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 poorman's solution to simple bounds optimization
constraints that can be used with simple optimizers like
SimplexOptimizer
.
A better solution is to use an optimizer that directly supports simple bounds like
CMAESOptimizer
or
BOBYQAOptimizer
.
One caveat of this poorman's 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.
MultivariateFunctionMappingAdapter
Constructor and Description 

MultivariateFunctionPenaltyAdapter(MultivariateFunction bounded,
double[] lower,
double[] upper,
double offset,
double[] scale)
Simple constructor.

Modifier and Type  Method and Description 

double 
value(double[] point)
Computes the underlying function value from an unbounded point.

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 functionlower
 lower bounds for each element of the input parameters array
(some elements may be set to Double.NEGATIVE_INFINITY
for
unbounded values)upper
 upper bounds for each element of the input parameters array
(some elements may be set to Double.POSITIVE_INFINITY
for
unbounded values)offset
 base offset of the penalty functionscale
 scale of the penalty functionMathIllegalArgumentException
 if lower bounds, upper bounds and
scales are not consistent, either according to dimension or to bounadary
valuespublic 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.
value
in interface MultivariateFunction
point
 unbounded pointCopyright © 20162022 CS GROUP. All rights reserved.