Dakota Reference Manual  Version 6.12
Explore and Predict with Confidence
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weights


Specify weights for each objective function

Specification

Alias: multi_objective_weights

Argument(s): REALLIST

Default: equal weights

Description

For multi-objective optimization problems (where the number of objective functions is greater than 1), then a weights specification provides a simple weighted-sum approach to combining multiple objectives into a single objective:

\[f = \sum_{i=1}^{n} w_{i}f_{i}\]

Length: The weights must have length equal to objective_functions. Thus, when scalar and/or field responses are specified, the number of weights must equal the number of scalars plus the number of fields, not the total elements in the fields.

Default Behavior If weights are not specified, then each response is given equal weighting:

\[f = \sum_{i=1}^{n} \frac{f_i}{n}\]

where, in both of these cases, a "minimization" responses-objectve-functions_sense will retain a positive weighting for a minimizer and a "maximization" sense will apply a negative weighting.

Usage Tips:

Weights are applied as multipliers, scales as charateristic values / divisors.

When scaling is active, it is applied to objective functions prior to any weights and multi-objective sum formation. See the equations in objective_functions.