MIPLIB 2010

This paper reports on the fifth version of the Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the community. The new version comprises 361 instances sorted into several groups. This includes the main benchmark test set of 87 instances, which are all solvable by today’s codes, and also the challenge test set with 164 instances, many of which are currently unsolved. For the first time, we include scripts to run automated tests in a predefined way. Further, there is a solution checker to test the accuracy of provided solutions using exact arithmetic.

[1]  Thorsten Koch,et al.  ParaSCIP: A Parallel Extension of SCIP , 2010, CHPC.

[2]  Rolf Niedermeier,et al.  Separator-based data reduction for signed graph balancing , 2010, J. Comb. Optim..

[3]  Alper Atamtürk,et al.  On the facets of the mixed–integer knapsack polyhedron , 2003, Math. Program..

[4]  Michal Pioro,et al.  SNDlib 1.0—Survivable Network Design Library , 2010 .

[5]  Martin Grötschel,et al.  Telebus Berlin: Vehicle Scheduling in a Dial-a-Ride System , 1999 .

[6]  Timo Berthold,et al.  Hybrid Branching , 2009, CPAIOR.

[7]  Robert E. Bixby,et al.  Solving Real-World Linear Programs: A Decade and More of Progress , 2002, Oper. Res..

[8]  Laurence A. Wolsey,et al.  A branch-and-cut algorithm for the single-commodity, uncapacitated, fixed-charge network flow problem , 2003, Networks.

[9]  Hartmut Stadtler,et al.  Multilevel Lot Sizing with Setup Times and Multiple Constrained Resources: Internally Rolling Schedules with Lot-Sizing Windows , 2003, Oper. Res..

[11]  G. Nemhauser,et al.  Integer Programming , 2020 .

[12]  Ralf Borndörfer,et al.  A Bundle Method for Integrated Multi-Depot Vehicle and Duty Scheduling in Public Transit , 2008 .

[13]  Martin W. P. Savelsbergh,et al.  A Computational Study of Search Strategies for Mixed Integer Programming , 1999, INFORMS J. Comput..

[14]  Leslie E. Trotter,et al.  On the maximum feasible subsystem problem, IISs and IIS-hypergraphs , 2003, Math. Program..

[15]  Alper Atamtürk,et al.  On splittable and unsplittable flow capacitated network design arc–set polyhedra , 2002, Math. Program..

[16]  Ashish Sabharwal,et al.  An Empirical Study of Optimization for Maximizing Diffusion in Networks , 2010, CP.

[17]  William J. Cook,et al.  Exact solutions to linear programming problems , 2007, Oper. Res. Lett..

[18]  Marco E. Lübbecke,et al.  A Branch-and-Price Algorithm for Multi-mode Resource Leveling , 2010, SEA.

[19]  Christian Liebchen,et al.  When Periodic Timetables Are Suboptimal , 2007, OR.

[20]  Michal Pióro,et al.  SNDlib 1.0—Survivable Network Design Library , 2010, Networks.

[21]  Milind Dawande,et al.  Effective Heuristics for Multiproduct Partial Shipment Models , 2006, Oper. Res..

[22]  Daniel G. Espinoza On Linear Programming, Integer Programming and Cutting Planes , 2006 .

[23]  Matthew Galati,et al.  Decomposition methods for integer linear programming , 2010 .

[24]  Natashia Boland,et al.  A strengthened formulation and cutting planes for the open pit mine production scheduling problem , 2010, Comput. Oper. Res..

[25]  Andrea Lodi,et al.  Performance Variability in Mixed-Integer Programming , 2013 .

[26]  W. Jäger,et al.  Mathematics – key technology for the future , 2003 .

[27]  Edmund K. Burke,et al.  A space-indexed formulation of packing boxes into a larger box , 2012, Oper. Res. Lett..

[28]  Alexander Martin Integer Programs with Block Structure , 1999 .

[29]  C. Colbourn,et al.  Handbook of Combinatorial Designs , 2006 .

[30]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[31]  Kerem Akartunali,et al.  A computational analysis of lower bounds for big bucket production planning problems , 2012, Computational Optimization and Applications.

[32]  Alain Chabrier,et al.  Solving a Network Design Problem , 2004, Ann. Oper. Res..

