Technologies for navigating complex networks such as road network or the Internet by finding the shortest path are fundamental to modern society. In this paper, a Rapid Physarum Algorithm (RPA)
is proposed to solve the classical shortest path (SP) problems. RPA is mainly based on the path finding mathematical model constructed in, which is inspired by the foraging process of the plasmodium of P. polycephalum. In order to avoid redundancy in computational procedures and to improve the efficiency of the model, the heuristics rule is extracted from experiments and statistics are integrated with the model in our proposed RPA. As the original model is proved
mathematically rigorously that the equilibrium point corresponding to shortest path is globally asymptotically stable for the model on Riemannian surface, the convergence properties is also obviously exhibited by RPA. The performance of the RPA has been compared with the model
by carrying out four experiments on different networks with different topology and varying number of nodes. According to the experimental results, it is proved that RPA is capable of finding the shortest path as the existing path finding model does. What is more, all the results are highly encouraging with much superior performance exhibited by the proposed RPA. Further studies could develop in terms of software, hardware and wetware. The software component of the algorithm could be improved to handle very large sets of data with millions of nodes
and dynamically changing links betweens the nodes and properties of the links. The algorithm can be also applied to motion planning, search on real-world maps and incorporated into controllers
for the autonomous mobile robots. Hardware implementation of