The Asymmetric Distance-Constrained Vehicle Routing Problem (ADVRP) is NP-hard as it is a natural extension of the NP-hard Vehicle Routing Problem. In ADVRP problem, each customer is visited exactly once by a vehicle; every tour starts and ends at a depot; and the traveled distance by each vehicle is not allowed to exceed a predetermined limit. We propose a hybrid metaheuristic algorithm combining the Randomized Variable Neighborhood Search (RVNS) and the Tabu Search (TS) to solve the problem. The combination of multiple neighborhoods and tabu mechanism is used for their capacity to escape local optima while exploring the solution space. Furthermore, the intensification and diversification phases are also included to deliver optimized and diversified solutions. Extensive numerical experiments and comparisons with all the state-of-the-art algorithms show that the proposed method is highly competitive in terms of solution quality and computation time, providing new best solutions for a number of instances.

中文翻译：

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混合元启发式算法，用于求解非对称距离受限的车辆路径问题

不对称的距离受限车辆路径问题（ADVRP）是NP-hard，因为它是NP-hard车辆路径问题的自然扩展。在ADVRP问题中，每辆车只拜访一次每个客户；每次旅行都在一个仓库开始和结束；并且每辆车的行驶距离不允许超过预定极限。我们提出了一种混合元启发式算法，该算法结合了随机变量邻域搜索（RVNS）和禁忌搜索（TS）来解决该问题。多个邻域和禁忌机制的组合被用于在探索解决方案空间时逃避局部最优的能力。此外，还包括强化和多样化阶段，以提供优化和多样化的解决方案。