Skip to main content

Integer Programming: Branch and Bound Methods

  • Reference work entry
Encyclopedia of Optimization

Article Outline

Keywords

Synonyms

Overview

Partitioning Strategies

Branching Variable Selection

Node Selection

Preprocessing and Reformulation

Heuristics

Continuous Reduced Cost Implications

Subproblem Solver

See also

References

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 2,500.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 2,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Andersen ED, Gondzio J, Mészáros C, Xu X (1996) Implementation of interior point methods for large scale linear programming. In: Terlaky T (ed) Interior Point Methods in Mathematical Programming. Kluwer, Dordrecht, ftp://ftp.sztaki.hu/pub/oplab/PAPERS/kluwer.ps.Z

    Google Scholar 

  2. Applegate D, Bixby RE, Chvátal V, Cook W (1998) On the solution of travelling salesman problems. Documenta Math no. Extra Vol. Proc. ICM III:645–656

    Google Scholar 

  3. Baker EK (1981) Efficient heuristic algorithms for the weighted set covering problem. Comput Oper Res 8:303–310

    Article  Google Scholar 

  4. Baker EK, Fisher ML (1981) Computational results for very large air crew scheduling problems. OMEGA Internat J Management Sci 19:613–618

    Article  Google Scholar 

  5. Balas E, Martin CH (1980) Pivot and complement: A heuristic for 0/1 programming. Managem Sci 26:86–96

    MathSciNet  MATH  Google Scholar 

  6. Baldick R (1992) A randomized heuristic for inequality-constrained mixed-integer programming. Techn Report Dept Electrical and Computer Engin Worcester Polytechnic Inst

    Google Scholar 

  7. Beale EML (1979) Branch and bound methods for mathematical programming systems. Ann Discret Math 5:201–219

    Article  MathSciNet  MATH  Google Scholar 

  8. Beale EML, Tomlin JA (1970) Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables. In: Lawerence J (ed) Proc. Fifth Internat. Conf. Oper. Res., Tavistock Publ., pp 447–454

    Google Scholar 

  9. Beasley JE, Chu PC (1996) A genetic algorithm for the set covering problem. Europ J Oper Res 194:392–404

    Article  Google Scholar 

  10. Benichou M, Gauthier JM, Girodet P, Hehntges G, Ribiere G, Vincent O (1971) Experiments in mixed integer linear programming. Math Program 1:76–94

    Article  MATH  Google Scholar 

  11. Benichou M, Gauthier JM, Hehntges G, Ribiere G (1977) The efficient solution of large-scale linear programming problems - some algorithmic techniques and computational results. Math Program 13:280–322

    Article  MATH  Google Scholar 

  12. Bixby RE, Cook W, Cox A, Lee EK (1995) Parallel mixed integer programming. Techn Report Center Res Parallel Computation, Rice Univ CRPC-TR95554

    Google Scholar 

  13. Bixby RE, Cook W, Cox A, Lee EK (1999) Computational experience with parallel mixed integer programming in a distributed environment. Ann Oper Res 90:19–43

    Article  MathSciNet  MATH  Google Scholar 

  14. Bixby RE, Lee EK (1998) Solving a truck dispatching scheduling problem using branch-and-cut. Oper Res 46:355–367

    MATH  Google Scholar 

  15. Bixby RE, Wagner DK (1987) A note on detecting simple redundancies in linear systems. Oper Res Lett 6:15–18

    Article  MathSciNet  MATH  Google Scholar 

  16. Bonomi E, Lutton JL (1984) The N-city traveling salesman problem: Statistical mechanics and the metropolis algorithm. SIAM Rev 26:551–568

    Article  MathSciNet  MATH  Google Scholar 

  17. Borchers B, Mitchell JE (March 1991) Using an interior point method in a branch and bound algorithm for integer programming. Techn Report Math Sci Rensselaer Polytech Inst 195

    Google Scholar 

  18. Bradley GH, Hammer PL, Wolsey L (1975) Coefficient reduction in 0–1 variables. Math Program 7:263–282

    Article  MathSciNet  Google Scholar 

  19. Brearley AL, Mitra G, Williams HP (1975) Analysis of mathematical programming problems prior to applying the simplex method. Math Program 5:54–83

    Article  MathSciNet  Google Scholar 

  20. Breu R, Burdet CA (1974) Branch and bound experiments in zero-one programming. Math Program 2:1–50

    MathSciNet  Google Scholar 

  21. Conn AR, Cornuejols G (1987) A projection method for the uncapacitated facility location problem. Techn Report Graduate School Industr Admin Carnegie-Mellon Univ 26-86-87

    Google Scholar 

  22. Crowder H, Johnson EL, Padberg M (1983) Solving large-scale zero-one linear programming problem. Oper Res 31:803–834

    MATH  Google Scholar 

  23. Dakin RJ (1965) A tree search algorithm for mixed integer programming problems. Comput J 8:250–255

    Article  MathSciNet  MATH  Google Scholar 

  24. Dietrich B, Escudero L (1990) Coefficient reduction for knapsack-like constraints in 0/1 programs with variable upper bounds. Oper Res Lett 9:9–14

