (2005) 71-90
    • (2005) Math Program , vol.102 , Issue.1 , pp. 71-90
    • Danna, E.1    Rothberg, E.2    Pape, C.L.3
  • 28
    • 1642408472 scopus 로고    scopus 로고
    • An integer programming formulation for a case study in university timetabling
    • Daskalaki S., Birbas T., and Housos E. An integer programming formulation for a case study in university timetabling. Eur J Oper Res 153 (2004) 117-135
    • (2004) Eur J Oper Res , vol.153 , pp. 117-135
    • Daskalaki, S.1    Birbas, T.2    Housos, E.3
  • 29
    • 3943104749 scopus 로고    scopus 로고
    • Efficient solutions for a university timetabling problem through integer programming
    • Daskalaki S., Birbas T., and Housos E. Efficient solutions for a university timetabling problem through integer programming. Eur J Oper Res 160 (2005) 106-120
    • (2005) Eur J Oper Res , vol.160 , pp. 106-120
    • Daskalaki, S.1    Birbas, T.2    Housos, E.3
  • 30
    • 70349283365 scopus 로고    scopus 로고
    • Di Gaspero L, McCollum B, Schaerf A. The second international timetabling competition (ITC-2007): curriculum-based course timetabling (Track 3). Technical Report QUB/IEEE 2007/08/01, University of Udine DIEGM, Udine, Italy; 2007.
    • Di Gaspero L, McCollum B, Schaerf A. The second international timetabling competition (ITC-2007): curriculum-based course timetabling (Track 3). Technical Report QUB/IEEE 2007/08/01, University of Udine DIEGM, Udine, Italy; 2007.
  • 31
    • 35248849915 scopus 로고    scopus 로고
    • Di Gaspero L, Schaerf A. Multi neighborhood local search with application to the course timetabling problem. In: Burke EK, Causmaecker PD, editors. 4th international conference on practice and theory of automated timetabling, PATAT 2002, Gent, Belgium, August 21-23, 2002. Lecture notes in computer science, 2740. Berlin: Springer; 2003. p. 262-75 [selected revised papers].
    • Di Gaspero L, Schaerf A. Multi neighborhood local search with application to the course timetabling problem. In: Burke EK, Causmaecker PD, editors. 4th international conference on practice and theory of automated timetabling, PATAT 2002, Gent, Belgium, August 21-23, 2002. Lecture notes in computer science, vol. 2740. Berlin: Springer; 2003. p. 262-75 [selected revised papers].
  • 32
    • 33645316775 scopus 로고    scopus 로고
    • Neighborhood portfolio approach for local search applied to timetabling problems
    • DiGaspero L., and Schaerf A. Neighborhood portfolio approach for local search applied to timetabling problems. J Math Model Algorithms 5 1 (2006) 65-89
    • (2006) J Math Model Algorithms , vol.5 , Issue.1 , pp. 65-89
    • DiGaspero, L.1    Schaerf, A.2
  • 33
    • 1642340391 scopus 로고    scopus 로고
    • An automated university course timetabling system developed in a distributed environment: a case study
    • Dimopoulou M., and Miliotis P. An automated university course timetabling system developed in a distributed environment: a case study. Eur J Oper Res 153 (2004) 136-147
    • (2004) Eur J Oper Res , vol.153 , pp. 136-147
    • Dimopoulou, M.1    Miliotis, P.2
  • 36
    • 0001488083 scopus 로고
    • On the complexity of timetable and multicommodity flow problems
    • Even S., Itai A., and Shamir A. On the complexity of timetable and multicommodity flow problems. SIAM J Comput 5 4 (1976) 691-703
    • (1976) SIAM J Comput , vol.5 , Issue.4 , pp. 691-703
    • Even, S.1    Itai, A.2    Shamir, A.3
  • 38
    • 3042564211 scopus 로고    scopus 로고
    • Local branching
    • Fischetti M., and Lodi A. Local branching. Math Program 98 1 (2003) 23-47
    • (2003) Math Program , vol.98 , Issue.1 , pp. 23-47
    • Fischetti, M.1    Lodi, A.2
  • 39
    • 70349269433 scopus 로고    scopus 로고
    • Forrest J, de la Nuez D, Lougee-Heimer R. CLP User guide. Technical Report, Yorktown Heights, NY; 2004.
    • Forrest J, de la Nuez D, Lougee-Heimer R. CLP User guide. Technical Report, Yorktown Heights, NY; 2004.
