OPTIMAL DESIGN WITH DISCRETE VARIABLES: SOME NUMERICAL EXPERIMENTS

ContinuousÐdiscrete variable non-linear optimization problems are deÞned and categorized into six di¤erent types. These include a full range of problems from continuous to purely discrete and non-di¤erentiable. Methods for solution of these problems are studied and their characteristics are catalogued. The branch and bound, simulated annealing and genetic algorithms are found to be the most general methods for solving discrete problems. After some enhancements, these and two other methods are implemented into a program for certain applications. Several example problems are solved to study performance of the methods. It is concluded that solution of the mixed variable non-linear optimization problems usually requires considerable more computational e¤ort compared to the continuous variable optimization problems. In addition, there is no guarantee that the best solution has been obtained; however, good practical solutions are usually obtained