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Lowering digit capacity of matrix elements for increasing speed of binary optimization algorithm


M. Yu. Malsagov

The goal of the paper is to make a random-search procedure used in binary minimization problems more effective. This sort of problems involves minimization of a quadratic functional built on a particular matrix in a -dimensional configurational space of states with discrete variables , . To solve binary optimization problems, neural net approaches are applied widely and quite successfully. Hopfield model is often used. In this paper, procedure of lowering digit capacity of matrix elements, called discretization, is proposed. In discretization, matrix elements are replaced by integers, which digit capacity lower than source elements; therefore, RAM requirements and algorithm speed are reduced. Zero also replaces elements near zero. Discretization procedure is described in details. Theoretical expressions of probability of local fields’ coincidence in random point for matrix with uniform and normal distributions of elements are obtained. Discretization is compared with same methods. Numerous experiments verify theoretical results.
June 24, 2020
May 29, 2020

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