Gradient-based algorithms are efficient for applications with
a large number of variables and/or constraints. They require computation of
derivatives, and can therefore only be used when the models are sufficiently
smooth.
Derivative-free algorithms are tailored for simulation-based
optimization, where gradients can either not be computed or are inaccurate.
They are restricted to applications of moderate size (number of variables),
and typically less efficient than gradient-based problems, but they can be accelerated
by using surrogate models for analysis.
Design of Experiments (DoE)-based sensitivity analysis samples
and explores the design space for determining the impact of inputs on outputs
in order to identify significant design variables. They are also useful for
determining educated initial guesses for the optimization process and subregions
of the design space within which the optimum is more likely to lie.
Simulation-based methods are geared to mixed use of DoE, metamodeling,
gradient-based, and derivative-free techniques, all of which are tailored to
specific problems wherein simulations can be used to perform the analysis, i.e.,
evaluate objective and constraint functions.
Multidisciplinary techniques coordinate the optimization process
when the analysis involves multiple disciplines that are coupled (outputs of
one discipline are inputs to others). Several implementation and coordination
algorithms are available according to feasibility requirements and co-simulation
needs.
Reliability-based methods employ algorithms for solving probabilistic
optimization problems wherein subsets of design variables and parameters are
random and constraints are formulated probabilistically (the constraints are
satisfied at a pre-specified reliability level). Nested (double-loop), single-loop,
and segregated optimization/analysis methods are used depending on design problem
and simulation requirements.
Design for robustness is employed for solving multi-objective
formulations of design optimization applications where uncertainties in design
variables and parameters cause variations of performance. These techniques identify
optimal designs that are less sensitive to variations.