We propose an industrial technological solution for the traveling salesman problem (TSP) by using the approximated cost matrix and an accelerated evolutionary computation (EC) algorithm. The cost matrix used by theoretical research on TSP mostly is the Euclidean distance between cities, which is not proper to the real condition in the industrial product's application. In this paper, we propose an approximation approach on cost matrix based on the geographic information data, so that it approaches to the actual cost matrix. Slow convergence is the main issue of EC. We propose an accelerating EC convergence approach by Lagrange interpolation method to approximate the EC search space landscape, and do a local search near the related best individuals' region. The experimental result shows that the EC convergence is accelerated, and this acceleration approach is also used in an actual TSP application in a vehicle navigation system, in which the product performance is improved by the accelerated EC approach with the approximated cost matrix.