Techniques and Algorithms

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.