Resilience is an important capability for many complex systems to mitigate the impact of extreme events as well as timely restoration of system performance in the aftermath of a disruptive event. In this paper, we investigate a bi-level pre-disaster resilience-based design optimization approach for the configuration of logistics service centers. In the bi-level program, the upper-level model considers the impact of potential disruptive events, and characterizes system planners’ decision regarding possible service center configuration that consists of two decision variables: construction of service center at candidate sites and their specific capacities. The optimization in the upper-level model considers both the travel time of each customer from their origins to the service centers and the within-center service time including average waiting time in the queue and mean processing time. The lower-level model captures customers’ behavior in choosing the distribution center to fulfill their requests with the goal of minimizing the cumulative travel time for all the customers. The objective of the formulated bi-level program is to maximize the resilience of the service center configuration, thereby increasing the ability of the system to withstand unexpected events. To tackle this NP-hard optimization problem, an adaptive importance sampling approach – cross entropy-based method – is leveraged to generate samples that gradually concentrates all its mass in the proximity of the optimal solution in an iterative way. A numerical example is used to illustrate the procedures of the developed method and demonstrate the effectiveness of the proposed methodology.

Safety, as the most important concern in civil aviation, needs to be maintained at an acceptable level at all times in the air transportation system. This paper aims to increase en-route flight safety through the development of deep learning models for trajectory prediction, where model prediction uncertainty is characterized following a Bayesian approach. The proposed methodology consists of four steps. In the first step, a large volume of raw messages in Flight Information Exchange Model (FIXM) format streamed from Federal Aviation Administration are processed with a distributed computing engine Apache Spark to extract trajectory information in an efficient manner. In the second step, two types of deep learning models are trained to predict flight trajectory from different perspectives. Specifically, deep feedforward neural networks (DNN) are trained to make a one-step-ahead prediction on the deviation along latitude and longitude between the actual flight trajectory and target flight trajectory. In parallel, deep Long Short-Term Memory (LSTM) neural networks are trained to make longer-term predictions on the flight trajectory over several subsequent time instants. The DNN model is more accurate but has a single-step prediction horizon, whereas the LSTM model is less accurate but longer prediction horizon. Therefore, in the third step, the two different types of deep learning models are blended together to create a multi-fidelity prediction. After quantifying the discrepancy between the two model predictions in the current time instant, the DNN prediction is used to correct the LSTM prediction of flight trajectory along subsequent time instants accordingly. The multi-fidelity approach is expanded to multiple flights, and is then used to assess safety based on horizontal and vertical separation distance between two flights. Computational results illustrate the promising performance of the blended model in predicting the flight trajectory and assessing en-route flight safety.