Solving the Multi-Objective Travelling Salesman Problem with Real Data Application

The aim of this paper is building a mathematical model for Travelling salesman problem (TSP) with multi-objective; the model describes the problem of (TSP) with three objectives (cost, distance, time), Real data were collected with a sample of twenty states of United State of America, Three methods were used (Branch and Bound algorithm, Nearest neighbor and two-way exchange improvement heuristic), The comparison was conducted among results reached. To solve the problem multi-objective of (TSP), The weighted model demonstrated the effectiveness and flexibility to solve real problems of multi-objective (TSP), where it can be said that it is impossible to solve this problem without resorting to multiple -objective mathematical models, In other words, the number of possible rout for the 20 town is , to find the optimal routs among these routs it takes very long time and a lot of effort, here stand out importance of two-way exchange improvement heuristic algorithm, where this rout is satisfactory to the decision maker in terms of cost, distance and time.