An ant colony optimization approach for solving shortest path problem with fuzzy constraints

This paper presents an Ant Colony Optimization Approach (ACO) to solve the shortest path problem, especially with fuzzy constraints. The proposed algorithm consists of five sequential steps. The first step is to determine the number of possible paths from the source to the target. The second step calculates the probability of each path of possible paths. The third step calculates the expected number of ants through each path of possible paths then calculates in the fourth step the new trail of each weight component for each path of possible paths, which leads to the final step to calculate the average trail of each path. The shortest path Problem (SPP) is an NP-hard combinatorial optimization problem that has long challenged researchers. The objective of the SPP is to find the path between two nodes with shortest length (weight). Some problems from references are solved using the proposed algorithm and an implementation study is presented. The implementation study shows the efficiency of the proposed algorithm.