[33]  Jonathan Eckstein,et al.  Parallel Branch-and-Bound Algorithms for General Mixed Integer Programming on the CM-5 , 1994, SIAM J. Optim..

[34]  Michael C. Ferris Solving the seymour problem , 2001 .

[35]  J F Barutt,et al.  AIRLINE CREW SCHEDULING : SUPERCOMPUTERS AND ALGORITHMS , 1990 .

[36]  Kerem Akartunali,et al.  A heuristic approach for big bucket multi-level production planning problems , 2009, Eur. J. Oper. Res..

[37]  Jeff T. Linderoth,et al.  Solving large Steiner Triple Covering Problems , 2011, Oper. Res. Lett..

[38]  Thorsten Koch,et al.  Integer Programming Approaches to Access and Backbone IP Network Planning , 2006, HPSC.

[39]  Paul A. Rubin,et al.  Combinatorial Benders Cuts for the Minimum Tollbooth Problem , 2009, Oper. Res..

[40]  T. Kürner,et al.  IST-Momentum project public deliverable 4.3: Mathematical methods for automatic optimization of UMTS radio networks , 2003 .

[41]  Tatsuya Akutsu,et al.  Integer programming-based methods for attractor detection and control of boolean networks , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[42]  Steffen Weider,et al.  Integration of Vehicle and Duty Scheduling in Public Transport , 2007 .

[43]  Christoph Helmberg,et al.  A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses , 2007, Oper. Res..

[44]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[45]  Oktay Günlük,et al.  Computational experience with a difficult mixedinteger multicommodity flow problem , 1995, Math. Program..

[46]  Leon W P Peeters,et al.  Cyclic Railway Timetable Optimization , 2003 .

[47]  Milind Dawande,et al.  A Class of Hard Small 0-1 Programs , 1998, INFORMS J. Comput..

[48]  Martin W. P. Savelsbergh,et al.  A Parallel, Linear Programming-based Heuristic for Large-Scale Set Partitioning Problems , 2001, INFORMS J. Comput..

[49]  Norman D. Curet,et al.  The Network Diversion Problem , 2001 .

[50]  Arie M. C. A. Koster,et al.  On cut‐based inequalities for capacitated network design polyhedra , 2011, Networks.

[51]  Thorsten Koch,et al.  On the Effects of Minor Changes in Model Formulations , 2008 .

[52]  Martin W. P. Savelsbergh,et al.  An Updated Mixed Integer Programming Library: MIPLIB 3.0 , 1998 .

[53]  Tobias Achterberg,et al.  The MCF-Separator – Detecting and Exploiting Multi-Commodity Flows in MIPs , 2010 .

[54]  François Margot,et al.  Small covering designs by branch-and-cut , 2003, Math. Program..

[55]  Joachim P. Walser Solving Linear Pseudo-Boolean Constraint Problems with Local Search , 1997, AAAI/IAAI.

[56]  Jonathan Eckstein,et al.  Parallel Branch-and-Bound Methods for Mixed Integer Programming , 1996, Applications on Advanced Architecture Computers.

[57]  Petr Holub,et al.  Data transfer planning with tree placement for collaborative environments , 2011, Constraints.

[58]  Ralf Borndörfer,et al.  Models for Railway Track Allocation , 2007, ATMOS.

[59]  Richard Laundy,et al.  Solving Hard Mixed-Integer Programming Problems with Xpress-MP: A MIPLIB 2003 Case Study , 2009, INFORMS J. Comput..

[60]  Fred W. Glover,et al.  The feasibility pump , 2005, Math. Program..

[61]  P. Harker,et al.  Scheduling a Major College Basketball Conference , 1998 .

[62]  Jorge J. Moré,et al.  Digital Object Identifier (DOI) 10.1007/s101070100263 , 2001 .

[63]  F. Malucelli,et al.  A Lagrangian relaxation approach for the design of networks with shared protection , 2003 .

[64]  William J. Cook,et al.  An Exact Rational Mixed-Integer Programming Solver , 2011, IPCO.

[65]  Jon C. Dattorro,et al.  Convex Optimization & Euclidean Distance Geometry , 2004 .

[66]  Leo G. Kroon,et al.  A Branch-and-Cut Approach for Solving Railway Line-Planning Problems , 2004, Transp. Sci..

