A Biologically Inspired Solution for Fuzzy Travelling Salesman Problem

Recently, biologically inspired methods have been proposed for solving combinatorial optimization problems like the travelling salesman problem (TSP). This is a well-known combinatorial optimization problem which belongs to NP-hard class. It is desired to find a minimum-cost tour while visiting each city once. This paper presents a variant of the TSP in which the traveling cost between each pair of cities is represented by fuzzy numbers instead of a deterministic value. To solve this fuzzy TSP, a bio-inspired algorithm based on physarum polycephalum model is used. This organism can find the shortest route through a maze by trying to locate the food sources placed at the exits. It also can attract the maximum amount of nutrients in the shortest possible time. Our algorithm is capable of finding an optimal solution for graphs with both crisp and fuzzy numbers as their cost of edges. Numerical examples of some networks are used to illustrate the efficiency of the proposed method.