Extremal optimization vs. learning automata: Strategies for spin selection in portfolio selection problems

Nowadays, various imitations of natural processes are used to solve challenging optimization problems faster and more accurately. Spin glass based optimization, specifically, has shown strong local search capability and parallel processing. But, spin glasses have a low rate of convergence since they use Monte Carlo simulation techniques such as simulated annealing (SA). Here, we propose two algorithms that combine the long range effect in spin glasses with extremal optimization (EO-SA) and learning automata (LA-SA). Instead of arbitrarily flipping spins at each step, these two strategies aim to choose the next spin and selectively exploiting the optimization landscape. As shown in this paper, this selection strategy can lead to faster rate of convergence and improved performance. The resulting two algorithms are then used to solve portfolio selection problem that is a non-polynomial (NP) complete problem. Comparison of test results indicates that the two algorithms, while being very different in strategy, provide similar performance and reach comparable probability distributions for spin selection. Furthermore, experiments show there is no difference in speed of LA-SA or EO-SA for glasses with fewer spins, but EO-SA responds much better than LA-SA for large glasses. This is confirmed by tests results of five of the world's major stock markets. In the last, the convergence speed is compared to other heuristic methods such as Neural Network (NN), Tabu Search (TS), and Genetic Algorithm (GA) to approve the truthfulness of proposed methods.

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► Spin glasses have a low rate of convergence by using SA.
► Two algorithms that combine the long range spin glasses with EO-SA and LA-SA are proposed.
► In comparison, while being very different in strategy, provide approximately similar performance.
► The resulting algorithms are applied to five different world stocks.