This paper proposes a prediction method based on chaos theory and an improved empirical-modal-decomposition particle-swarm-optimization long short-term-memory (EMD-PSO-LSTM)-combined optimization process for passenger flow data with high nonlinearity and dynamic space-time dependence, using EMD to process the original passenger flow data and generate several eigenmodal functions (IMFs) and residuals with different characteristic scales. Based on the chaos theory, each component of the PSO algorithm was improved by introducing an inertia factor to facilitate the adjustment of its search capability to improve optimization. Each subsequence of the phase-space reconstruction was built into an improved PSO-LSTM prediction model, and the output of each prediction model was summed to determine the final output. Experimental studies were performed using data from the North Railway Station of Chengdu Rail Transit, and the results showed that the proposed model can generate better prediction results. The proposed model obtained root mean square error (RMSE) and mean absolute error (MAE) of 16.0908 and 11.3704, respectively. Compared with the LSTM, the improved PSO-LSTM, the improved EMD-PSO-LSTM, and the model proposed in this paper improved the RMSE values by 25.53%, 29.97%, and 58.76%, respectively, and the MAE values by 30.41%, 40.13%, and 63.08%, respectively, of the prediction results.

This study proposes an improved vector-weighted averaging algorithm (IDEINFO) for the optimization of different problems. The original vector-weighted optimization algorithm (INFO) uses weighted averaging for entity structures and uses three core procedures to update the positions of the vectors. First, the update rule phase is based on the law of averaging and convergence acceleration to generate new vectors. Second, the vector combination phase combines the obtained vectors with the update rules to achieve a promising solution. Third, the local search phase helps the algorithm eliminate low-precision solutions and improve exploitability and convergence. However, this approach pseudo-randomly initializes candidate solutions, and therefore risks falling into local optima. We, therefore, optimize the initial distribution uniformity of potential solutions by using a two-stage backward learning strategy to initialize the candidate solutions, and a difference evolution strategy to perturb these vectors in the combination stage to produce improved candidate solutions. In the search phase, the search range of the algorithm is expanded according to the probability values combined with the t-distribution strategy, to improve the global search results. The IDEINFO algorithm is, therefore, a promising tool for optimal design based on the considerable efficiency of the algorithm in the case of optimization constraints.