Neural Networks for Combinatorial Optimization: a Review of More Than a Decade of Research
INFORMS Journal on Computing
New Optimization Algorithms in Physics
New Optimization Algorithms in Physics
Eigenvalue problem approach to discrete minimization
ICANN'05 Proceedings of the 15th international conference on Artificial neural networks: formal models and their applications - Volume Part II
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The paper deals with the minimization of a quadratic functional in the configuration space of binary states. To increase the efficiency of the random-search algorithm, we offer changing the functional by raising the matrix it is based on to a power. 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. The experiment shows that use of the approach results in a considerable displacement of the spectrum of sought-for minima to the area of greater depths, while the probability to find the global minimum increases abruptly (by a factor of 103 in the case of a two-dimensional Ising model).