Spin Glass Energy Minimization through Learning and Evolution
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pin Glass Energy Minimization through Learning and Evolution V. G. Red’ko* Scientific Research Institute for System Analysis, Russian Academy of Sciences, Moscow, 117218 Russia *e-mail: [email protected] Received April 24, 2020; revised May 12, 2020; accepted June 2, 2020
Abstract—The research considers the minimization of spin glass energy via learning and evolution. The Sherrington-Kirkpatrick spin-glass model is used. A population of autonomous agents is considered. The genotype and phenotype of each agent are chains consisting of a great number of spins. The energy of spin glasses is minimized through learning and evolution of agents. The genotypes of agents are optimized by evolution; the phenotypes are optimized by learning. The evolution of a population of agents is analyzed. In the evolution the fitness of agents is determined by the energy of the spin glass of final phenotypes resulted from learning: the lower the energy is, the higher the fitness of the agent is. In the next generation agents are selected with probabilities corresponding to their fitnesses. Agents-descendants get mutationally modified genotypes of agents-ancestors. The interaction between learning and evolution during the spin glass energy minimization is investigated. The research involves the computer simulation. Keywords: spin glass energy minimization, autonomous agents, learning and evolution of agents, genotypes, phenotypes DOI: 10.3103/S1060992X20030054
1. INTRODUCTION The paper deals with spin glass energy minimization via learning and evolution of autonomous agents. The model of learning and evolution of autonomous agents is formed. A population of agents is considered. Each agent has a genotype and phenotype that are spin chains of great length N. Both the genotype and phenotype determine the spin glass energy calculated with the use of the Sherrington-Kirkpatrick model [1, 2]. The learning process, which aims at the phenotype-dependent decrease of the spin glass energy, underlies the phenotype optimization. The genotype is optimized in evolution as a result of selection and mutations. Each generation of the evolution lasts T time periods (t = 1, 2, …, T). The life time of each agent is T. At the beginning of the new generation (at t = 1), the genotypes of all its agents repeat the mutationally modified genotypes of ancestors-agents of the preceding generation. At birth the phenotype of an agent is identical to its genotype. Over the population lifetime the phenotypes of agents change through the learning, the genotypes staying the same. The learning of an agent decreases the spin glass energy, which is determined by the phenotype of this agent. When the generation ends at t = T, the parent agents are selected to produce descendants of the next generation. The agents fitnesses underlie the selection. The fitness of each agent is determined by the spin glass energy set by the final phenotype of this agent: the lower the energy is, the higher fitness the agent has. It is important that the number of local minima of the spin glass
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