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
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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
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
Baker EK (1981) Efficient heuristic algorithms for the weighted set covering problem. Comput Oper Res 8:303–310
Baker EK, Fisher ML (1981) Computational results for very large air crew scheduling problems. OMEGA Internat J Management Sci 19:613–618
Balas E, Martin CH (1980) Pivot and complement: A heuristic for 0/1 programming. Managem Sci 26:86–96
Baldick R (1992) AÂ randomized heuristic for inequality-constrained mixed-integer programming. Techn Report Dept Electrical and Computer Engin Worcester Polytechnic Inst
Beale EML (1979) Branch and bound methods for mathematical programming systems. Ann Discret Math 5:201–219
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
Beasley JE, Chu PC (1996) A genetic algorithm for the set covering problem. Europ J Oper Res 194:392–404
Benichou M, Gauthier JM, Girodet P, Hehntges G, Ribiere G, Vincent O (1971) Experiments in mixed integer linear programming. Math Program 1:76–94
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
Bixby RE, Cook W, Cox A, Lee EK (1995) Parallel mixed integer programming. Techn Report Center Res Parallel Computation, Rice Univ CRPC-TR95554
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
Bixby RE, Lee EK (1998) Solving a truck dispatching scheduling problem using branch-and-cut. Oper Res 46:355–367
Bixby RE, Wagner DK (1987) A note on detecting simple redundancies in linear systems. Oper Res Lett 6:15–18
Bonomi E, Lutton JL (1984) The N-city traveling salesman problem: Statistical mechanics and the metropolis algorithm. SIAM Rev 26:551–568
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
Bradley GH, Hammer PL, Wolsey L (1975) Coefficient reduction in 0–1 variables. Math Program 7:263–282
Brearley AL, Mitra G, Williams HP (1975) Analysis of mathematical programming problems prior to applying the simplex method. Math Program 5:54–83
Breu R, Burdet CA (1974) Branch and bound experiments in zero-one programming. Math Program 2:1–50
Conn AR, Cornuejols G (1987) AÂ projection method for the uncapacitated facility location problem. Techn Report Graduate School Industr Admin Carnegie-Mellon Univ 26-86-87
Crowder H, Johnson EL, Padberg M (1983) Solving large-scale zero-one linear programming problem. Oper Res 31:803–834
Dakin RJ (1965) A tree search algorithm for mixed integer programming problems. Comput J 8:250–255
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
Driebeek NJ (1966) An algorithm for the solution of mixed integer programming problems. Managem Sci 21:576–587
Erlenkotter D (1978) A dual-based procedure for uncapacitated facility location. Oper Res 26:992–1009
Fenelon M (1991) Branching strategies for MIP. CPLEX
Fisher ML, Jaikumer R (1981) A generalized assignment heuristic for vehicle routing. Networks 11:109–124
Forrest JJ, Hirst JPH, Tomlin JA (1974) Practical solution of large mixed integer programming problems with UMPIRE. Managem Sci 20:736–773
Garey MR, Johnson DS (1979) Computers and intractability – A guide to the theory of NP-completeness. Freeman, New York
Gauthier JM, Ribiere G (1977) Experiments in mixed integer programming using pseudo-costs. Math Program 12:26–47
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, Reading, MA
Guignard M, Spielberg K (1981) Logical reduction methods in zero-one programming. Oper Res 29:49–74
Hoffman KL, Padberg M (1991) Improving LP‑representations of zero-one linear programs for branch-and-cut. ORSA J Comput 3:121–134
Hoffman KL, Padberg M (1992) Solving airline crew-scheduling problems by branch-and-cut. Managem Sci 39:657–682
Ibarra OH, Kim CE (1975) Fast approximation algorithms for the knapsack and sum of subset problems. J ACM 22:463–468
Kruskal JB (1956) On the shortest spanning subtree of a graph and the traveling salesman problem. Proc Amer Math Soc 7:48–50
Kuehn AA, Hamburger MJ (1963) A heuristic program for locating warehouses. Managem Sci 19:643–666
Land AH, Doig AG (1960) An automatic method for solving discrete programming problems. Econometrica 28:497–520
Land AH, Powell S (1979) Computer codes for problems of integer programming. Ann Discret Math 5:221–269
Lawler EL (1979) Fast approximation algorithms for the knapsack problems. Math Oper Res 4:339–356
Lee EK, Mitchell JE (1996) Computational experience in nonlinear mixed integer programming. In: The Oper. Res. Proc. 1996. Springer, Berlin, pp 95–100
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).
Lin S, Kernighan BW (1973) An effective heuristic algorithm for the traveling salesman problem. Oper Res 21:498–516
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
Manne AS (1964) Plant location under economies of scale-decentralization and computation. Managem Sci 11:213–235
Mitra G (1973) Investigations of some branch and bound strategies for the solution of mixed integer linear programs. Math Program 4:155–170
Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New York
Padberg M, Rinaldi G (1989) A branch-and-cut approach to a traveling salesman problem with side constraints. Managem Sci 35:1393–1412
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
Parker RG, Rardin RL (1988) Discrete optimization. Acad. Press, New York
Rosenkrantz DJ, Stearns RE, Lewis PM (1977) An analysis of several heuristics for the traveling salesman problem. SIAM J Comput 6:563–581
Sahni S (1975) Approximate algorithms for the 0–1 knapsack problem. J ACM 22:115–124
Savelsbergh MWP (1994) Preprocessing and probing for mixed integer programming problems. ORSA J Comput 6:445–454
de Silva A, Abramson D (1998) A parallel interior point method and its application to facility location problems. Comput Optim Appl 9:249–273
Spielberg K (1969) Algorithms for the simple plant location problem with some side-conditions. Oper Res 17:85–111
Tomlin JA (1971) An improved branch and bound method for integer programming. Oper Res 19:1070–1075
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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
DOI: https://doi.org/10.1007/978-0-387-74759-0_286
Publisher Name: Springer, Boston, MA
Print ISBN: 978-0-387-74758-3
Online ISBN: 978-0-387-74759-0
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering