{'fraction_non_alphanumeric': 0.021139705882352942, 'fraction_numerical': 0.0, 'mean_word_length': 5.443786982248521, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Dynamic passenger demand-oriented train scheduling optimization considering flexible short-turning strategy

Abstract In this study, we focus on improving the efficiency of an urban rail transit line under the circumstance of spatially unbalanced passenger demand. A flexible short-turning strategy is integrated into the train scheduling problem, aiming to obtain a train timetable and the corresponding circulation plan adapted to a time-dependent passenger demand. First, we formulate the dynamic passenger demand-oriented train scheduling problem as a multi-commodity network flow optimization model in a two-layer space-time network. The proposed model is then decomposed into train scheduling and passenger assignment sub-problems by relaxing the coupling constraint. Therefore, an optimal solution of the original model can be obtained by iteratively solving two easy-to-solve sub-problems in a Lagrangian relaxation solution framework. The effectiveness of the model is evaluated using a series of simple experiments and a real-world case study based on the Beijing Yizhuang Line.