Optimization methods can be categorized, with respect to their search technique, as
iterative or exploratory. Iterative techniques can be either a local or global
approximation.
Local Approximation Method (Gradient Based)
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.
Local approximation methods require design sensitivity analysis (DSA) and are most
suitable for linear static, dynamic and multi-body simulations.
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. Figure 1. Gradient-Based Optimization Methods Algorithm
Global Approximation Method (Response Surface Based)
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. Figure 2. Approximation-Based Optimization Methods Algorithm
Exploratory Methods
Exploratory methods do not show the typical convergence of other optimization
algorithms. These algorithms efficiently search the design space, however they are
computationally expensive as they require large number of analysis. Rather than
exhibiting conventional convergence characteristics, a maximum number of evaluations
is defined. Figure 3. Exploratory Optimization Methods Algorithm
