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Glossary

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 Pareto optimal
A multi-objective design is Pareto-optimal if none of the objectives can be improved without at least one objective being affected adversely. Also referred to as functionally efficient.
 Point selection scheme
Same as experimental design.
 Preference function
A function of objectives used to combine several objectives into a single one suitable for the standard MP formulation.
 Preprocessor
A graphical tool used to prepare the input for a solver.
 Random error
The total error – the difference between the exact and computed response - is composed of a random and a bias component. The random component is, as the name implies, a random deviation from the nominal value of the exact response, often assumed to be normally distributed around the nominal value. (See also bias error).
 Reasonable design space
A subregion of the design space within the region of interest. It is bounded by lower and upper bounds of the response values.
 Region of interest
A sub-region of the design space. Usually defined by a mid-point design and a range of each design variable. Usually dynamic.
 Reliability-based design optimization (RBDO)
The performing of design optimization while considering reliability-based failure criteria in the constraints of the design optimization formulation. This implies the inclusion of random variables in the generation of responses and then extracting the standard deviation of the responses about their mean values due to the random variance and including the standard deviation in the constraint(s) calculation.
 Residual
The difference between the computed response (using simulation) and the predicted response (using a response surface).
 Response
A numerical indicator of the performance of the design. A function of the design variables approximated using a metamodel which can be used for optimization. Symbolized by f. Collected over all design iterations for plotting. (See also history).
 Response quantity
See response.
 Response Surface
A mathematical expression which relates the response variables to the design parameters. Typically computed using statistical methods.
 Result
A numerical indicator of the performance of the design. A result is not associated with a metamodel, but is typically used for intermediate calculations in metamodel-based analysis.
 RSM
Response Surface Methodology.
 Saturated design
An experimental design in which the number of points equals the number of unknown coefficients of the approximation. For a saturated design no test can be made for the lack of fit.
 Scale factor
A factor which is specified as a divisor of a response in order to normalize the response.
 Sensitivity
See Design sensitivity.
 Sequential Random Search
An iterative method in which the best design is selected from all the simulation results of each iteration. A Monte Carlo based point selection scheme is typically applied to generate a set of design points.
 Simulation
The analysis of a physical process or entity in order to compute useful responses. See Function evaluation.
 Slack constraint
A constraint with a slack variable. The violation of this constraint can be minimized.
 Slack variable
The variable which is minimized to find a feasible solution to an optimization problem, e.g. e in: min e subject to g j ( x) ≤ e; e ≥ 0. See Strictness.
 Solver
A computational tool used to analyze a structure or fluid using a mathematical model. See Discipline.
 Solver directory
A subdirectory of the work directory that bears the name of a solver and where database files resulting from extraction and the optimization process are stored.
 Space Filling Experimental Design
A class of experimental designs that employ an algorithm to maximize the minimum distance between any two points.
 Space Mapping
A technique which uses a fine design model to improve a coarse surrogate model. The hope is, that if the misalignment between the coarse and fine models is not too large, only a few fine model simulations will be required to significantly improve the coarse model. The coarse model can be a response surface.
 Stochastic
Involving or containing random variables. Involving probability or chance.
 Stopping Criterion
A mathematical criterion for terminating an iterative procedure.
 Strictness
A number between 0 and 1 which signifies the strictness with which a design constraint must be treated. A zero value implies that the constraint may be violated. If a feasible design is possible all constraints will be satisfied. Used in the design formulation to minimize constraint violations. See Slack variable.
 Subproblem
The approximate design subproblem constructed using response surfaces. It is solved to find an approximate optimum.
 Subregion
See region of interest.