    Article  MathSciNet  MATH  Google Scholar 

  25. Driebeek NJ (1966) An algorithm for the solution of mixed integer programming problems. Managem Sci 21:576–587

    Google Scholar 

  26. Erlenkotter D (1978) A dual-based procedure for uncapacitated facility location. Oper Res 26:992–1009

    MathSciNet  MATH  Google Scholar 

  27. Fenelon M (1991) Branching strategies for MIP. CPLEX

    Google Scholar 

  28. Fisher ML, Jaikumer R (1981) A generalized assignment heuristic for vehicle routing. Networks 11:109–124

    Article  MathSciNet  Google Scholar 

  29. Forrest JJ, Hirst JPH, Tomlin JA (1974) Practical solution of large mixed integer programming problems with UMPIRE. Managem Sci 20:736–773

    MathSciNet  MATH  Google Scholar 

  30. Garey MR, Johnson DS (1979) Computers and intractability – A guide to the theory of NP-completeness. Freeman, New York

    MATH  Google Scholar 

  31. Gauthier JM, Ribiere G (1977) Experiments in mixed integer programming using pseudo-costs. Math Program 12:26–47

    Article  MathSciNet  MATH  Google Scholar 

  32. Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA

    MATH  Google Scholar 

  33. Guignard M, Spielberg K (1981) Logical reduction methods in zero-one programming. Oper Res 29:49–74

    MathSciNet  MATH  Google Scholar 

  34. Hoffman KL, Padberg M (1991) Improving LP‑representations of zero-one linear programs for branch-and-cut. ORSA J Comput 3:121–134

    MATH  Google Scholar 

  35. Hoffman KL, Padberg M (1992) Solving airline crew-scheduling problems by branch-and-cut. Managem Sci 39:657–682

    Google Scholar 

  36. Ibarra OH, Kim CE (1975) Fast approximation algorithms for the knapsack and sum of subset problems. J ACM 22:463–468

    Article  MathSciNet  MATH  Google Scholar 

  37. Kruskal JB (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Amer Math Soc 7:48–50

    Article  MathSciNet  Google Scholar 

  38. Kuehn AA, Hamburger MJ (1963) A heuristic program for locating warehouses. Managem Sci 19:643–666

    Google Scholar 

  39. Land AH, Doig AG (1960) An automatic method for solving discrete programming problems. Econometrica 28:497–520

    Article  MathSciNet  MATH  Google Scholar 

  40. Land AH, Powell S (1979) Computer codes for problems of integer programming. Ann Discret Math 5:221–269

    Article  MathSciNet  MATH  Google Scholar 

  41. Lawler EL (1979) Fast approximation algorithms for the knapsack problems. Math Oper Res 4:339–356

    MathSciNet  MATH  Google Scholar 

  42. Lee EK, Mitchell JE (1996) Computational experience in nonlinear mixed integer programming. In: The Oper. Res. Proc. 1996. Springer, Berlin, pp 95–100

    Google Scholar 

  43. Lee EK, Mitchell JE (2000) Computational experience of an interior-point SQP algorithm in a parallel branch-and-bound framework. In: Frenk H et al (eds.) High Performance Optimization. Kluwer, Dordrecht, pp 329–347 (Chap. 13).

    Google Scholar 

  44. Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling salesman problem. Oper Res 21:498–516

    MathSciNet  MATH  Google Scholar 

  45. Lustig IJ, Marsten RE, Shanno DF (1994) Interior point methods for linear programming: Computational state of the art. ORSA J Comput 6(1):1–14. see also the following commentaries and rejoinder

    MathSciNet  MATH  Google Scholar 

  46. Manne AS (1964) Plant location under economies of scale-decentralization and computation. Managem Sci 11:213–235

    Google Scholar 

  47. Mitra G (1973) Investigations of some branch and bound strategies for the solution of mixed integer linear programs. Math Program 4:155–170

    Article  MATH  Google Scholar 

  48. Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New York

    MATH  Google Scholar 

  49. Padberg M, Rinaldi G (1989) A branch-and-cut approach to a traveling salesman problem with side constraints. Managem Sci 35:1393–1412

    MathSciNet  MATH  Google Scholar 

  50. Padberg M, Rinaldi G (1991) A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems. SIAM Rev 33:60–100

    Article  MathSciNet  MATH  Google Scholar 

  51. Parker RG, Rardin RL (1988) Discrete optimization. Acad. Press, New York

    MATH  Google Scholar 

  52. Rosenkrantz DJ, Stearns RE, Lewis PM (1977) An analysis of several heuristics for the traveling salesman problem. SIAM J Comput 6:563–581

    Article  MathSciNet  MATH  Google Scholar 

  53. Sahni S (1975) Approximate algorithms for the 0–1 knapsack problem. J ACM 22:115–124

    Article  MathSciNet  MATH  Google Scholar 

  54. Savelsbergh MWP (1994) Preprocessing and probing for mixed integer programming problems. ORSA J Comput 6:445–454

    MathSciNet  MATH  Google Scholar 

  55. de Silva A, Abramson D (1998) A parallel interior point method and its application to facility location problems. Comput Optim Appl 9:249–273

    Article  MathSciNet  MATH  Google Scholar 

  56. Spielberg K (1969) Algorithms for the simple plant location problem with some side-conditions. Oper Res 17:85–111

    MATH  Google Scholar 

  57. Tomlin JA (1971) An improved branch and bound method for integer programming. Oper Res 19:1070–1075

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag

About this entry

Cite this entry

Lee, E.K., Mitchell, J.E. (2008). Integer Programming: Branch and Bound Methods . In: Floudas, C., Pardalos, P. (eds) Encyclopedia of Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-74759-0_286

Download citation

Publish with us

Policies and ethics