Search for the ground states of ising spin clusters by using the genetic algorithms

Abstract

Genetic algorithms (GAs) were applied to the search for ground states of randomly generated spin clusters. Two types of hybrid GAs and one type of pure GA modified by crossover operation were developed especially for the search for the ground state on Ising spin clusters. In the hybrid GAs, we used the 1-neighborhood search and the hill-climbing search for local searches. For modification of GAs, we also proposed a new crossover operator, x̄ crossover, which turns all spins upside down. The fitness function (F(x)) was defined in terms of the energies obtained by the Ising Hamiltonian. For the Ising spin clusters, the effective magnetic interaction (Jab) values were calculated with the unrestricted Hartree-Fock method. These GAs worked well on the searches for the ground states, because the improved GAs avoided being trapped in the local minima frequently and picked up the global minima more effectively than the p standard GAs. © 2005 Wiley Periodicals, Inc.