# weights

Specify weights for each objective function

**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
`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”
`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`

.