Generating Set Partitioning Test Problems with Known Optimal Integer Solutions

  • Edward K. Baker
  • Anito Joseph
  • Brenda Rayco
Conference paper
Part of the Operations Research/Computer Science Interfaces Series book series (ORCS, volume 29)


In this work, we investigate methods for generating set partitioning test problems with known integer solutions. The problems are generated with various cost structures so that their solution by well-known integer programming methods can be shown to be difficult. Computational results are obtained using the branch and bound methods of the CPLEX solver. Possible extensions are considered to the area of cardinality probing of the solutions

Key words

integer programming test problems branch and bound cardinality probing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

6. References

  1. Arabeyre, J., Fearnley, J., Steiger, F., and Teather, W., 1969, The airline crew scheduling problem: a survey, Transportation Science 3: 140–163.Google Scholar
  2. Baker, E.K., Bodin, L.D., Finnegan, W.F. and Ponder, R.J., 1979, Efficient heuristic solutions to an airline crew scheduling problem, AIIE Trans. 11: 79–85.Google Scholar
  3. Balinski, M. and Quandt, R., 1964, On an integer program for a delivery problem, Operations Research 12: 300–304.Google Scholar
  4. Beasley, J.E., 1990, OR-Library: Distributing test problems by electronic mail, Journal of the Operational Research Society 41: 1069–1072.CrossRefGoogle Scholar
  5. Benichou, M., Gauthier, J.M., Girodet, P., Hentges, G., Ribiere, G. and Vincent, O., 1971, Experiments in mixed-integer linear programming, Math. Prog. 1: 76–94.zbMATHMathSciNetCrossRefGoogle Scholar
  6. Bixby, R., Boyd, A., Dadmehr, S., and Indovina, R., 1996, The MIPLIB mixed integer programming library, Mathematical Programming Society Committee on Algorithms, Bulletin 22: 2–5.Google Scholar
  7. Bixby, R.E., Fenelon, M., Zonghao, G., Rotheberg, E., and Wunderling, R., 1999, MIP: Theory and practice-closing the gap, System Modeling and Optimization Methods, Theory and Applications, M.J.D Powell and S. Scholtes, eds., Kluwer, The Netherlands.Google Scholar
  8. Crainic, T.G. and Rousseau, J.M., 1987, The column generation principle and the airline crew scheduling problem, INFOR 25:136–151.zbMATHGoogle Scholar
  9. Floudas, C.A. and Pardalos, P.M., 1990, A collection of test problems for constrained optimization algorithms, Lecture Notes in Computer Science, No. 455. Springer-Verlag, Heidelberg, Germany.zbMATHGoogle Scholar
  10. Floudas, C.A., Pardalos, P.M., Adjiman, C.S., Esposito, W.R., Gumus, S.T., Harding, Z.H., Klepeis, J.L., Meyer, C.A., and Schweiger C.A., 1999, Handbook of Test Problems in Local and Global Optimization, Nonconvex Optimization and Its Applications. Kluwer, Dordrecht, The Netherlands.Google Scholar
  11. Forrest, J.J.H., Hirst J.P.H. and Tomlin, J.A., 1974, Practical solution of large scale mixed integer programming problems with UMPIRE, Management Science 20: 736–773.zbMATHMathSciNetGoogle Scholar
  12. Garfinkel, R.S. and Nemhauser, G.L., 1969, The set-partitioning problem: set covering with equality constraints, Ops. Res. 17: 848–856.zbMATHGoogle Scholar
  13. Garfinkel, R.S. and Nemhauser, G.L., 1970, Optimal political districting by implicit enumeration techniques, Management Science 14: B495–B508.Google Scholar
  14. Garfinkel, R.S. and Nemhauser, G.L., 1972, Integer Programming. J. Wiley and Sons. New York.zbMATHGoogle Scholar
  15. Gay, D.M. 1985. Electronic mail distribution of linear programming test problems. Mathematical Programming Society COAL Newsletter.Google Scholar
  16. Hillier, F., 1969, Efficient heuristic procedures for integer linear programming with an interior, Operations Research 17: 600–637.zbMATHMathSciNetGoogle Scholar
  17. Hoffman, K.L. and Padberg, M., 1993, Solving airline crew scheduling problems by branch-and-cut, Management Science 39: 657–682.zbMATHGoogle Scholar
  18. Joseph, A., 1995, A parametric formulation of the general integer linear programming problem, Computers and Operations Research 22: 883–892.zbMATHMathSciNetCrossRefGoogle Scholar
  19. Joseph, A., Gass, S. I., and Bryson, N., 1998, An objective hyperplane search procedure for solving the general integer linear programming problem, European Journal of Operational Research 104: 601–614.zbMATHCrossRefGoogle Scholar
  20. Joseph, A., 2003, Cardinality corrections for set partitioning, Research Report, Mgt. Science Department. Univ. of Miami, Coral Gables, Florida.Google Scholar
  21. Land, H. and Doig, A.G., 1960, An automatic method for solving discrete programming problems, Econometrica 28: 497–520.zbMATHMathSciNetCrossRefGoogle Scholar
  22. Linderoth, J.T. and Savelsbergh, M.W.P., 1999, A computational study of search strategies for mixed integer programming, INFORMS Journal on Computing 11: 173–187zbMATHMathSciNetGoogle Scholar
  23. Marsten, R.E., 1974, An algorithm for large set partitioning problems, Management Science 20: 774–787.zbMATHMathSciNetGoogle Scholar
  24. Marsten, R.E. and Shepherdson, F., 1981, Exact solution of crew scheduling problems using the set partitioning model: recent successful applications, Networks 11: 165–177.Google Scholar
  25. Mitra, G., 1973, Investigation of some branch and bound strategies for the solution of mixed integer linear programs, Math. Prog. 4: 155–170.zbMATHCrossRefGoogle Scholar
  26. Mingozzi, A., Boschetti, M.A., Ricciarde S., and Bianco, L., 1999, A set partitioning approach to the crew scheduling problem, Operations Research 47: 873–888.zbMATHGoogle Scholar
  27. Mehrotra, A., Nemhauser, G.L. and Johnson, E., 1998, An Optimization-Based Heuristic for Political Districting, Mgt. Sci. 44: 1100–1114.zbMATHGoogle Scholar
  28. Mulvey, J. M. (ed.) 1982. Evaluating Mathematical Programming Techniques, Lecture Notes in Economics and Mathematical Systems 199, Springer-Verlag, Berlin.zbMATHGoogle Scholar
  29. Padberg, M. and Balas, E., 1972, On the set-covering problem, Operations Research 20: 1152–1161.zbMATHMathSciNetCrossRefGoogle Scholar
  30. Savelsbergh, M.W.P., 1994, Preprocessing and probing for mixed-integer models. Computational Optimization and Applications 3: 317–331.MathSciNetCrossRefGoogle Scholar
  31. Thiriez, H., 1969, Airline crew scheduling: a group theoretic approach, MIT Department of Aeronautics and Astronautics Report R69-1. Cambridge, MA.Google Scholar
  32. Yildiz, H., 2004, A large neighborhood search heuristic for graph coloring, Working Paper, Graduate School of Industrial Administration, Carnegie Mellon University, Pittsburgh, PA.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Edward K. Baker
    • 1
  • Anito Joseph
    • 1
  • Brenda Rayco
    • 2
  1. 1.Department of Management ScienceUniversity of MiamiCoral Gables
  2. 2.Department of MathematicsSouthern Illinois UniversityEdwardsville

Personalised recommendations