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Finding an energy minimum in the Ising model is an exemplar objective,associated with many combinatorial optimization problems, that iscomputationally hard in general, but occurs in all areas of modern science.There are several numerical methods, providing solution for the medium sizeIsing spin systems. However, they are either computationally slow and badlyparallelized, or do not give sufficiently good results for the large systems.In this paper, we present a highly parallel algorithm, called Mean-fieldAnnealing from a Random State (MARS), incorporating the best features of theclassical simulated annealing (SA) and Mean-Field Annealing (MFA) methods. Thealgorithm is based on the mean-field descent from a randomly selectedconfiguration and temperature. Since a single run requires little computationaleffort, the effectiveness can be achieved by massive parallelisation. MARSshows excellent performance both on the large Ising spin systems and on the setof exemplary maximum cut benchmark instances in terms of both solution qualityand computational time.

Highly parallel algorithm for the Ising ground state searching problem