public class MultivariateFunctionPenaltyAdapter extends Object implements MultivariateFunction
Adapter extending bounded
MultivariateFunction to an unbouded
domain using a penalty function.
This adapter can be used to wrap functions subject to simple bounds on parameters so they can be used by optimizers that do not directly support simple bounds.
The principle is that the user function that will be wrapped will see its
parameters bounded as required, i.e when its
value method is called
with argument array
point, the elements array will fulfill requirement
lower[i] <= point[i] <= upper[i] for all i. Some of the components
may be unbounded or bounded only on one side if the corresponding bound is
set to an infinite value. The optimizer will not manage the user function by
itself, but it will handle this adapter and it is this adapter that will take
care the bounds are fulfilled. The adapter
value(double) method will
be called by the optimizer with unbound parameters, and the adapter will check
if the parameters is within range or not. If it is in range, then the underlying
user function will be called, and if it is not the value of a penalty function
will be returned instead.
This adapter is only a poor man solution to simple bounds optimization constraints
that can be used with simple optimizers like
MultiDirectionalSimplex. A better solution is to use
an optimizer that directly supports simple bounds like
BOBYQAOptimizer. One caveat of this poor man solution is that if start point
or start simplex is completely outside of the allowed range, only the penalty function
is used, and the optimizer may converge without ever entering the range.
|Constructor and Description|
public MultivariateFunctionPenaltyAdapter(MultivariateFunction bounded, double lower, double upper, double offset, double scale)
When the optimizer provided points are out of range, the value of the penalty function will be used instead of the value of the underlying function. In order for this penalty to be effective in rejecting this point during the optimization process, the penalty function value should be defined with care. This value is computed as:
penalty(point) = offset + ∑i[scale[i] * √|point[i]-boundary[i]|]where indices i correspond to all the components that violates their boundaries.
So when attempting a function minimization, offset should be larger than the maximum expected value of the underlying function and scale components should all be positive. When attempting a function maximization, offset should be lesser than the minimum expected value of the underlying function and scale components should all be negative. minimization, and lesser than the minimum expected value of the underlying function when attempting maximization.
These choices for the penalty function have two properties. First, all out of range points will return a function value that is worse than the value returned by any in range point. Second, the penalty is worse for large boundaries violation than for small violations, so the optimizer has an hint about the direction in which it should search for acceptable points.
bounded- bounded function
lower- lower bounds for each element of the input parameters array (some elements may be set to
Double.NEGATIVE_INFINITYfor unbounded values)
upper- upper bounds for each element of the input parameters array (some elements may be set to
Double.POSITIVE_INFINITYfor unbounded values)
offset- base offset of the penalty function
scale- scale of the penalty function
DimensionMismatchException- if lower bounds, upper bounds and scales are not consistent, either according to dimension or to bounadary values
public double value(double point)
This method simply returns the value of the underlying function if the unbounded point already fulfills the bounds, and compute a replacement value using the offset and scale if bounds are violated, without calling the function at all.
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