.. _responses-objective_functions-weights:

"""""""
weights
"""""""


Specify weights for each objective function


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* multi_objective_weights 

- *Arguments:* 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: 
.. math:: f = \sum_{i=1}^{n}
w_{i}f_{i}
Length: The ``weights`` must have length equal to
:dakkw:`responses-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: 
.. math:: f = \sum_{i=1}^{n}
\frac{f_i}{n}
where, in both of these cases, a "minimization"
:dakkw:`responses-objective_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
:dakkw:`responses-objective_functions`.