Local approximation methods are effective when the sensitivities (derivatives) of the system output responses with respect to input variables can be computed easily and inexpensively.

These methods can be applied for linear static and dynamic problems. Design sensitivity analysis (DSA) must be available. Since finite difference calculations are expensive, DSA are preferred to be calculated directly and therefore these methods are mostly integrated with FEA Solvers. These methods are not feasible for non-linear solvers since they are locally-oriented methods.

Algorithm for Gradient-Based Optimization Methods

Global approximation methods are very efficient and hence they are preferred methods when dealing with noisy non-linear output responses. Global optimization methods use higher order polynomials to approximate the original structural optimization problem over a wide range of input variables.

Algorithm for Approximation-Based Optimization Methods

Exploratory methods are suitable for discrete problems such as finding the optimum number of cars to manufacture. These methods do not show the typical convergence of other optimization algorithms. Users typically select a maximum number of simulations to be evaluated. These algorithms are good in search on nonlinear domains however they are computationally expensive as they require large number of analysis. Gradient information is not needed in exploratory methods. They are suitable to nonlinear simulations.

Algorithm for Exploratory Optimization Methods