Abstract
This chapter introduces a theoretical framework for methods solving combinatorial optimization problems by examining successively subsets of the set of solutions until one of the solutions located in one of the subsets is proved to be optimal, or unitl some user’s defined termination conditions are verified. This type of methods includes Branch and Bound and related procedures, Implicit Enumeration and Heuristic Search.
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References
Kolesar, Peter J., “A branch and Bound Algorithm for the Knapsack Problem”, Man. Sci., 13, 723 (1967).
Greenberg, H., and Hegerich, R.L., “A branch Search Algorithm for the Knapsack Problem”, Man. Sci., 16, 327 (1970)
Granot, F., and P. Hammer, “On the Use of Boolean Functions in 0–1 Programming”, Opns. Res. Statistics and Economics, Pub. 70, Technion, Haifa, Israel (1970).
Balas, Egon, “An Additive Algorithm for Solving Linear Programs with 0–1 Variables”, Opns. Res., 13, 517 (1965).
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© 1975 CISM, Udine
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Barthès, J.P. (1975). Branching Methods in Combinatorial Optimization. In: Rinaldi, S. (eds) Topics in Combinatorial Optimization. CISM International Centre for Mechanical Sciences, vol 175. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3291-3_8
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DOI: https://doi.org/10.1007/978-3-7091-3291-3_8
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-81339-3
Online ISBN: 978-3-7091-3291-3
eBook Packages: Springer Book Archive