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Abstract: In this paper, firstly a modified particle swarm optimization algorithm (MPSO) is developed, in which the mean value of past optimal positions for each particle and the mutation operation are considered for avoiding premature. In the optimization test, MPSO performs better than particle swarm optimization algorithm (PSO). Then MPSO is applied to solve four portfolio optimization models with the real data from the Hong Kong Stock Market, and optimal values are obtained when the number of swarm , respectively. Finally, actual return rates of these models are calculated in numerical experiments, and it is illustrated from these graphs of actual return rates that when considering higher return, Cai’s model performs better in short-term investment. [Copyright &y& Elsevier]

Given generalized reflection matrices R, S, i.e., R* = R, R2 = I, S* = S, S2 = I, a complex matrix A is said to be generalized reflexive (or anti-reflexive), if RAS = A (or RAS = -A). In this paper, Smarandache iterative algorithm is proposed to solve matrix equation AXB + CY D = F with generalized reflexive matrix dual (X,Y ). For any initial iterative matrix pair (X1; Y1), we show that a solution of this equation can be obtained within finite iteration steps in the absence of roundoff errors. Some numerical examples illustrate the feasibility and efficiency of this algorithm. [ABSTRACT FROM AUTHOR]