  • 40
    • 24344436349 scopus 로고    scopus 로고
    • 1984-2004-20 years of multiobjective metaheuristics. But what about the solution of combinatorial problems with multiple objectives?
    • Coello C.A.C., Aguirre A.H., and Zitzler E. (Eds), Springer, Berlin
    • Gandibleux X., and Ehrgott M. 1984-2004-20 years of multiobjective metaheuristics. But what about the solution of combinatorial problems with multiple objectives?. In: Coello C.A.C., Aguirre A.H., and Zitzler E. (Eds). Evolutionary multi-criterion optimization. Lecture notes in computer science vol. 3410 (2005), Springer, Berlin 33-46
    • (2005) Evolutionary multi-criterion optimization. Lecture notes in computer science , vol.3410 , pp. 33-46
    • Gandibleux, X.1    Ehrgott, M.2
  • 43
    • 0345792410 scopus 로고    scopus 로고
    • Progress in linear programming-based algorithms for integer programming: an exposition
    • Johnson E.L., Nemhauser G.L., and Savelsbergh M.W. Progress in linear programming-based algorithms for integer programming: an exposition. INFORMS J Comput 12 1 (2000) 2-23
    • (2000) INFORMS J Comput , vol.12 , Issue.1 , pp. 2-23
    • Johnson, E.L.1    Nemhauser, G.L.2    Savelsbergh, M.W.3
  • 44
    • 85057110593 scopus 로고    scopus 로고
    • Curriculum based course timetabling: Optimal solutions to the udine benchmark instances
    • Burke EK, Gendreau M, editors, Montréal, Canada, August 19-22, Montréal, Canada: Université de Montréal;, 2008
    • Lach G, Lübbecke ME. Curriculum based course timetabling: optimal solutions to the udine benchmark instances. In: Burke EK, Gendreau M, editors. Proceedings of the 7th international conference on practice and theory of automated timetabling, PATAT 2008, Montréal, Canada, August 19-22, 2008. Montréal, Canada: Université de Montréal; 2008.
    • (2008) Proceedings of the 7th international conference on practice and theory of automated timetabling, PATAT
    • Lach, G.1    Lübbecke, M.E.2
  • 45
    • 45449087055 scopus 로고    scopus 로고
    • Optimal university course timetables and the partial transversal polytope
    • McGeoch C.C. (Ed), Springer, Berlin
    • Lach G., and Lübbecke M.E. Optimal university course timetables and the partial transversal polytope. In: McGeoch C.C. (Ed). WEA. Lecture notes in computer science vol. 5038 (2008), Springer, Berlin 235-248
    • (2008) WEA. Lecture notes in computer science , vol.5038 , pp. 235-248
    • Lach, G.1    Lübbecke, M.E.2
  • 46
    • 0010603512 scopus 로고
    • An integer linear programming model of a school timetabling problem
    • Lawrie N.L. An integer linear programming model of a school timetabling problem. Comput J 12 (1969) 307-316
    • (1969) Comput J , vol.12 , pp. 307-316
    • Lawrie, N.L.1
  • 48
    • 84908780328 scopus 로고
    • Computer solutions to the travelling salesman problems
    • Lin S. Computer solutions to the travelling salesman problems. Bell Syst Tech J 44 10 (1965) 2245-2269
    • (1965) Bell Syst Tech J , vol.44 , Issue.10 , pp. 2245-2269
    • Lin, S.1
  • 49
    • 38549140043 scopus 로고    scopus 로고
    • McCollum B. A perspective on bridging the gap between theory and practice in university timetabling. In: Burke EK, Rudová H, editors. 6th international conference on practice and theory of automated timetabling, PATAT 2006, Brno, The Czech Republic, August 30-September 1, 2006. Lecture notes in computer science, 3867. Berlin: Springer; 2007. p. 3-23 [selected revised papers].
    • McCollum B. A perspective on bridging the gap between theory and practice in university timetabling. In: Burke EK, Rudová H, editors. 6th international conference on practice and theory of automated timetabling, PATAT 2006, Brno, The Czech Republic, August 30-September 1, 2006. Lecture notes in computer science, vol. 3867. Berlin: Springer; 2007. p. 3-23 [selected revised papers].
