This paper proposes a new hybrid metaheuristic algorithm that is composed of the adaptive large neighbourhood search (ALNS) and the variable neighbourhood search (VNS) algorithms to tackle the location routing problem (LRP) with capacity constraints. The rationale of the proposed hybrid metaheuristic algorithm is to enhance the performance of the ALNS algorithm by incorporating the VNS algorithm as an elitist local search. Therefore, the diversification and intensification strategies of the proposed hybrid metaheuristic algorithm are realized via the ALNS and VNS algorithms, respectively. The performance evaluation tests of the proposed hybrid metaheuristic algorithm are performed on the three classical LRP benchmark sets taken from the related literature, and the obtained results are compared against some of the formerly proposed and published methods in terms of solution quality. Computational results indicate that the proposed hybrid metaheuristic algorithm has a satisfactory performance in solving the LRP instances and is a competitive algorithm.

本文提出了一种新的混合元启发式算法，该算法由自适应大邻域搜索（ALNS）和可变邻域搜索（VNS）算法组成，以解决具有容量约束的位置路由问题（LRP）。提出的混合元启发式算法的基本原理是通过将VNS算法合并为精英本地搜索来增强ALNS算法的性能。因此，分别通过ALNS和VNS算法实现了所提出的混合元启发式算法的多样化和强化策略。拟议的混合元启发式算法的性能评估测试是根据相关文献中的三个经典LRP基准集进行的，并将获得的结果与解决方案质量方面的某些先前提出和公开的方法进行比较。计算结果表明，所提出的混合元启发式算法在求解LRP实例方面具有令人满意的性能，是一种竞争性算法。