A decoding-priority-based self-adaptive prairie dog optimizer for cyclic cross-period bidirectional milk-run vehicle scheduling problem

In the context of mass customization , the milk-run model has emerged as a predominant logistics strategy. However, traditional milk-run models fail to exploit the potential of integrating transportation tasks across multiple periods. Additionally, growing environmental concerns necessitate the inclusion of reverse logistics. This paper investigates a Cyclic Cross-Period Bidirectional Milk-run Vehicle Scheduling Problem (CCBMVSP) that aims to minimize both economic costs (total operational cost) and service levels (total earliness and tardiness) simultaneously. To address this problem, we develop a mixed-integer programming model and apply the epsilon-constraint method to obtain exact solutions for small-scale instances. Given the NP-hard nature of the problem, we propose a multi-objective optimization algorithm, the Decoding-priority-based Self-adaptive Prairie Dog Optimizer (DSPDO). The encoding and decoding procedures are specifically designed with a constraint-oriented solution repair strategy. Chaotic mapping is introduced to enhance the diversity of the initial population. Moreover, we propose a multi-elite iteration strategy and a variable neighborhood search strategy to strengthen the algorithm’s exploration and exploitation capabilities. Based on decoding priority, an adaptive exploration–exploitation balance strategy is also introduced. Finally, extensive numerical experiments demonstrate that the proposed algorithm outperforms benchmark methods when solving larger-scale instances.