An anticipation mechanism for the shortest path problem based on Physarum polycephalum

In this paper, we put forward an anticipation mechanism for the existing Physarum-inspired shortest path finding method. The Physarum-based shortest path finding model can be implemented by an iterative algorithm and has wide applications in many fundamental network optimization problems. In this paper, we mainly focus on the Physarum-inspired shortest path tree model. Normally, we stop the program when the difference between two consecutive iterations is less than a predefined threshold. However, we do not know how to set the specific value for the threshold variable. In order to find out the optimal solution, we need to set the threshold as a very small number. This in turn will consume a lot of time. From this point of view, this algorithm lacks an efficient and reliable mechanism to judge when the optimal solution will be found. In this paper, we introduce an anticipation mechanism to address this issue. Numerical examples are used to demonstrate its reliability and efficiency.