This work presents a multistart algorithm for solving the capacitated vehicle routing problem with 2D loading constraints (2L-CVRP) allowing for the rotation of goods. Research dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics, such as the Constructive Genetic Algorithm (CGA) to construct promising initial solutions; a Tabu Search (TS) to improve the initial solutions on the routing problem, and a Large Neighborhood Search (LNS) for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multithreading programming to improve the performance. Additionally, memory structures such as hash-tables were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest to the community involved in symmetry studies, such as graph algorithms and graph theory.

中文翻译：

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求解具有二维载荷约束的载重车辆路径问题的多起点算法

这项工作提出了一种多起点算法，用于解决具有 2D 载荷约束 (2L-CVRP) 的有容量车辆路径问题，允许货物旋转。致力于图论和对称性的研究将车辆路径问题视为经典应用。这个问题具有复杂的方面，刺激了在图中使用高级算法和对称性。使用无向图对 2L-CVRP 问题进行图建模允许算法的高性能。开发的算法基于元启发式，例如构造遗传算法（CGA）来构建有希望的初始解决方案；使用禁忌搜索 (TS) 改进路由问题的初始解决方案，以及用于加载子问题的大型邻域搜索 (LNS)。尽管这些算法中的每一种都可以解决 2L-CVRP 的部分问题，但这三种算法的组合来解决这个问题在科学文献中是前所未有的。在我们的方法中，使用多线程编程实现了一种用于检查路由加载可行性的并行机制，以提高性能。此外，通过存储和查询先前评估的路由加载可行性结果，实现了诸如哈希表之类的内存结构以节省时间。对于基准，测试是在文献中可用的众所周知的实例上进行的。结果证明该框架匹配或优于大多数以前的方法。作为主要贡献，这项工作为纯 CVRP 的大型实例带来了更高质量的解决方案。这篇论文涉及symmetry期刊相关的主题，主要是复杂算法，图，搜索策略，复杂度，图建模，遗传算法。此外，本文特别关注与对称研究相关的社区特别感兴趣的主题相关方面，例如图算法和图论。