  • 50
  • 51
    • 33644908527 scopus 로고    scopus 로고
    • A computational approach to enhancing course timetabling with integer programming
    • Mirhassani S.A. A computational approach to enhancing course timetabling with integer programming. Appl Math Comput 175 (2006) 814-822
    • (2006) Appl Math Comput , vol.175 , pp. 814-822
    • Mirhassani, S.A.1
  • 52
    • 85007158545 scopus 로고    scopus 로고
    • Müller T. Itc2007 solver description: a hybrid approach. In: Burke EK, Gendreau M, editors. In: Proceedings of the 7th international conference on practice and theory of automated timetabling, PATAT 2008, Montréal, Canada, August 19-22, 2008. Montréal, Canada: Université de Montréal; 2008.
    • Müller T. Itc2007 solver description: a hybrid approach. In: Burke EK, Gendreau M, editors. In: Proceedings of the 7th international conference on practice and theory of automated timetabling, PATAT 2008, Montréal, Canada, August 19-22, 2008. Montréal, Canada: Université de Montréal; 2008.
  • 53
    • 38549145846 scopus 로고    scopus 로고
    • Murray K, Müller T, Rudová H. Modeling and solution of a complex university course timetabling problem. In: Burke EK, Rudová H, editors. 6th international conference on practice and theory of automated timetabling, PATAT 2006, Brno, The Czech Republic, August 30-September 1, 2006. Lecture notes in computer science, 3867. Berlin: Springer; 2007. p. 189-209 [selected revised papers].
    • Murray K, Müller T, Rudová H. Modeling and solution of a complex university course timetabling problem. In: Burke EK, Rudová H, editors. 6th international conference on practice and theory of automated timetabling, PATAT 2006, Brno, The Czech Republic, August 30-September 1, 2006. Lecture notes in computer science, vol. 3867. Berlin: Springer; 2007. p. 189-209 [selected revised papers].
  • 56
    • 33846068585 scopus 로고    scopus 로고
    • A general heuristic for vehicle routing problems
    • Pisinger D., and Røpke S. A general heuristic for vehicle routing problems. Comput Oper Res 34 (2007) 2403-2435
    • (2007) Comput Oper Res , vol.34 , pp. 2403-2435
    • Pisinger, D.1    Røpke, S.2
  • 57
    • 26444552169 scopus 로고    scopus 로고
    • Combining metaheuristics and exact algorithms in combinatorial optimization: a survey and classification
    • Mira J., and Álvarez J.R. (Eds), Springer, Berlin
    • Puchinger J., and Raidl G.R. Combining metaheuristics and exact algorithms in combinatorial optimization: a survey and classification. In: Mira J., and Álvarez J.R. (Eds). IWINAC (2). Lecture notes in computer science vol. 3562 (2005), Springer, Berlin 41-53
    • (2005) IWINAC (2). Lecture notes in computer science , vol.3562 , pp. 41-53
    • Puchinger, J.1    Raidl, G.R.2
  • 59
    • 33750076966 scopus 로고    scopus 로고
    • A unified view on hybrid metaheuristics
    • Almeida F., Aguilera M.J.B., Blum C., Moreno-Vega J.M., Pérez M.P., Roli A., and Sampels M. (Eds), Springer, Berlin
    • Raidl G.R. A unified view on hybrid metaheuristics. In: Almeida F., Aguilera M.J.B., Blum C., Moreno-Vega J.M., Pérez M.P., Roli A., and Sampels M. (Eds). Hybrid metaheuristics. Lecture notes in computer science vol. 4030 (2006), Springer, Berlin 1-12
    • (2006) Hybrid metaheuristics. Lecture notes in computer science , vol.4030 , pp. 1-12
    • Raidl, G.R.1
  • 60
    • 31744439169 scopus 로고    scopus 로고
    • Decomposition and dynamic cut generation in integer linear programming
    • Ralphs T.K., and Galati M.V. Decomposition and dynamic cut generation in integer linear programming. Math Program 106 2 (2006) 261-285
    • (2006) Math Program , vol.106 , Issue.2 , pp. 261-285
    • Ralphs, T.K.1    Galati, M.V.2
  • 61
    • 33749348467 scopus 로고    scopus 로고
    • An improved algorithm for solving biobjective integer programs
    • Ralphs T.K., Saltzman M.J., and Wiecek M.M. An improved algorithm for solving biobjective integer programs. Ann Oper Res 147 (2006) 43-70
    • (2006) Ann Oper Res , vol.147 , pp. 43-70
    • Ralphs, T.K.1    Saltzman, M.J.2    Wiecek, M.M.3
  • 62
    • 33751011598 scopus 로고    scopus 로고
    • An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows
    • Røpke S., and Pisinger D. An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transport Sci 40 (2006) 455-472
    • (2006) Transport Sci , vol.40 , pp. 455-472
    • Røpke, S.1    Pisinger, D.2
  • 63
    • 35248845686 scopus 로고    scopus 로고
    • Rudová H, Murray K. University course timetabling with soft constraints. In: Burke EK, Causmaecker PD, editors. 4th international conference on practice and theory of automated timetabling, PATAT 2002, Gent, Belgium, August 21-23, 2002. Lecture notes in computer science, 2740. Berlin: Springer; 2003. p. 310-328 [selected revised papers].
