Abstract
This paper concerns the heterogeneous fleet vehicle routing problem with two-dimensional loading constraints (2L-HFVRP), which is a more complicated version of the vehicle routing problem as it combines heterogeneous vehicles and two-dimensional loading constraints. We give a detailed description of the problem and propose an improved Particle Swarm Optimization with Heuristic Local Search (PSO_HLS) to solve the problem. The PSO_HLS, based on the classical PSO algorithm, introduces the idea of heuristic local search to increase the diversity of the solutions. To effectively improve the loading efficiency, a new packing heuristic algorithm, called the fitness sorting depth-first heuristic (FSDFH), is designed. Additionally, the area contraction coefficient is introduced to optimize the routing and loading algorithm. The robustness and effectiveness of the proposed approach is verified by computational tests performed on widely used benchmark instances. The numerical results obtained show that the proposed approach outperforms the existing method and improves the best known solutions in some testing instances.
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