Abstract: This paper establishes a two-objective model with possibilistic mean, possibilistic variance and covariance instead of the mean value, variance and covariance in probability. The two-objective model is transformed into a single-objective model by using the linear weighting method of weighting the target, then a hybrid algorithm combined with particle swarm optimization and artificial fish swarm algorithm is designed to solve the problem. In this algorithm, the result of particle swarm optimization algorithm is taken as the initial fish group of artificial fish swarm algorithm, and the further search is made to avoid the shortcoming of particle swarm optimization. At the same time, the best position in the fish population is fed back to the velocity updating formula of the particle swarm to guide the motion of the particles and accelerate its convergence. Finally, the empirical analysis indicates that the hybrid algorithm of PSO and AFSA is effective, and the global optimum solution obtained by the hybrid algorithm is better than the one obtained by PSO.

Key words: portfolio selection;particle swarm optimization algorithm, artificial fish swarm algorithm;linear weighting;global search

摘要： 针对模糊不确定的证券市场,用可能性均值、下可能性方差和协方差分别替换了投资组合模型中概率均值、方差和协方差,构建了双目标均值-方差投资组合模型。然后采用线性加权法将双目标模型转化为单目标模型,进而提出了一个PSO-AFSA混合算法对其求解。该混合算法中,将粒子群算法搜索的结果作为人工鱼群算法初始鱼群,进一步搜索,这样能有效的避免粒子群算法陷入局部最优。同时,将人工鱼群中的最好位置反馈到粒子群算法的速度更新公式中,指引粒子运动,加快算法收敛。最后,进行实例分析,结果表明:PSO-AFSA混合算法是有效的,混合算法搜索到的全局最优值好于基本粒子群算法搜索到的全局最优值。

关键词: 投资组合, 粒子群算法, 人工鱼群算法, 线性加权, 全局搜索