Increasing the attraction area of the global minimum in the binary optimization problem

The problem of binary minimization of a quadratic functional in the configuration space is discussed. In order to increase the efficiency of the random-search algorithm it is proposed to change the energy functional by raising to a power the matrix it is based on. We demonstrate that this brings about changes of the energy surface: deep minima displace slightly in the space and become still deeper and their attraction areas grow significantly. Experiments show that this approach results in a considerable displacement of the spectrum of the sought-for minima to the area of greater depth, and the probability of finding the global minimum increases abruptly (by a factor of 10<Superscript>3</Superscript> in the case of the 10 × 10 Edwards–Anderson spin glass). Copyright Springer Science+Business Media, LLC. 2013