Time-dependent rural postman problem: time-space network formulation and genetic algorithm (original) (raw)
Abstract
In this paper, a new time-space network model is proposed for addressing the time-dependent rural postman problem (TDRPP) of a single vehicle. The proposed model follows the idea of arc-path alternation to form a feasible and complete route. Based on the proposed model, the time dependency of the TDRPP is better described to capture its dynamic process, compared to the existing methods using a piecewise constant function with limited intervals. Furthermore, the property of first-in-first-out (FIFO) can be satisfied with the time spent on each arc. We investigate the FIFO property for the considered time-dependent network and key optimality property for the TDRPP. Based on this property, a dedicated genetic algorithm (GA) is proposed to efficiently solve the considered TDRPP that suffers from computational intractability for large-scale cases. Comprehensive simulation experiments are conducted for various time-dependent networks to show the effectiveness of the proposed GA.
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Acknowledgements
This research is supported by the National Natural Science Foundation of China under Grant 61703372 and the Outstanding Foreign Scientist Project in Henan Province under Grant GZS2019008.
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Authors and Affiliations
- School of Electrical Engineering, Zhengzhou University, Science Road 100, Zhengzhou, 450001, China
Jianbin Xin, Benyang Yu & Heshan Wang - Dipartimento di Ingegneria, Università Degli Studi Roma Tre, via della Vasca Navale, 79 - 00146, Roma, Italy
Andrea D’Ariano - Department of Transport and Planning, Delft University of Technology, Mekelweg 2, 2628 CN , Delft, The Netherlands
Meng Wang
Authors
- Jianbin Xin
- Benyang Yu
- Andrea D’Ariano
- Heshan Wang
- Meng Wang
Corresponding author
Correspondence toHeshan Wang.
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Appendix
Appendix
- The total time spent \(f_{\pi }(t_{s})\) can be calculated by Algorithm 3. In Algorithm 3, the term \(\{v^{k}_{1},v^{k}_{2},...,v^{k}_{n_k}\}\) represents the node sequence corresponding to transition path \(p_{k}\), while \(n_k\) represents the number of nodes included in \(p_{k}\).
- The number of constraints and decision variables of the proposed TSN model for each scenario is provided in Table 11.
- A description of the VNS and ACO algorithms used in this paper can be found in Hansen et al. (2017); Halim and Ismail (2019). In order to compare with GA fairly, the maximum fitness evaluation times of the two algorithms are 144000(360*400). The neighborhood structure used by the VNS algorithm in the shaking and improvement procedure is “2-opt move”, “Insertion-1 move” and “Insertion-2 move”. The ant colony size and iteration number of the ACO algorithm are 360 and 400, which are consistent with those of the GA. The other parameters of ACO are optimized by the cross validation, and the specific parameters are shown in Table 12.
Table 11 The number of constraints and decision variables corresponding to the time-space network model
Table 12 VNS and ACO algorithm parameters
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Xin, J., Yu, B., D’Ariano, A. et al. Time-dependent rural postman problem: time-space network formulation and genetic algorithm.Oper Res Int J 22, 2943–2972 (2022). https://doi.org/10.1007/s12351-021-00639-0
- Received: 10 August 2020
- Revised: 25 March 2021
- Accepted: 10 April 2021
- Published: 03 May 2021
- Version of record: 03 May 2021
- Issue date: July 2022
- DOI: https://doi.org/10.1007/s12351-021-00639-0