Searching Ground States of Ising Spin Glasses with a Tree Bond-Based Representation

Ising spin glasses are a rich source of challenging highly multimodal optimization problems.The Ising model is one of the most widely used models for disordered systems in statistical physics.Finding the ground state of an Ising spin glass can be expressed as the problem of determining the minimum weighted cut in a graph.The classical approach when dealing with a spin glasses system is to encode the state of the system based on the states of spins.This paper presents a new representation for the states of Ising spin glasses based on the bonds between spins.This encoding is used with a specially designed Genetic Algorithm to search for low energy states of such systems, with the goal of finding ground states.To this end, special genetic operators are also defined and presented in detail in the paper.The results of preliminary experiments are very promising for this class of problems.