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Standard scheduled flight block time (SBT) setting is of great concern for Civil Aviation Administration of China (CAAC) and airlines in China. However, the standard scheduled flight block times are set in the form of on-site meetings in practice and current literature has not provided any efficient mathematical models to calculate the flight block times fairly among the airlines. The objective of this paper is to develop and solve a mathematical model for standard SBT setting with consideration of both fairness and reliability. We use whale optimization algorithm (WOA) and an improved version of the whale optimization algorithm (IWOA) to solve the SBT setting problem. A novel nonlinear update equation of convergence factor for random iterations is used in place of the original linear one in the proposed IWOA algorithm. Experimental results show that the suggested approach is effective, and IWOA performs better than WOA in the concerned problem, whose solutions are better compared to the flight block times released by CAAC. In particular, it is interesting to find that MSE, RMSE, MAE, MAPE and Theil of the reliability in 60%–70% range are always the smallest and the average fairness of airlines is better than that of 60%–75% range. The model and solving approach presented in this article have great potential to be applied by CAAC to determine the standard SBTs strategically. [ABSTRACT FROM AUTHOR]

Stock index forecasting is an important tool for both the investors and the government organizations. However, due to the inherent large volatility, high noise, and nonlinearity of the stock index, stock index forecasting has been a challenging task for a long time. This paper aims to develop a novel hybrid stock index forecasting model named BSO-GNN based on the brain storm optimization (BSO) approach and the grey neural network (GNN) model by taking full advantage of the grey model in dealing with data with small samples and the neural network in handling nonlinear fitting problems. Moreover, the new developed BSOGNN, which initializes the parameters in grey neural network with the BSO algorithm, has great capability in overcoming the deficiencies of the traditional GNN model with randomly initialized parameters through solving the local optimum and low forecasting accuracy problems. The performance of the proposed BSO-GNN model is evaluated under the normalization and nonnormalization preprocessing situations. Experimental results from the Shanghai Stock Exchange (SSE) Composite Index, the Shenzhen Composite Index, and the HuShen 300 Index opening price forecasting show that the proposed BSO-GNN model is effective and robust in the stock index forecasting and superior to the individual GNN model. [ABSTRACT FROM AUTHOR]