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A dual heuristic for mixed integer programming. (English) Zbl 1408.90200
Summary: In linear programming based branch-and-bound algorithms, many heuristics have been developed to improve primal solutions, but on the dual side we rely solely on cutting planes to improve dual bounds. We design a dual heuristic which incorporates relaxation algorithms within a branch-and-bound framework to improve dual bounds. We study the effect of solving various relaxations with dual heuristics by conducting a series of computational tests on the multi-dimensional knapsack problem.

MSC:
90C11 Mixed integer programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
90C59 Approximation methods and heuristics in mathematical programming
Software:
FEASPUMP
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[1] Beasley, J., OR—library: distributing test problems by electronic mail, J. Oper. Res. Soc., 41, 11, 1069-1072, (1990)
[2] Carvajal, R.; Ahmed, S.; Nemhauser, G.; Furman, K.; Goel, V.; Shao, Y., Using diversification, communication and parallelism to solve mixed-integer linear programs, Oper. Res. Lett., 42, 2, 186-189, (2014)
[3] Chu, P.; Beasley, J., A genetic algorithm for the multidimensional knapsack problem, J. Heuristics, 4, 1, 63-86, (1998)
[4] Danna, E.; Rothberg, E.; Pape, C., Exploring relaxation induced neighborhoods to improve MIP solutions, Math. Program., 102, 1, 71-90, (2005)
[5] Fischetti, M.; Glover, F.; Lodi, A., The feasibility pump, Math. Program., 104, 1, 91-104, (2005)
[6] Fischetti, M.; Lodi, A., Local branching, Math. Program., 98, 1, 23-47, (2003)
[7] Freville, A.; Plateau, G., Hard 0-1 multiknapsack test problems for size reduction methods, Investig. Oper., 1, 251-270, (1990)
[8] Martello, S.; Toth, P., Knapsack problems: algorithms and computer implementations, (1990), John Wiley & Sons, Inc.
[9] Lodi, A., Mixed integer programming computation, (2010), Springer
[10] Osorio, M.; Glover, F.; Hammer, P., Cutting and surrogate constraint analysis for improved multidimensional knapsack solutions, Ann. Oper. Res., 117, 1, 71-93, (2002)
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