Fuzzy travelling salesman problem and simulated annealing algorithm

The travelling salesman problem is to find a shortest path from the travelling salesman's hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling salesman problem with fuzzy travelling time. In order to compare different paths with fuzzy travelling time, some concepts are proposed: expected shortest path, a-path and the most credible path. Correspondingly, by using the concepts as decision criteria, some fuzzy programming models for TSP are proposed based on credibility theory. The deterministic equivalents of the models are also given. Finally, a simulated annealing method is designed to solve these models, and a numerical example is provided to illustrate its effectiveness.