A novel multi-objective artificial bee colony algorithm for solving the two-echelon load-dependent location-routing problem with pick-up and delivery

This study considers a two-echelon load-dependent location routing problem with pick-up and delivery (2E-LDLRPPD). As a variant of the two-echelon vehicle routing problem with pick-up and delivery (2E-VRPPD), the 2E-LDLRPPD includes additional variants such as two-echelon location-routing problem (2E-LRP) and load-dependent vehicle routing problem (LDVRP). However, much of the existing research work has traditionally focused on a single objective, predominantly aimed to minimize costs. In our case, we build a multi-objective model that concurrently minimizes costs, carbon emissions, and the number of vehicles used. Heuristic algorithms are commonly used to solve complex location-routing problems. Therefore, we propose a hybrid heuristic algorithm named the improved elite-guided multi-objective artificial bee colony algorithm with variable neighborhood search (IEMOABC-VNS). Base on elite-guided multi-objective artificial bee colony algorithm (EMOABC), a two-archive elite-guide strategy is deployed to strike a balance between diversity and convergence. The efficacy of the IEMOABC-VNS is compared experimentally with four other hybrid heuristic algorithms on test instances and a real-world case. Computational results demonstrate that the IEMOABC-VNS outperforms the competing algorithms in solving 2E-LDLRPPD, and obtains a high-quality Pareto front in a relatively short time. Especially, the algorithm exhibits significant performance enhancements when applied to large-scale instances.