It is agreed that portfolio selection models are of great importance for the financial market. In this article, a constrained multiperiod multiobjective portfolio model is established. This model introduces several constraints to reflect the trading restrictions and quantifies future security returns by fuzzy random variables to capture fuzzy and random uncertainties in the financial market. Meanwhile, it considers terminal wealth, conditional value at risk (CVaR), and skewness as tricriteria for decision making. Obviously, the proposed model is computationally challenging. This situation gets worse when investors are interested in a larger financial market since the data they need to analyze may constitute typical big data. Whereafter, a novel intelligent hybrid algorithm is devised to solve the presented model. In this algorithm, the uncertain objectives of the model are approximated by a simulated annealing resilient back propagation (SARPROP) neural network which is trained on the data provided by fuzzy random simulation. An improved imperialist competitive algorithm, named IFMOICA, is designed to search the solution space. The intelligent hybrid algorithm is compared with the one obtained by combining NSGA-II, SARPROP neural network, and fuzzy random simulation. The results demonstrate that the proposed algorithm significantly outperforms the compared one not only in the running time but also in the quality of obtained Pareto frontier. To improve the computational efficiency and handle the large scale securities data, the algorithm is parallelized using MPI. The conducted experiments illustrate that the parallel algorithm is scalable and can solve the model with the size of securities more than 400 in an acceptable time.

中文翻译：

---

大规模证券数据模糊随机收益的多期多目标投资组合选择模型

人们一致认为，投资组合选择模型对金融市场非常重要。本文建立了一个有约束的多周期多目标投资组合模型。该模型引入了几个约束来反映交易限制，并通过模糊随机变量量化未来的证券收益，以捕捉金融市场中的模糊和随机不确定性。同时，它将最终财富、条件风险价值 (CVaR) 和偏度视为决策的标准。显然，所提出的模型在计算上具有挑战性。当投资者对更大的金融市场感兴趣时，这种情况会变得更糟，因为他们需要分析的数据可能构成典型的大数据。此后，设计了一种新颖的智能混合算法来解决所提出的模型。在这个算法中，该模型的不确定目标由模拟退火弹性反向传播 (SARPROP) 神经网络逼近，该网络根据模糊随机模拟提供的数据进行训练。一种改进的帝国主义竞争算法，名为 IFMOICA，旨在搜索解决方案空间。将智能混合算法与NSGA-II、SARPROP神经网络和模糊随机模拟相结合得到的算法进行比较。结果表明，所提出的算法不仅在运行时间上显着优于比较算法，而且在获得的帕累托前沿的质量上也明显优于对比算法。为了提高计算效率和处理大规模证券数据，算法使用 MPI 并行化。