Short-term traffic flow forecasting is an essential part of intelligent transportation systems. However, it is challenging to model traffic flow accurately due to its rapid changes over time. The Kolmogorov–Arnold Network (KAN) has shown parameter efficiency with lower memory and computational overhead via spline-parametrized functions to handle high-dimensional temporal data. In this paper, we propose to unlock the potential of the Kolmogorov–Arnold network for traffic flow forecasting by optimizing its parameters with a heuristic algorithm. The gravitational search algorithm learns to understand optimized KANs for different traffic scenarios. We conduct extensive experiments on four real-world benchmark datasets from Amsterdam, the Netherlands. The RMSE of GSA-KAN is reduced by $3.95\%$, $6.96\%$, $2.71\%$, and $2.29\%$, and the MAPE of GSA-KAN is reduced by $6.66\%$, $5.88\%$, $6.41\%$, and $4.87\%$ on the A1, A2, A4, and A8 datasets, respectively. The experimental results demonstrate that GSA-KAN performs advanced parametric and nonparametric models.

In multivariate and multistep time series prediction research, we often face the problems of insufficient spatial feature extraction and insufficient time-dependent mining of historical series data, which also brings great challenges to multivariate time series analysis and prediction. Inspired by the attention mechanism and residual module, this study proposes a multivariate time series prediction method based on a convolutional-residual gated recurrent hybrid model (CNN-DA-RGRU) with a two-layer attention mechanism to solve the multivariate time series prediction problem in these two stages. Specifically, the convolution module of the proposed model is used to extract the relational features among the sequences, and the two-layer attention mechanism can pay more attention to the relevant variables and give them higher weights to eliminate the irrelevant features, while the residual gated loop module is used to extract the time-varying features of the sequences, in which the residual block is used to achieve the direct connectivity to enhance the expressive power of the model, to solve the gradient explosion and vanishing scenarios, and to facilitate gradient propagation. Experiments were conducted on two public datasets using the proposed model to determine the model hyperparameters, and ablation experiments were conducted to verify the effectiveness of the model; by comparing it with several models, the proposed model was found to achieve good results in multivariate time series-forecasting tasks.

The Pathfinder Algorithm (PFA) is a bionic swarm intelligence optimization algorithm inspired by simulating the cooperative movement of animal groups in nature to search for prey. Based on fitness, the algorithm classifies search individuals into leaders and followers. However, PFA fails to effectively balance the optimization capabilities of leaders and followers, leading to problems such as insufficient population diversity and slow convergence speed in the original algorithm. To address these issues, this paper proposes an enhanced pathfinder algorithm based on multi-strategy (EODE-PFA). Through the synergistic effects of multiple improved strategies, it effectively solves the balance problem between global exploration and local optimization of the algorithm. To verify the performance of EODE-PFA, this paper applies it to CEC2022 benchmark functions, three types of complex engineering optimization problems, and six sets of feature selection problems, respectively, and compares it with eight mature optimization algorithms. Experimental results show that in three different scenarios, EODE-PFA has significant advantages and competitiveness in both convergence speed and solution accuracy, fully verifying its engineering practicality and scenario universality. To highlight the synergistic effects and overall gains of multiple improved strategies, ablation experiments are conducted on key strategies. To further verify the statistical significance of the experimental results, the Wilcoxon signed-rank test is performed in this study. In addition, for feature selection problems, this study selects UCI real datasets with different real-world scenarios and dimensions, and the results show that the algorithm can still effectively balance exploration and exploitation capabilities in discrete scenarios.