Makespan minimized multi-agent path planning (MAPP) requires the minimization of the time taken by the slowest agents to reach its destination. The resulting minimax objective function is non-smooth and the search for an optimal solution in MAPP can be intractable. In this work, a maximum entropy function is adopted to approximate the minimax objective function. An iterative algorithm named probabilistic iterative makespan minimization (PIMM) is then proposed to approximate a makespan minimized MAPP solution by solving a sequence of computationally hard MAPP minimization problems with a linear objective function. At each iteration, a novel local search algorithm called probabilistic iterative path coordination (PIPC) is used to find a sufficiently good solution for each MAPP minimization problem. Experimental results from comparative studies with existing MAPP algorithms show that the proposed algorithm strikes a good tradeoff between the quality of the makespan minimized solution and the computational cost incurred. 
A stochastic algorithm for makespan minimized multi-agent path planning in discrete space