Mathematics

Accurate prediction of peak particle velocity (PPV) in open-pit mine blasting is critical for ensuring operational safety and effective vibration control. This study proposes a hybrid modeling approach that integrates the Centered Collision Optimization (CCO) algorithm with Extreme Gradient Boosting (XGBoost), enhanced by SHAP-based sensitivity analysis to improve model transparency and mechanistic interpretability. A comprehensive dataset was constructed based on 193 field-measured blasting records collected from the Panzhihua Iron Mine in China, incorporating nine key input parameters. Model performance was rigorously evaluated using four widely recognized metrics: coefficient of determination (R²), root mean square error (RMSE), mean absolute error (MAE), and variance accounted for (VAF). The results demonstrate that the CCO–XGBoost model achieves superior predictive performance, with R² = 0.967, RMSE = 0.110, MAE = 0.067, and VAF = 96.35%, outperforming conventional approaches. SHAP-based sensitivity analysis reveals that blast-to-monitor distance (R) is the dominant negative predictor of PPV, contributing 43% to the total influence, with its vibration attenuation effect intensifying significantly when R exceeds 54 m. Charge per hole (q) and total charge per delay (Q) are identified as the primary positive influencing factors, accounting for 24% and 20% of the total contribution, respectively: the positive promoting effect of q on PPV strengthens markedly when q exceeds 17 kg, while Q exerts a continuous positive increasing influence on PPV when it exceeds 253 kg. Compared to existing hybrid models, the CCO–XGBoost uniquely avoids local optima and ensures higher global stability. This study fills the gap by providing quantifiable engineering thresholds for practical vibration control, making the model directly applicable to on-site blasting optimization.

This paper investigates the distributed event-triggered fixed-time time-varying formation control problem for a class of nonlinear multi-agent systems subject to model uncertainties and unknown time-varying disturbances. To address issues in traditional formation control methods, such as convergence time dependence on initial states and high communication resource consumption, a distributed cooperative control scheme integrating fixed-time control, event-triggered mechanisms, and dynamic surface control is proposed. Firstly, a fixed-time disturbance observer is designed to accurately estimate the agents’ lumped disturbances within a fixed time independent of initial conditions. Secondly, by incorporating dynamic surface control techniques, a distributed event-triggered formation control law is constructed, effectively reducing communication and computational resource usage. Furthermore, using Lyapunov stability theory, the closed-loop system is proven to exhibit practical fixed-time stability, and the existence of a positive lower bound for triggering intervals precludes Zeno behavior. Finally, numerical simulations validate the superiority of the proposed method in terms of convergence speed, control accuracy, and resource efficiency. This research provides an efficient, robust, and resource-friendly solution for cooperative control of multi-agent systems in complex environments.

The Capacitated Vehicle Routing Problem (CVRP) has a wide range of applications in logistics and transportation. Current metaheuristics typically rely on manually added constraints. A hyper-heuristic framework can reduce the dependency on domain-specific knowledge. Therefore, this research proposes a Clustered Simulated Annealing algorithm (CSA). When generating the initial solution of the distribution path, the CSA adopts the Clustered Clarke–Wright Savings algorithm (CCW), the core of which is to use the K-means algorithm to cluster according to the Euclidean distances between the distribution points. The CCW can reduce the search range of the optimization problem by clustering and generating the initial solution quickly, enabling the CSA to perform better in data processing and real-time updates. The CSA then optimizes the initial solution using the Improved Simulated Annealing Hyper-Heuristic algorithm (ISAHH), divided into upper and lower layers. The Improved Simulated Annealing High-Level Heuristic strategy (ISAHLH) is used to select the Low-Level Heuristic operators (LLHs). At the same time, LLHs are used to generate new distribution paths. This research designs an Improved Tabu Low-Level Heuristic operator (ITabuLLH), which can search for several different paths simultaneously in a single iteration, thus improving the convergence speed of the algorithm. ISAHLH and ITabuLLH both use the Unequal Probability Selection mode (UEPS) to speed up the search process. The CSA is tested on the Uchoa benchmark set, and the results verify that the optimal value improvement of the CSA solution is higher than 20% when compared to eleven other algorithms.