In the Multi-Objective Shortest Path Problem (MO-SPP), one has to find paths on a graph that simultaneously minimize multiple objectives. It is not guaranteed that there exists a path that minimizes all objectives, and the problem thus aims to find the set of Pareto-optimal paths from the start to the goal vertex. A variety of multi-objective A*-based search approaches have been developed for this purpose. Typically, these approaches maintain a front set at each vertex during the search process to keep track of the Pareto-optimal paths that reach that vertex. Maintaining these front sets becomes burdensome and often slows down the search when there are many Pareto-optimal paths. In this article, we first introduce a framework for MO-SPP with the key procedures related to the front sets abstracted and highlighted, which provides a novel perspective for understanding the existing multi-objective A*-based search algorithms. Within this framework, we develop two different, yet closely related approaches to maintain these front sets efficiently during the search. We show that our approaches can find all cost-unique Pareto-optimal paths, and analyze their runtime complexity. We implement the approaches and compare them against baselines using instances with three, four and five objectives. Our experimental results show that our approaches run up to an order of magnitude faster than the baselines.

中文翻译：

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EMOA*：基于搜索的多目标路径规划框架


在多目标最短路径问题 （MO-SPP） 中，必须在图上找到同时最小化多个目标的路径。不能保证存在最小化所有目标的路径，因此该问题旨在找到从起点到目标顶点的帕累托最优路径集。为此，已经开发了多种基于 A* 的多目标检索方法。通常，这些方法在搜索过程中在每个顶点处维护一个前集，以跟踪到达该顶点的 Pareto 最优路径。维护这些前集变得很麻烦，并且当有许多 Pareto 最优路径时，通常会减慢搜索速度。在本文中，我们首先介绍了一个 MO-SPP 框架，抽象并突出显示了与前集相关的关键过程，为理解现有的基于多目标 A* 的搜索算法提供了一个新的视角。在这个框架内，我们开发了两种不同但密切相关的方法，以在搜索过程中有效地维护这些前沿集。我们表明，我们的方法可以找到所有成本独特的 Pareto 最优路径，并分析它们的运行时复杂性。我们实施这些方法，并使用具有 3、4 和 5 目标的实例将它们与基线进行比较。我们的实验结果表明，我们的方法比基线快一个数量级。