Affiliations: [a] School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, Jiangsu, China | [b] Key Laboratory of Advanced Process Control for Light Industry (Jiangnan University), Ministry of Education, Wuxi, Jiangsu, China | [c] School of Computer Science and Engineering, Anhui University of Science & Technology, Huainan, Anhui, China | [d] Department of Radiology, University of Pennsylvania, Philadelphia, PA, USA
Correspondence:
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Corresponding author: Hong-Wei Ge, School of Artificial Intelligence and Computer Science, Jiangnan University, Wuxi, Jiangsu 214122, China. E-mail: ghw8601@163.com.
Abstract: In this paper, the mathematical model of Vehicle Routing Problem with Time Windows (VRPTW) is established based on the directed graph, and a 3-stage multi-modal multi-objective differential evolution algorithm (3S-MMDEA) is proposed. In the first stage, in order to expand the range of individuals to be selected, a generalized opposition-based learning (GOBL) strategy is used to generate a reverse population. In the second stage, a search strategy of reachable distribution area is proposed, which divides the population with the selected individual as the center point to improve the convergence of the solution set. In the third stage, an improved individual variation strategy is proposed to legalize the mutant individuals, so that the individual after variation still falls within the range of the population, further improving the diversity of individuals to ensure the diversity of the solution set. Based on the synergy of the above three stages of strategies, the diversity of individuals is ensured, so as to improve the diversity of solution sets, and multiple equivalent optimal paths are obtained to meet the planning needs of different decision-makers. Finally, the performance of the proposed method is evaluated on the standard benchmark datasets of the problem. The experimental results show that the proposed 3S-MMDEA can improve the efficiency of logistics distribution and obtain multiple equivalent optimal paths. The method achieves good performance, superior to the most advanced VRPTW solution methods, and has great potential in practical projects.
