Conflict-Based Search with Optimal Task Assignment

We consider a variant of the Multi-Agent Path-Finding problem that seeks both task assignments and collision-free paths for a set of agents navigating on a graph, while minimizing the sum of costs of all agents. Our approach extends Conflict-Based Search (CBS), a framework that has been previously used to find collision-free paths for a given fixed task assignment. Our approach is based on two key ideas: (i) we operate on a search forest rather than a search tree; and (ii) we create the forest on demand, avoiding a factorial explosion of all possible task assignments. We show that our new algorithm, CBS-TA, is complete and optimal. The CBS framework allows us to extend our method to ECBS-TA, a bounded suboptimal version. We provide extensive empirical results comparing CBS-TA to task assignment followed by CBS, Conflict-Based Min-Cost-Flow (CBM), and an integer linear program (ILP) solution, demonstrating the advantages of our algorithm. Our results highlight a significant advantage in jointly optimizing the task assignment and path planning for very dense cases compared to the traditional method of solving those two problems independently. For large environments with many robots we show that the traditional approach is reasonable, but that we can achieve similar results with the same runtime but stronger suboptimality guarantees.