Abstract
When regarded as a shortest route problem, an integer program can be seen to have a particularly simple structure. This allows the development of an algorithm for finding thek th best solution to an integer programming problem with max{O(kmn), O(k logk)} operations. Apart from its value in the parametric study of an optimal solution, the approach leads to a general integer programming algorithm consisting of (1) problem relaxation, (2) solution of the relaxed problem parametrically by dynamic programming, and (3) generation ofk th best solutions until a feasible solution is found. Elementary methods based on duality for reducingk for a given problem relaxation are then outlined, and some examples and computational aspects are discussed.
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Wolsey, L.A. Generalized dynamic programming methods in integer programming. Mathematical Programming 4, 222–232 (1973). https://doi.org/10.1007/BF01584662
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DOI: https://doi.org/10.1007/BF01584662