Abstract
In the paper we deal with the NP-complete problem of minimization a quadratic form of N binary variables. The minimization approach based on extensive random search is considered. To increase the efficiency of the random-search algorithm, we vary the attraction area of the deepest minima of the functional by changing the matrix T it is based on. The new matrix M, called mix-matrix, is a mixture of T and T 2. We demonstrate that such a substitution brings about changes of the energy surface: deep minima displace very slightly in the space (the Hemming distance of the shift is of about 0.01*N ), they become still deeper and their attraction areas grow significantly. At the same time the probability of finding close to optimal solutions increases abruptly (by 2-3 orders of magnitude in case of a 2D Ising model of size 12×12 and in case of dense instances of size 500).
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Karandashev, I., Kryzhanovsky, B. (2012). The Mix-Matrix Method in the Problem of Binary Quadratic Optimization. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds) Artificial Neural Networks and Machine Learning – ICANN 2012. ICANN 2012. Lecture Notes in Computer Science, vol 7552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33269-2_6
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DOI: https://doi.org/10.1007/978-3-642-33269-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33268-5
Online ISBN: 978-3-642-33269-2
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