Minimum cost route for a highway in heterogeneous terrain

The saving in cost achieved by the minimum cost route relative to the direct route between two given terminals can be significant. This paper shows that the minimum cost route should satisfy the Snell's law of light refraction and this can be done by successive iteration, in either a forward or backward direction. The number of iterations required for full convergence depends on the geometry of the problem and the cost ratio between each of the two neighbouring cost regions.