A Constraint Relaxation Co-Evolutionary Algorithm for the Two-Echelon Vehicle Routing Problem with Load-Dependent Drones

Abstract

Two-echelon Vehicle Routing Problems (2E-VRPs) model parcel delivery and pickup in logistics transportation using two echelons of vehicles and transshipment facilities. With the widespread adoption of drones in modern last-mile logistics, optimizing 2E-VRPs that incorporate drones must account for the real-time impacts of cargo weight on drone power consumption and endurance. The optimization requirements for this expanded variant, the Two-Echelon Vehicle Routing Problem with Load-dependent Drones (2E-VRPLD), introduce more complexity than merely identifying the shortest transportation path. To tackle this challenge, we propose a novel Constraint Relaxation Co-evolutionary Algorithm (CRCEA), which includes a customer-satellite matching mechanism that minimizes drone endurance redundancy and a minimal-impact assessment strategy for route segment merging. We assess the performance of the CRCEA through systematic experiments on modified benchmark instances from the existing literature. Compared to conventional heuristic algorithms, the CRCEA consistently achieves superior solution quality. Additionally, we perform sensitivity analyses to investigate the influence of key characteristics on the algorithm's performance and the 2E-VRPLD problem.

Keywords: Two-echelon vehicle routing problems, drone energy consumption management, co-evolutionary, constraint relaxation