MGCBS: An Optimal and Efficient Algorithm for Solving Multi-Goal Multi-Agent Path Finding Problem

TL;DR

This paper tackles the MG-MAPF problem, where each agent must visit multiple goals without conflicts, a generalization of MAPF that is NP-hard. It introduces MGCBS, a two-level solver that decouples the safe-interval visiting order search (DSS) from single-agent pathfinding, and couples it with the Time-Interval-Space Forest (TIS Forest) to accelerate many shortest-path queries. The authors prove the optimality and completeness of MGCBS and demonstrate substantial empirical gains, achieving optimal solutions consistently and up to 7x faster than state-of-the-art DVS-based methods. The approach offers a scalable and principled solution for large-scale multi-goal multi-agent planning in robotics, with public code available for replication.

Abstract

With the expansion of the scale of robotics applications, the multi-goal multi-agent pathfinding (MG-MAPF) problem began to gain widespread attention. This problem requires each agent to visit pre-assigned multiple goal points at least once without conflict. Some previous methods have been proposed to solve the MG-MAPF problem based on Decoupling the goal Vertex visiting order search and the Single-agent pathfinding (DVS). However, this paper demonstrates that the methods based on DVS cannot always obtain the optimal solution. To obtain the optimal result, we propose the Multi-Goal Conflict-Based Search (MGCBS), which is based on Decoupling the goal Safe interval visiting order search and the Single-agent pathfinding (DSS). Additionally, we present the Time-Interval-Space Forest (TIS Forest) to enhance the efficiency of MGCBS by maintaining the shortest paths from any start point at any start time step to each safe interval at the goal points. The experiment demonstrates that our method can consistently obtain optimal results and execute up to 7 times faster than the state-of-the-art method in our evaluation.

Figures (4)

• Figure 1: An example of the MG-MAPF with three agents. The grey cells represent the impassable areas occupied by obstacles. The solid circles indicate the start point of the agent, and the number marked inside is the agent ID. The dotted circles represent the goal points of the agent in the corresponding color. The colored arrow marks the path that can visit all goal points from the start point of the agent.
• Figure 2: An example of the MG-MAPF with two agents is represented in a planar graph. The agent $1$ starts at vertex $B$ and has two goals located at vertex $A$ and vertex $E$. The agent $2$ starts at the vertex $C$ and only has one goal at vertex $F$.
• Figure 3: The left subfigure shows the graph on which the TIS Tree was built. The number in the circle is the vertex ID. The right subfigure shows the TIS Tree whose seed GSI is $[2, +\infty]$ at vertex $1$. The constraint set includes two vertex constraints, including vertex $1$ at time step $1$, and vertex $5$ at time step $4$. The block represents the node in the tree, where the number in the block is the cost of the node. The number under the block is the vertex ID. The bracketed number represents the time interval of the TIS state of the node. The arrow represents the edge of the TIS Tree pointing from the parent node to the child node. The self-point arrow at vertices $2$ and $3$ indicates waiting for one time step.
• Figure 4: The grid maps used in the experiment.

Theorems & Definitions (12)

• Theorem 1
• proof
• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Theorem 2
• proof