General information
Schedule
Contents
Introductory Classes
Week | Topics and Slides | Recommended reading |
---|---|---|
14 | MILP Languages and Solvers. MILP Formulations for Traveling Salesman Problem | Python/SCIP |
Cutting Planes for TSP | TSP ; [P] or [DFJ] or [MTZ] or [A] or [ABCC] or [OAL] | |
Exercises | Sheet 1; Solutions; | |
15 | Cut-and-Solve | Cut-n-solve; [CZ] |
Modeling and Preprocessing | Modeling; Preprocessing [KN1,KN2,ABGRW] | |
Exercises | Sheet 2 | |
17 | Modeling Timetabling | Timetabling; Timetabling; [LL] |
Advanced Methods for MILP | Theory; [AMO ch 15]; [Wo ch 10] | |
Exercises | Sheet 3 | |
18 | Dantzig Wolfe decomposition and Column Generation | Theory; [Wo ch 11] |
Column Generation | Theory; [Wo ch 11] | |
Exercises on Lagrangian Relaxation | Sheet 4; [IB]; [Fi2]; [JB]; Solutions Assignment |
|
19 | Vehicle Routing | CVRP; CVRP-CG; [Fe] |
Vehicle Routing | CVRP-BB; [Fe] | |
Exercises on Column Generation | Sheet 5; Solutions 1; Solutions 2 | |
20 | Vehicle Scheduling | Slides; [BCG]; [CG] |
Vehicle Scheduling | ||
Exercises | Sheet 6 | |
21 | Crew Scheduling | Slides; RCSP; [SGSK]; [GM] |
Crew Scheduling | ||
Exercises | Sheet 7 | |
22 | Benders Decomposition | [DJ, sec 3.5]; Video |
Exercise |
Literature
- [PRKM] João Pedro Pedroso, Abdur Rais, Mikio Kubo and Masakazu Muramatsu. Mathematical Optimization: Solving Problems using SCIP and Python
Further Reading
-
[A] David L. L. Applegate, Robert E. E. Bixby, Vasek Chvátal, William J. J. Cook. The traveling salesman problem: a computational study. 2006
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[ABCC] David Applegate, Robert Bixby, Vasek Chvatal, William Cook. Implementing the Dantzig-Fulkerson-Johnson algorithm for large traveling salesman problems. Mathematical Programming, Series B. 97. 2003
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[DFJ] G. Dantzig, R. Fulkerson and S. Johnson. Solution of a Large-Scale Traveling-Salesman Problem. Journal of the Operations Research Society of America, Vol. 2, No. 4 (Nov., 1954), pp. 393-410
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[P] Gabor Pataki. Teaching Integer Programming Formulations Using the Traveling Salesman Problem SIAM Review 45(1), 2003
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[MTZ] C. E. Miller, A. W. Tucker, R. A. Zemlin Integer Programming Formulation of Traveling Salesman Problems Journal of the ACM. 7(4), 1960
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[OAL] Temel Öncana, I. Kuban Altınelb, Gilbert Laporte. A comparative analysis of several asymmetric traveling salesman problem formulations Computers & Operations Research 36 (2009) 6
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[CZ] Sharlee Climer, Weixiong Zhang. Cut-and-solve: An iterative search strategy for combinatorial optimization problems. Artificial Intelligence Volume 170, Issues 8–9, June 2006, Pages 714-738
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[KN1] Ed Klotz, Alexandra M. Newman. Practical guidelines for solving difficult linear programs Surveys in Operations Research and Management Science, 18 (1–2) (2013), pp. 1-17
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[KN2] Ed Klotz Alexandra M. Newman. Practical guidelines for solving difficult mixed integer linear programs Surveys in Operations Research and Management Science Volume 18, Issues 1–2, October 2013, Pages 18-32
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[ABGRW] Tobias Achterberg, Robert E. Bixby, Zonghao Gu, Edward Rothberg, Dieter Weninger Presolve Reductions in Mixed Integer Programming INFORMS Journal on Computing, 2019 (accepted for publication, preprint available as ZIB-Report 16-44)
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[AMO] R.K. Ahuja, T.L. Magnanti and J.B. Orlin. Network Flows: Theory, Algorithms, and Applications. Chapters 16 and 17 (in BB). Prentice Hall, 1993
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[Fi] M.L. Fisher. The Lagrangian Relaxation Method for Solving Integer Programming Problems. Management Science, 2004, 50(12), 1861-1871
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[Fi2] M.L. Fisher. An applications oriented guide to Lagrangian relaxation Interfaces 15:2, 10-21, 1985.
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[Fe] Feillet, D. A tutorial on column generation and branch-and-price for vehicle routing problems. 4OR-Q J Oper Res (2010) 8: 407.
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[LL] G. Lach and M. Lübbecke. Optimal University Course Timetables and the Partial Transversal Polytope. C. McGeoch (ed.). 7th International Workshop on Efficient and Experimental Algorithms (WEA08), Springer, 2008, 5038() , 235-248
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[Wo] L.A. Wolsey. Integer programming. Chapters 10 and 11 (in BB). John Wiley & Sons, New York, USA, 1998
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[BCG] A.A. Bertossi, P. Carraresi and G. Gallo. On some matching problems arising in vehicle scheduling models. Networks, Wiley, 1987, 17(3), 271-281
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[CG] P. Carraresi and G. Gallo. Network models for vehicle and crew scheduling. European Journal of Operational Research , 1984, 16(2) , 139 - 151
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[SGSK] I. Steinzen, V. Gintner, L. Suhl and N. Kliewer. A Time-Space Network Approach for the Integrated Vehicle- and Crew-Scheduling Problem with Multiple Depots. Transportation Science, 2010, 44(3), 367-382
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[GM] S. Gualandi and F. Malucelli. Resource Constrained Shortest Paths with a Super Additive Objective Function. M. Milano (ed.). CP, Springer, 2012, 7514, 299-315
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[IB] S. Ilker Birbil. Lagrangian Relaxation. 2016
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[JB] J. E. Beasley. Integer Programming Solution Methods.
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[DJ] Dirickx YMI & Jennergren LP (1979). Systems Analysis by Multilevel Methods: With Applications to Economics and Management. Chichester, UK: John Wiley & Sons. ISBN 978-0-471-27626-5
Links:
- [RM] PySCIPOpt: Python Interface to the SCIP Optimization Suite. Reference Manual; SCIP Parameters