Evolutionary minimization of spin glass energy

Abstract

The current work describes the model of evolutionary minimization of energy of spin glasses. The population of agents (modeled organisms) is considered. The genotypes of agents are coded by a large number of spins of the spin glass. The energy of the spin glass is calculated in accordance with the Sherrington-Kirkpatrick model. This energy determines the fitness of agents. The process of evolutionary minimization of the spin glass energy is analyzed by means of computer simulation. Several properties of spin glasses that are related to the model of evolutionary search are analyzed. In particular, the global energy minima of spin glasses and the variation of energy at one-spin mutation are estimated. The process of the gradual decrease of the spin glass energy is also analyzed. The gradual decrease is performed by sequential changes of signs of separate spins of spin glass. The computer simulation demonstrates that evolutionary optimization results in the finding of essentially deeper energy minima as compared with the gradual decrease. The rate and efficiency of evolutionary minimization of energy of spin glasses have been estimated and checked by computer simulation.