Memetic Search for Green Vehicle Routing Problem with Private Capacitated Refueling Stations

TL;DR

The paper tackles the Green Vehicle Routing Problem with Private Capacitated Alternative Fuel Stations (GrVRP-PCAFS), where limited refueling capacity induces waiting times that must be managed within route duration and energy constraints. It introduces METS, a memetic algorithm with a separate constraint-based tour split (SCTS) for exploration, a comprehensive fitness function balancing cost, feasibility, and diversity, and a local-search core with conditional AFS insertion (CAI) moves and constant-time evaluations for exploitation. METS achieves 31 new best-known solutions across 40 benchmark instances and establishes a large-scale Beijing dataset up to 1000 customers, with open-source code to enable replication and future work. Overall, METS demonstrates superior solution quality and robustness over state-of-the-art methods, highlighting the value of decoupled constraint handling, diversity-aware fitness, and efficient neighborhood search for complex VRPs with station-capacity constraints.

Abstract

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.

Figures (6)

• Figure 1: Illustrations of vehicle waiting caused by the limited capacity at AFS in GrVRP-PCAFS with three AFVs, eight customers, and one AFS that can serve one vehicle at the same time. (a) Three AFVs depart from the depot. (b) During service, AFV 2 is refueling while AFV 3 arrives at the same station and must wait. (c) AFS 3 exceeds the route duration limit due to waiting for refueling. (d) After adjusting the route plan (the blue line), AFS 3 serves customers first and then refuels at the AFS, thus avoiding crowding at the AFS. (e) All AFVs complete their routes within the route duration limit.
• Figure 2: Illustrative examples of all move operators used. Dashed lines represent the removed arcs, while solid lines indicate the new arcs added due to the move. The symbol “minAFS” represents an additional AFS inserted when the CAI rule is applied.
• Figure 3: The convergence profiles of METS-WNM and METS on the M-Central50_3, M-Central50_8, M-Central100_2, and M-Central100_4 instances across 30 independent runs. The lines represent the average best values with respect to the number of iterations.
• Figure 4: The average ratio of visited solutions and the average runtime per generation of METS and METS-Wfast on nine instances of different sizes. Solid blue lines represent the runtime of METS, while dashed lines represent the runtime of METS-Wfast.
• Figure 5: The convergence profiles of METS on four representative instances in terms of feasibility violation difference. The lines represent the average of difference between the number of feasible and infeasible individuals among the last 20 individuals for each constraint type: overtime, over-mileage, and over-capacity. Positive values indicate more feasible individuals.