Abstract
A new approach resulting in a new group of algorithms for finding globally optimal solutions to discrete programming problems with Boolean variables is proposed. It is proved that the effectiveness of this method depends only on the number of variables of the problem to be solved and of the amount of RAM of used computer. The main difference from the existing methods of implicit enumeration is in the ability for some of the modular enumeration procedures to a priori predict, solving any extreme problem with Boolean variables, the number of iterations, the gain in running time in comparison with the traditional enumeration scheme, as well as the amount of RAM used. The experimental results confirm high efficiency of the proposed approaches.
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