Chance Left Constraint Model for TSP and Its GASO Algorithm

The cost of travelling from one city to another is often uncertain in travelling salesman problem. The probability distribution of some parameters which are called random variables can be based on sufficient history sample data. However, the sample data of some parameters is not sufficient or can not be trusted for the impact of external environment. New methods provided by uncertainty theory and chance theory to deal with two kinds of uncertainty in a system. A new model, the objective is to minimize the expect value of uncertain random cost and the constraint is chance that uncertain random cost is less than or equal to own expected value, is established. It is called chance left constraint model of travelling salesman problem. And a new algorithm is given which is combined with simulations of chance measure and genetic algorithm. Finally, a numerical example is given to illustrate the effectiveness of the model and its algorithm.