Optimization Method Classification

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