Optimal route selection based on Monte Carlo method and adaptive amoeba algorithm under uncertain environment

The fuzzy optimal path under uncertainty is one of the basic network optimization problems. Considering the uncertain environment, many fuzzy numbers are used to represent the edge weights, such as interval number and triangular fuzzy number. Then, these fuzzy numbers are converted to real numbers directly. This converting makes the optimal path the shortest path selection problem. However, much information of uncertainty get lost when converting fuzzy numbers to real numbers. In order to ensure all the origan data complete, in this paper, a fuzzy optimal path solving model based on the Monte Carlo method and adaptive amoeba algorithm is proposed. In Monte Carlo process, a random number which belongs to the fuzzy number is generated. Then, Physarum polycephalum algorithm is used to solve the shortest path every time and record the result. After many times calculation, many shortest paths have been found and recorded. At last, by analysing the characters of all the results, the optimal path can be selected. Several numerical examples are given to illustrate the effectiveness of the proposed method, the results show that the proposed method can deal with the fuzzy optimal path problems effectively.