Optimal Run Orders in Factorial Designs

It is often necessary to obtain some run orders in factorial designs which have a small number of factor level changes and a small linear time trend. In this paper we propose an algorithm to find optimal or near-optimal run orders for $2^4, 2^5, 3^2$ and $2\cdot 3^2$ factorial designs under the criterion that the number of factor level changes and the linear time trend should be simultaneously small.