This paper discusses a technique for the development of a discrete time integration operator to be used in the simulation process. The integration operator can be optimized for a particular system subjected to a set of specified inputs. The class of systems being investigated are those which can be represented by a set of state equations. A discrete time integration operator with certain free parameters is hypothesized. An adaptive random search optimization (ARSO) technique is used to find the optimum values for these parameters. Examples are presented to show the effectiveness of this technique.