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Abstract
New approaches are proposed to the solution of discrete programming problems on the basis of searching for lexicographic vector ordering for which the optimal solution to a problem coincides with the lexicographic extremum of the set of feasible solutions of the problem or is located rather close to it in the lexicographic sense. A generalized scheme of this lexicographic search and possibilities of its modification are described. Considerable advantages of this approach over the standard lexicographic search algorithm in efficiency are illustrated.
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