Strategies for optimal design

The nonlinear programming approach to mechanical design synthesis is considered with emphasis on strategies to enhance reliability, efficiency and the interaction between the design engineer and the mathematical model. Failure conditions are derived for several popular algorithms. A new algorithm based on a general conjugate direction recursion formula and an acceptable point univariate strategy is constructed and tested using classical test functions and industrial problems. A comparison in terms of equivalent function evaluations and multivariate iterations is made with the quasi-Newton methods. The role of the mathematical model in the solution is then considered. Practical examples are presented in detail and it is shown that a convex formulation with linear constraints may be derived from a nonconvex formulation, with nonlinear constraints.