The Shortest Path Problem (SPP) is among the most studied problems in Operations Research, for its theoretical aspects but also because it appears as sub-problem in many combinatorial optimization problems, e.g. Vehicle Routing and Maximum Flow-Minimum Cost problems. Given a sequence of SPPs, suppose that two subsequent instances solely differ by a slight change in the graph structure: that is the set of nodes, the set of arcs or both have changed; then, the goal of the reoptimization consists in solving the $k^{th}$ SPP of the sequence by reusing valuable information gathered in the solution of the $(k-1{)}^{th}$ one. We focused on the most general scenario, i.e. multiple changes for any subset of arcs, for which, only the description of a dual-primal approach has been proposed so far [S. Pallottino and M.G. Scutell‘a, A new algorithm for reoptimizing shortest paths when the arc costs change, Oper. Res. Lett. 31 (2003), pp. 149-160.]. We implemented this framework exploiting efficient data structures, i.e. the Multi Level Bucket. In addition, we compare the performance of our proposal with the well-known Dijkstra's algorithm, applied for solving each modified problem from scratch. In this way, we draw the line – in terms of cost, topology, and size – among the instances where the reoptimization approach is efficient from those that should be solved from scratch.

最短路径问题（SPP）是运筹学中研究最多的问题之一，因为它的理论方面，也因为它在许多组合优化问题中出现，例如车辆路线和最大流量最小成本问题。给定一个 SPP 序列，假设两个后续实例仅通过图结构的微小变化而有所不同：即节点集、弧集或两者都发生了变化；那么，重新优化的目标在于解决${ķ}^{吨H}$序列的 SPP 通过重用在解决方案中收集的有价值的信息$(ķ-1{)}^{吨H}$一。我们专注于最一般的场景，即任何弧子集的多重变化，到目前为止，仅提出了对偶原始方法的描述[S. Pallottino 和 MG Scutell'a，一种在弧成本变化时重新优化最短路径的新算法，Oper。水库。莱特。31 (2003)，第 149-160 页。]。我们利用高效的数据结构（即多级存储桶）实现了这个框架。此外，我们将我们提议的性能与著名的 Dijkstra 算法进行了比较，该算法适用于从头开始解决每个修改后的问题。通过这种方式，我们在成本、拓扑和大小方面划定了重新优化方法有效的实例与应该从头解决的实例之间的界限。