Complex & Intelligent Systems

Motivated by express and e-commerce companies’ distribution practices, we study a two-echelon electric vehicle routing problem. In this problem, fuel-powered vehicles are used to transport goods from a depot to intermediate facilities (satellites) in the first echelon, whereas electric vehicles, which have limited driving ranges and need to be recharged at recharging stations, are used to transfer goods from the satellites to customers in the second echelon. We model the problem as an arc flow model and decompose the model into a master problem and pricing subproblem. We propose a branch-and-price algorithm to solve it. We use column generation to solve the restricted master problem to provide lower bounds. By enumerating all the subsets of the satellites, we generate feasible columns by solving the elementary shortest path problem with resource constraints in the first echelon. Then, we design a bidirectional labeling algorithm to generate feasible routes in the second echelon. Comparing the performance of our proposed algorithm with that of CPLEX in solving a set of small-sized instances, we demonstrate the former’s effectiveness. We further assess our algorithm in solving two sets of larger scale instances. We also examine the impacts of some model parameters on the solution.

We aim to develop a deep-learning-based method for automatic proximal femur segmentation in quantitative computed tomography (QCT) images. We proposed a spatial transformation V-Net (ST-V-Net), which contains a V-Net and a spatial transform network (STN) to extract the proximal femur from QCT images. The STN incorporates a shape prior into the segmentation network as a constraint and guidance for model training, which improves model performance and accelerates model convergence. Meanwhile, a multi-stage training strategy is adopted to fine-tune the weights of the ST-V-Net. We performed experiments using a QCT dataset which included 397 QCT subjects. During the experiments for the entire cohort and then for male and female subjects separately, 90% of the subjects were used in ten-fold stratified cross-validation for training and the rest of the subjects were used to evaluate the performance of models. In the entire cohort, the proposed model achieved a Dice similarity coefficient (DSC) of 0.9888, a sensitivity of 0.9966 and a specificity of 0.9988. Compared with V-Net, the Hausdorff distance was reduced from 9.144 to 5.917 mm, and the average surface distance was reduced from 0.012 to 0.009 mm using the proposed ST-V-Net. Quantitative evaluation demonstrated excellent performance of the proposed ST-V-Net for automatic proximal femur segmentation in QCT images. In addition, the proposed ST-V-Net sheds light on incorporating shape prior to segmentation to further improve the model performance.