This paper presents a "cooperative vehicle sorting" strategy that seeks to optimally sort connected and automated vehicles (CAVs) in a multi-lane platoon to reach an ideally organized platoon. In the proposed method, a CAV platoon is firstly discretized into a grid system, where a CAV moves from one cell to another in the discrete time-space domain... Then, the cooperative sorting problem is modeled as a path-finding problem in the graphic domain. The problem is solved by the deterministic Astar algorithm with a stepwise strategy, where only one vehicle can move within a movement step. The resultant shortest path is further optimized with an integer linear programming algorithm to minimize the sorting time by allowing multiple movements within a step. To improve the algorithm running time and address multiple shortest paths, a distributed stochastic Astar algorithm (DSA) is developed by introducing random disturbances to the edge costs to break uniform paths (with equal path cost). Numerical experiments are conducted to demonstrate the effectiveness of the proposed DSA method. The results report shorter sorting time and significantly improved algorithm running time due to the use of DSA. In addition, we find that the optimization performance can be further improved by increasing the number of processes in the distributed computing system. (read more)