    • Rudová H, Murray K. University course timetabling with soft constraints. In: Burke EK, Causmaecker PD, editors. 4th international conference on practice and theory of automated timetabling, PATAT 2002, Gent, Belgium, August 21-23, 2002. Lecture notes in computer science, vol. 2740. Berlin: Springer; 2003. p. 310-328 [selected revised papers].
  • 64
    • 0032656663 scopus 로고    scopus 로고
    • A survey of automated timetabling
    • Schaerf A. A survey of automated timetabling. Artif Intell Rev 13 2 (1999) 87-127
    • (1999) Artif Intell Rev , vol.13 , Issue.2 , pp. 87-127
    • Schaerf, A.1
  • 65
    • 34547212268 scopus 로고    scopus 로고
    • Application of a real-world university-course timetabling model solved by integer programming
    • Schimmelpfeng K., and Helber S. Application of a real-world university-course timetabling model solved by integer programming. OR Spectrum 29 (2007) 783-803
    • (2007) OR Spectrum , vol.29 , pp. 783-803
    • Schimmelpfeng, K.1    Helber, S.2
  • 66
    • 0007939495 scopus 로고    scopus 로고
    • Record breaking optimization results using the ruin and recreate principle
    • Schrimpf G., Schneider J., Stamm-Wilbrandt H., and Dueck G. Record breaking optimization results using the ruin and recreate principle. J Comput Phys 159 2 (2000) 139-171
    • (2000) J Comput Phys , vol.159 , Issue.2 , pp. 139-171
    • Schrimpf, G.1    Schneider, J.2    Stamm-Wilbrandt, H.3    Dueck, G.4
  • 67
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • Tenenbaum J.B., de Silva V., and Langford J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (2000) 2319-2323
    • (2000) Science , vol.290 , pp. 2319-2323
    • Tenenbaum, J.B.1    de Silva, V.2    Langford, J.C.3
  • 69
    • 0021603760 scopus 로고
    • School timetabling-a case in large binary integer linear programming
    • Tripathy A. School timetabling-a case in large binary integer linear programming. Manage Sci 30 (1984) 1473-1489
    • (1984) Manage Sci , vol.30 , pp. 1473-1489
    • Tripathy, A.1
  • 70
    • 0002076006 scopus 로고
    • An upper bound for the chromatic number of a graph and its application to timetabling problems
    • Welsh D.J.A., and Powell M.B. An upper bound for the chromatic number of a graph and its application to timetabling problems. Comput J 10 1 (1967) 85-86
    • (1967) Comput J , vol.10 , Issue.1 , pp. 85-86
    • Welsh, D.J.A.1    Powell, M.B.2
  • 71
    • 0347754958 scopus 로고
    • The reformulation of two mixed integer programming problems
    • Williams H.P. The reformulation of two mixed integer programming problems. Math Programm 14 3 (1978) 325-331
    • (1978) Math Programm , vol.14 , Issue.3 , pp. 325-331
    • Williams, H.P.1
  • 72
    • 0004027076 scopus 로고    scopus 로고
    • Paralleler und objektorientierter simplex-algorithmus
    • TR-96-09; 1996
    • Wunderling R. Paralleler und objektorientierter simplex-algorithmus. ZIB Technical Report TR-96-09; 1996.
    • ZIB Technical Report
    • Wunderling, R.1
  • 73
    • 0030230721 scopus 로고    scopus 로고
    • Using anytime algorithms in intelligent systems
    • Zilberstein S. Using anytime algorithms in intelligent systems. AI Mag 17 3 (1996) 73-83
    • (1996) AI Mag , vol.17 , Issue.3 , pp. 73-83
    • Zilberstein, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.