Traveling salesperson problem

The traveling salesperson problem (TSP) is a popular example of optimization problem, which has wide application in planning and logistics. The description is given below.

A salesperson has to travel through n cities. Any arbitrary two cities are always connected by a straight line. The salesperson do not want to visit any city twice. What is the shortest route for the salesperson to travel?

Objective function: find the route (the order of cities visited) that has minimum cost (cost = total distance)
Constraint: each point (city) is visited only once.

An illustration of the problem is given in Figure 1.

TSP animation
Figure 1. Illustration of the Traveling salesperson problem