Optimum design analysis in engineering is generally formulated as a problem of nonlinear programming or nonlinear mixed integer programming including selection among alternatives. However, all working methods presently available for linear mixed integer programming are confined essentially to linear problems and are short of versatility. To overcome this situation, a new procedure for nonlinear mixed integer programming with constraint functions was developed for solving general optimum design problems. In this paper, an application study on well design is presented as an example to verify the usefulness of the developed optimization procedure.