The mix-matrix method in the problem of binary quadratic optimization

  • Authors:

  • Iakov Karandashev;Boris Kryzhanovsky

  • Affiliations:

  • Center of Optical Neural Technologies, Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia;Center of Optical Neural Technologies, Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, Russia

  • Venue:
  • ICANN'12 Proceedings of the 22nd international conference on Artificial Neural Networks and Machine Learning - Volume Part I
  • Year:
  • 2012

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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 T2. 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).