The green vehicle routing problem with private capacitated alternative fuel stations (GrVRP-PCAFS) extends the traditional green vehicle routing problem by considering capacitated refueling stations, where a limited number of vehicles can refuel simultaneously and additional vehicles must wait. This feature presents new challenges for route planning, as waiting times at stations must be managed while keeping route durations within limits and reducing total travel distance. This article presents METS, a novel memetic algorithm (MA) with separate constraint-based tour segmentation (SCTS) and a local search procedure tailored for solving GrVRP-PCAFS. METS balances exploration and exploitation through three key components. For exploration, the SCTS strategy splits giant tours to generate diverse solutions, and the search process is guided by a comprehensive fitness evaluation function to dynamically control feasibility and diversity to produce solutions that are both diverse and near-feasible. For exploitation, the local search procedure incorporates tailored move operators with constant-time evaluation mechanisms, enabling efficient examination of large solution neighborhoods. Experimental results demonstrate that METS discovers 31 new best-known solutions out of 40 instances in existing benchmark sets, achieving substantial improvements over current state-of-the-art methods. Additionally, a new large-scale benchmark set based on real-world logistics data is introduced to facilitate future research.

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