中文摘要：

在马克维茨投资组合的均值-方差模型框架下,给出限制投资数量的自融资投资组合优化模型.在金融市场上有广泛应用,为了有效地求解此类问题的最优解,采用一种基于广义学习策略的约束粒子群算法（CPSO）.CPSO算法具有广义的学习策略,极大地提升了种群的多样性,进而提升种群跳出局部最优解的能力.在基准函数测试中,结果显示CPSO算法有较好的运行结果.在自融资投资组合优化模型上,优化结果表明CPSO算法是可行的,有效的,并有较好的优化结果.

英文摘要：

Based on Markowitz＇s mean-variance portfolio model,a self-financing portfolio optimal model with constraints of invest proportions is proposed,which is widely used in financial market.In order to effectively solve the optimal solution of this model,a comprehensive learning constraint PSO algorithm is proposed（CPSO for short）.In CPSO,the comprehensive learning strategy is adopted,which greatly improve the diversity of the swarm and improve the ability to escape from local optima.The experiments on benchmarks indicate that the proposed algorithm has good performance.And in self-financing portfolio optimal model,the CPSO algorithm is feasible and effective,and the more effective results.