多目标多智能体路径搜索的子维扩展
Subdimensional Expansion for Multi-objective Multi-agent Path Finding
摘要：
传统的多智能体路径规划器通常确定优化单个目标（诸如路径长度）的路径。然而，许多应用可能需要在规划过程中同时优化多个目标，例如完成时间和燃料使用。这些标准往往不容易比较，有时相互竞争。简单地将标准多目标搜索算法应用于多代理路径查找可能被证明是低效的，因为可能的解的空间的大小，即，帕累托最优集合可以随着代理的数量（搜索空间的维度）呈指数增长。本文提出了一种方法，绕过这个所谓的灾难的维度，利用我们以前的多智能体的工作与一个框架，称为子维扩展。当应用于A* 时，子维扩展的一个示例被称为M*，并且M* 被限制为单个目标函数。我们结合优势和子维扩展的原则，创建一个新的算法命名为多目标M*（M *），动态耦合代理规划只有当这些代理必须“互动”与对方。* * 有效地计算多个代理的完整帕累托最优集，并自然地权衡帕累托最优集的次优近似和计算效率。我们的方法是能够找到完整的帕累托最优集的问题实例与数百个解决方案，标准的多目标A* 算法无法在有限的时间内找到。
英文摘要：
Conventional multi-agent path planners typically determine a path that optimizes a single objective, such as path length. Many applications, however, may require multiple objectives, say time-to-completion and fuel use, to be simultaneously optimized in the planning process. Often, these criteria may not be readily compared and sometimes lie in competition with each other. Simply applying standard multi-objective search algorithms to multi-agent path finding may prove to be inefficient because the size of the space of possible solutions, i.e., the Pareto-optimal set, can grow exponentially with the number of agents (the dimension of the search space). This paper presents an approach that bypasses this so-called curse of dimensionality by leveraging our prior multi-agent work with a framework called subdimensional expansion. One example of subdimensional expansion, when applied to A*, is called M* and M* was limited to a single objective function. We combine principles of dominance and subdimensional expansion to create a new algorithm named multi-objective M* (MOM*), which dynamically couples agents for planning only when those agents have to "interact" with each other. MOM* computes the complete Pareto-optimal set for multiple agents efficiently and naturally trades off sub-optimal approximations of the Pareto-optimal set and computational efficiency. Our approach is able to find the complete Pareto-optimal set for problem instances with hundreds of solutions which the standard multi-objective A* algorithms could not find within a bounded time.
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