A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph
The Dynamic Interval (DI) graph models the updating uncertainty of the arc cost in the graph, which shows great application prospects in unstable-road transportation planning and management. This paper studies the Real-time Shortest Path (RTSP) problems in the DI graph. First, the RTSP problem is de...
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MDPI AG
2025-01-01
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| author | Bo Xu Xiaodong Ji Zhengrong Cheng |
| author_facet | Bo Xu Xiaodong Ji Zhengrong Cheng |
| author_sort | Bo Xu |
| collection | DOAJ |
| description | The Dynamic Interval (DI) graph models the updating uncertainty of the arc cost in the graph, which shows great application prospects in unstable-road transportation planning and management. This paper studies the Real-time Shortest Path (RTSP) problems in the DI graph. First, the RTSP problem is defined in mathematical equations. Second, three models for RTSP are proposed, which are the Dynamic Robust Shortest Path (DRSP) model, the Dynamic Greedy Robust Shortest Path (DGRSP) model and the Dynamic Mean Shortest Path (DMSP) model. Then, three solution methods are designed. Finally, a numerical study is conducted to compare the efficiency of the models and corresponding solution methods. It shows that the DGRSP model and DMSP model generally present better results than the others. In the real road network test, they have the minimum average-regret-ratio of DGSP 7.8% and DMSP 7.1%; while in the generated network test, they both have a minimum average-regret-ratio of 0.5%. |
| format | Article |
| id | doaj-art-fd90fa23af4f45769aac38aa657c7a38 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-fd90fa23af4f45769aac38aa657c7a382025-01-10T13:18:22ZengMDPI AGMathematics2227-73902025-01-0113113410.3390/math13010134A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval GraphBo Xu0Xiaodong Ji1Zhengrong Cheng2Business School, University of Shanghai for Science and Technology, Shanghai 200093, ChinaSchool of Management, Shanghai University of Engineering Science, Shanghai 201620, ChinaSchool of Business Information, Shanghai Business School, Shanghai 201499, ChinaThe Dynamic Interval (DI) graph models the updating uncertainty of the arc cost in the graph, which shows great application prospects in unstable-road transportation planning and management. This paper studies the Real-time Shortest Path (RTSP) problems in the DI graph. First, the RTSP problem is defined in mathematical equations. Second, three models for RTSP are proposed, which are the Dynamic Robust Shortest Path (DRSP) model, the Dynamic Greedy Robust Shortest Path (DGRSP) model and the Dynamic Mean Shortest Path (DMSP) model. Then, three solution methods are designed. Finally, a numerical study is conducted to compare the efficiency of the models and corresponding solution methods. It shows that the DGRSP model and DMSP model generally present better results than the others. In the real road network test, they have the minimum average-regret-ratio of DGSP 7.8% and DMSP 7.1%; while in the generated network test, they both have a minimum average-regret-ratio of 0.5%.https://www.mdpi.com/2227-7390/13/1/134dynamic interval graphreal-time shortest pathnested Dijkstra algorithmdynamic vehicle routing |
| spellingShingle | Bo Xu Xiaodong Ji Zhengrong Cheng A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph Mathematics dynamic interval graph real-time shortest path nested Dijkstra algorithm dynamic vehicle routing |
| title | A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph |
| title_full | A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph |
| title_fullStr | A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph |
| title_full_unstemmed | A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph |
| title_short | A Comparison of Three Real-Time Shortest Path Models in Dynamic Interval Graph |
| title_sort | comparison of three real time shortest path models in dynamic interval graph |
| topic | dynamic interval graph real-time shortest path nested Dijkstra algorithm dynamic vehicle routing |
| url | https://www.mdpi.com/2227-7390/13/1/134 |
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