This paper presents a reliable emergency facility location optimization model that considers complex polygon barriers and the risk of facility disruption. From a sustainable perspective, with capacity, cost, and demand constraints, the model maximizes time satisfaction and minimizes cost as the objective function to determine the optimal facility location and allocation. The paper proposes the barrier path optimization algorithm and the Kepler optimization algorithm (KOA) to solve the model and validates the model and algorithm through simulation experiments of various scales. Finally, the paper conducts a sensitivity analysis of the disruption probability using the control variable method to explore the impact of parameter changes on the decision results and compare the advantages of considering a sustainable perspective versus not considering it. The results show that the model and algorithm designed in this paper can effectively optimize the barrier path and obtain the optimal location-allocation scheme. The research findings will provide mathematical models and methodological strategies for emergency facility location decision-making.

Emergency facility location and layout are critical to the efficiency of emergency rescue and resource allocation. However, practical emergency scenarios are plagued by two key challenges: the risk of facility failure due to various uncertain factors and the presence of complex polygonal barriers (including convex and concave polygons) that hinder transportation. Existing studies often overlook concave polygonal barriers or fail to prioritize time satisfaction, a core demand in emergency response. To address these gaps, this paper proposes a reliable emergency facility location optimization model with the objective of maximizing time satisfaction, considering constraints such as capacity, cost, and demand. The model integrates three key methods: a convex hull algorithm to convert concave barriers into convex ones for simplified calculation, a path optimization algorithm to find the shortest bypass routes around barriers, and an Artificial Ecosystem Optimization (AEO) algorithm to solve the nonlinear programming model. Through numerical experiments (single-facility, multi-facility, and medium-scale scenarios) and a practical case study in the Meknès region of Morocco for ambulance deployment, the feasibility and effectiveness of the model and algorithms are verified. The results show that the model achieves high time satisfaction (all above 0.8, with most exceeding 0.9) and efficiently optimizes facility locations and resource allocation. Sensitivity analysis indicates that increased failure risk parameters ($\alpha$ and $\theta$) lead to a gradual decrease in average time satisfaction. This research provides a systematic mathematical model and practical method for emergency facility location decision-making, effectively addressing the challenges of complex barriers and facility failure.

The issue of emergency facility location is a long-term strategic issue, and the complexity and diversity of the decision-making environment force decision-makers to focus on multiple objectives when making location decisions. We develop a multi-objective optimization system centered on cost-effectiveness, service balance, and fairness, targeting three core objectives: minimizing total costs, minimizing differences in service quality among demand points, and minimizing material shortage gaps between demand points. To address the issue of limited facility service capacity induced by material shortages, we establish a multi-objective optimization model for the reliable location of emergency facilities. By combining the model’s characteristics with the Non-Dominated Sorting Genetic Algorithm (NSGA-II) and an elite retention strategy, the Pareto frontier solution set of the multi-objective model is obtained, and the model’s feasibility is verified through various examples of different scales. Finally, sensitivity analysis was conducted on the reliability location model of emergency facilities under different disruption risks using the control variable method, and the topology structure of the reliability location allocation network for emergency facilities under different disruption situations is obtained. The research findings provide decision-makers with actionable references and technical support for selecting reliable locations for emergency facilities amid disruption risks.

Accurate long-term prediction of GNSS satellite clock errors is essential for autonomous navigation, real-time precise point positioning (PPP), and continuous positioning, navigation, and timing (PNT) services when real-time clock products are unavailable or delayed. However, conventional methods, such as quadratic polynomial fitting and Kalman filtering, have limited capability in modeling nonlinear and non-stationary clock behaviors over long prediction intervals, especially under abnormal onboard atomic clock conditions. To address this issue, an inter-satellite comparison data (ISCD)-based radial basis function neural network (RBFNN) model is proposed for long-term satellite clock error prediction. Through correlation analysis, reference satellite clocks closely related to the target satellite are selected, and both ISCD and satellite-ground comparison data are integrated to establish a nonlinear prediction model. Experiments using GPS and Galileo satellite clock datasets demonstrate that the proposed method significantly improves long-term prediction accuracy. For 180-day prediction, the proposed model reduces the RMSE by more than 60% for GPS satellites and approximately 99% for Galileo satellites with abnormal clock behavior compared with conventional methods. Rolling prediction experiments further verify the robustness and stability of the proposed model.