scaling
Turn on scaling for variables, responses, and constraints
Topics
method_independent_controls
Specification
Alias: None
Arguments: None
Default: no scaling
Description
Some optimization and calibration methods support scaling of
continuous design variables, objective functions, calibration terms,
and constraints. This is activated with the scaling
keyword.
Discrete variable scaling is not supported.
When scaling is enabled, variables, functions, gradients, Hessians, etc., are transformed such that the method iterates in scaled variable space, whereas evaluations of the computational model as specified in the interface are performed on the original problem scale. Therefore using scaling does not require rewriting the interface to the simulation code.
Scaling also requires the specification of additional keywords
*scale_types
and/or *scales
in the variables
and
responses
blocks. When the scaling
keyword is omitted from
method
, these scaling type and value specifications are ignored in the
variables and responses sections.
This page describes the usage of all scaling related keywords. The additional keywords come in pairs, one pair for each set of quantities (variables, primary responses, or constraints) to be scaled.
a
*scales
keyword, which gives characteristic values (divisors)a
*scale_types
keyword, which determines how to use the characteristic values
The pair of keywords both take argument(s), and the length of the
arguments can be either be one or equal to the number of quantities to
be scaled (see details in responses
for lengths when field
responses are active). If one argument is given, it will apply to all
quantities in the set. See the examples below.
Scale Types
There are three scale types:
value
- characteristic value scaling The target quantity will be scaled (divided) by the specified characteristic value.auto
- automatic scaling First the quantity is scaled by any characteristic value, then automatic scaling will be attempted according to the following scheme:
two-sided bounds scaled into the interval [0,1];
one-sided bound or targets are scaled by the characteristic value, moving the bound or target to 1 and changing the sense of inequalities where necessary;
no bounds or targets: no automatic scaling possible, therefore no scaling for this component Automatic scaling is not available for objective functions nor calibration terms since they lack bound constraints. Futher, when automatically scaled, linear constraints are scaled by characteristic values only, not affinely scaled into [0,1].
log
- logarithmic scaling First, any characteristic values from the optional*_scales
specification are applied. Then logarithm base 10 scaling is applied. Logarithmic scaling is not available for linear constraints. When continuous design variables are log scaled, linear constraints are not allowed.
Scales
The *scales
keywords are used to specify the characteristic values.
These must be non-zero real numbers. The numbers are used according to
the corresponding *scale_types
, as described above. A value of 1.0
can be used to selectively omit some quantities in a vector from being
scaled.
Depending on the scale type, the characteristic values may be required or optional.
auto
,log
- optionalvalue
- required.
A warning is issued if scaling would result in division by a value smaller in magnitude than <tt>1.0e10*DBL_MIN</tt>. User-provided values violating this lower bound are accepted unaltered, whereas for automatically calculated scaling, the lower bound is enforced.
Examples
The two examples below are equivalent:
responses
objective_functions 3
sense "maximize"
primary_scale_types = "value"
primary_scales = 1 1 100
responses
objective_functions 3
sense "maximize"
primary_scale_types = "value" "value" "value"
primary_scales = 1 1 100