[67]  Jeff T. Linderoth,et al.  MILP Software , 2010 .

[68]  William J. Cook,et al.  Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin a Hybrid Branch-and-bound Approach for Exact Rational Mixed-integer Programming , 2022 .

[69]  M. Jünger,et al.  50 Years of Integer Programming 1958-2008 - From the Early Years to the State-of-the-Art , 2010 .

[70]  Michael R. Bussieck,et al.  A fast algorithm for near cost optimal line plans , 2004, Math. Methods Oper. Res..

[71]  Marc E. Pfetsch,et al.  Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin Branch-and-cut for the Maximum Feasible Subsystem Problem Branch-and-cut for the Maximum Feasible Subsystem Problem , 2022 .

[72]  Michael R. Bussieck,et al.  A fast algorithmfor near cost optim al line plans , 2004 .

[73]  Arjen K. Lenstra,et al.  Market Split and Basis Reduction: Towards a Solution of the Cornue'jols-Dawande Instances , 1999, INFORMS J. Comput..

[74]  Alper Atamtürk,et al.  On capacitated network design cut–set polyhedra , 2002, Math. Program..

[75]  Miyashiro Ryuhei,et al.  On the Maximum Number of Strings in Go , 2007 .

[76]  Armin Fügenschuh,et al.  Polyhedral Aspects of Self-Avoiding Walks , 2011 .

[77]  R. Borndörfer,et al.  Aspects of Set Packing, Partitioning, and Covering , 1998 .

[78]  Tobias Achterberg,et al.  The Mcf-separator: detecting and exploiting multi-commodity flow structures in MIPs , 2010, Math. Program. Comput..

[79]  Magnus Wahlström,et al.  A Faster Fixed-Parameter Approach to Drawing Binary Tanglegrams , 2009, IWPEC.

[80]  Mathieu Van Vyve,et al.  A General Heuristic for Production Planning Problems , 2004, INFORMS J. Comput..

[81]  Martin Grötschel,et al.  Duty Scheduling in Public Transit , 2003 .

[82]  Boris Goldengorin,et al.  Complexity evaluation of benchmark instances for the p-median problem , 2011, Math. Comput. Model..

[83]  Matteo Fischetti,et al.  Local branching , 2003, Math. Program..

[84]  Matthew T. Stamps,et al.  A GENETIC ALGORITHM FOR THE MINIMUM TOLLBOOTH PROBLEM , 2005 .

[85]  David M. Panton,et al.  Mission Planning for Synthetic Aperture Radar Surveillance , 1999, Interfaces.

[86]  Shirley Dex,et al.  JR 旅客販売総合システム(マルス)における運用及び管理について , 1991 .

[87]  Hana Rudová,et al.  Integer Programming for Media Streams Planning Problem , 2010, MEMICS.

[88]  Jonathan Eckstein Control strategies for parallel mixed integer branch and bound , 1994, Proceedings of Supercomputing '94.

[89]  Andreas Bley,et al.  Multi-layer Network Design - A Model-Based Optimization Approach , 2008 .

[90]  Mathematik Und Information on MIPLIB's timetab-instances , 2003 .

[91]  David B. Shmoys,et al.  Maximizing the Spread of Cascades Using Network Design , 2010, UAI.

[92]  Minghe Sun,et al.  A tabu search heuristic procedure for the fixed charge transportation problem , 1998, Eur. J. Oper. Res..

[93]  Thorsten Koch,et al.  Rapid mathematical programming , 2005 .

[94]  Thorsten Koch,et al.  Konrad-zuse-zentrum F ¨ Ur Informationstechnik Berlin Miplib 2003 , 2022 .

[95]  G. Ribiere,et al.  Experiments in mixed-integer linear programming , 1971, Math. Program..

[96]  Jayant Kalagnanam,et al.  A Column-Generation Approach to the Multiple Knapsack Problem with Color Constraints , 2006, INFORMS J. Comput..

[97]  Matteo Fischetti,et al.  A Heuristic Method for the Set Covering Problem , 1999, Oper. Res..

[98]  Harald Schilly,et al.  Modellierung und Implementation eines Vorlesungsplaners , 2007 .

[99]  Robert H. Halstead,et al.  Matrix Computations , 2011, Encyclopedia of Parallel Computing.