Adaptive large neighborhood search incorporating mixed-integer linear programming for electric vehicle routing problem with mobile charging and nonlinear battery degradation

Abstract

The limited driving range and short battery life are obstacles to the widespread adoption of electric vehicles in urban logistics. This study proposes an electric vehicle routing problem with time window, mobile charging, and nonlinear battery degradation. Mobile charging vehicles (MCVs) can be flexibly scheduled to charge the electric delivery vehicles (EDVs) at customer locations, reducing the electricity consumption caused by the detours to the charging stations. The proposed problem is formulated into an arc-based model that incorporates nonlinear battery degradation costs associated with State of Charge (SOC) and charging strategies, thereby enhancing the complexity of the spatio-temporal synchronization mechanism. Constraining a lower SOC can mitigate the battery degradation of EDVs, but it leads to increased charging demands and makes searching for feasible routing solutions more challenging due to the interdependence between MCVs and EDVs. A hybrid adaptive large neighborhood search heuristic algorithm is developed. Dynamic programming is embedded in the algorithm framework to devise charging schemes considering nonlinear battery degradation for the given EDVs’ routes. A mixed-integer linear programming model is formulated to select the combination of labels with continuous charging decisions and design MCVs’ routes. Extensive numerical experiments are conducted to verify the proposed model and algorithm. Experimental results indicate considering battery degradation in the objectives significantly improves the total system costs by optimizing the SOC and charging quantity. Mobile charging can be an alternative for constructing fixed charging facilities due to the charging flexibility of MCVs. The performance of our algorithm is demonstrated through both large-scale instances and a real-world case study on urban logistics.