Conflict-Based Steiner Search for Multi-Agent Combinatorial Path Finding

—Conventional Multi-Agent Path Finding (MAPF) problems aim to compute an ensemble of collision-free paths for multiple agents from their respective starting locations to pre-allocated destinations. This work considers a generalized version of MAPF called Multi-Agent Combinatorial Path Finding (MCPF) where agents must collectively visit a large number of intermediate target locations along their paths before arriving at destinations. This problem involves not only planning collision-free paths for multiple agents but also assigning targets and specifying the visiting order for each agent (i.e. multi-target sequencing). To solve the problem, we leverage the well-known Conflict-Based Search (CBS) for MAPF and propose a novel framework called Conflict-Based Steiner Search (CBSS). CBSS interleaves (1) the conflict resolving strategy in CBS to bypass the curse of dimensionality in MAPF and (2) multiple traveling salesman algorithms to handle the combinatorics in multi-target sequencing, to compute optimal or bounded sub-optimal paths for agents while visiting all the targets. Our extensive tests verify the advantage of CBSS over baseline approaches in terms of computing shorter paths and improving success rates within a runtime limit for up to 20 agents and 50 targets. We also evaluate CBSS with several MCPF variants, which demonstrates the generality of our problem formulation and the CBSS framework.