PS-ECBS: A New Algorithm for Multi-Agent Path Finding With Optimal Task Assignment

Multi-agent path finding (MAPF) problem in warehouse automation consists of optimal task assignment and path planning, where small runtime is necessary. In this paper, we present a new MAPF algorithm related to dynamic start and end positions of the robots, called Position-Selection Enhanced Conflict-Based Search (PS-ECBS). Conflict-Based Search (CBS) is a well-known framework that has been used to find collision-free paths for a given fixed task assignment, while ECBS is a bounded-suboptimal variant of CBS that uses focal search to speed up CBS. The mixed integer linear programming (MILP) is introduced to formulate the dynamic model for optimal task assignment, and the successful combination of MILP and ECBS results in PS-ECBS algorithm. The solving process of the PS-ECBS consists of multiple iterations, and in each iteration an additional constraint is added to modify the model. In the computational experiment, the processes of picking up and putting back shelves in the warehouse could occur at the same time by PS-ECBS. We also analyzed the iterative principle of PS-ECBS, and compared its performance with that of ECBS-TA. The computational results demonstrate that PS-ECBS runs significantly faster and has an obvious advantage in jointly optimizing task assignment and path planning for large-scale warehouse.