Multi Scale Spin Glass Based Portfolio Selection

One of the techniques to resolve the problem more quickly is using the multi-scale spatial dimension reduction. In classical theory, system analysis based on multi-scaling is extremely difficult, because it is dependent on the behavior of every component analysis and understanding the relationship between them. The new achievements in this field show that most systems cannot be scaled at any condition. Regardless to this property of the system, Kadanoff's theory shows a necessary condition of scaling. Based on this theory, the best condition of scaling occurs in the phase transition condition at the critical temperatures of material. In this condition, upper-scale system behavior is approximately similar to the main-scale system behavior. This article is benefited from this theory and is presented the new algorithm that is named Simulated Annealing Multi-Scaling (SAMS). This algorithm is based on the spin glass paradigm to solve the NP-complete portfolio selection problem as a case study. Due to many relationships between stocks, the problem scaling, is equivalent to loss of part of the data, hence the possibility to achieve the ground state decline so much. By using this theory, it is shown that the best time to change the scale of the problem with minimum error occurs during its phase transition. Tests on five major stock exchange data show, this algorithm, in addition to confirming Kadanoff's theory in application, has more convergence speed than traditional methods such as SA and also, provides the possibility of using parallel processing in optimization problems.