coliny_pattern_search
Pattern search, derivative free optimization method
Topics
package_scolib, package_coliny, global_optimization_methods
Specification
Alias: None
Arguments: None
Child Keywords:
Required/Optional |
Description of Group |
Dakota Keyword |
Dakota Keyword Description |
---|---|---|---|
Optional |
Use a simple weighted penalty to manage feasibility |
||
Optional |
Don’t allow expansion of the search pattern |
||
Optional |
Set the factor by which a search pattern can be expanded |
||
Optional |
Pattern basis selection |
||
Optional |
Generate trial points in random order |
||
Optional |
Total number of points in search pattern |
||
Optional |
Exploratory moves selection |
||
Optional |
Select how Dakota schedules a batch of concurrent function evaluations in a parallel algorithm |
||
Optional |
Amount by which step length is rescaled |
||
Optional |
Multiplier for the penalty function |
||
Optional |
Initial step size for derivative-free optimizers |
||
Optional |
Step length-based stopping criteria for derivative-free optimizers |
||
Optional |
Stopping criteria based on objective function value |
||
Optional |
Seed of the random number generator |
||
Optional |
Show algorithm parameters not exposed in Dakota input |
||
Optional |
Set method options not available through Dakota spec |
||
Optional |
Number of iterations allowed for optimizers and adaptive UQ methods |
||
Optional |
Stopping criterion based on objective function or statistics convergence |
||
Optional |
Number of function evaluations allowed for optimizers |
||
Optional |
Turn on scaling for variables, responses, and constraints |
||
Optional |
Identifier for model block to be used by a method |
Description
Pattern search techniques are nongradient-based optimization methods which use a set of offsets from the current iterate to locate improved points in the design space.
See the page :ref:`topic-package_scolib` for important information regarding all SCOLIB methods
coliny_pattern_search
supports concurrency up to the size of
the search pattern
Traditional pattern search methods search with a fixed pattern of
search directions to try to find improvements to the current iterate.
The SCOLIB pattern search methods generalize this simple algorithmic
strategy to enable control of how the search pattern is adapted, as
well as how each search pattern is evaluated. The stochastic
and
synchronization
specifications denote how the the trial points are
evaluated. The stochastic
specification indicates that the trial
points are considered in a random order. For parallel pattern search,
synchronization
dictates whether the evaluations are scheduled
using a blocking
scheduler or a nonblocking
scheduler. In the
blocking
case, all points in the pattern are evaluated (in
parallel), and if the best of these trial points is an improving
point, then it becomes the next iterate. These runs are reproducible,
assuming use of the same seed in the stochastic
case. In the
nonblocking
case, all points in the pattern may not be evaluated,
since the first improving point found becomes the next iterate. Since
the algorithm steps will be subject to parallel timing variabilities,
these runs will not generally be repeatable. The synchronization
specification has similar connotations for sequential pattern
search. If blocking
is specified, then each sequential iteration
terminates after all trial points have been considered, and if
nonblocking
is specified, then each sequential iteration terminates
after the first improving trial point is evaluated. In this release,
both blocking
and nonblocking
specifications result in blocking
behavior (except in the case where exporatory_moves
below is set to
adaptive_pattern
). Nonblocking behavior will be re-enabled after
some underlying technical issues have been resolved.
The particular form of the search pattern is controlled by the
pattern_basis
specification. If pattern_basis
is coordinate
basis, then the pattern search uses a plus and minus offset in each
coordinate direction, for a total of 2n function evaluations in the
pattern. This case is depicted in Figure 5.3 for three coordinate
dimensions.
image html pattern_search.jpg “Figure 5.3 Depiction of coordinate pattern search algorithm” image latex pattern_search.eps “Depiction of coordinate pattern search algorithm” width=10cm
If pattern_basis
is simplex
, then pattern search uses a minimal
positive basis simplex for the parameter space, for a total of n+1
function evaluations in the pattern. Note that the simplex
pattern
basis can be used for unbounded problems only. The
total_pattern_size
specification can be used to augment the basic
coordinate
and simplex
patterns with additional function
evaluations, and is particularly useful for parallel load balancing.
For example, if some function evaluations in the pattern are dropped
due to duplication or bound constraint interaction, then the
total_pattern_size
specification instructs the algorithm to generate
new offsets to bring the total number of evaluations up to this
consistent total.
The exploratory_moves
specification controls how the search pattern
is adapted. (The search pattern can be adapted after an improving
trial point is found, or after all trial points in a search pattern
have been found to be unimproving points.) The following exploratory
moves selections are supported by SCOLIB:
The
basic_pattern
case is the simple pattern search approach, which uses the same pattern in each iteration.The
multi_step
case examines each trial step in the pattern in turn. If a successful step is found, the pattern search continues examining trial steps about this new point. In this manner, the effects of multiple successful steps are cumulative within a single iteration. This option does not support any parallelism and will result in a serial pattern search.The
adaptive_pattern
case invokes a pattern search technique that adaptively rescales the different search directions to maximize the number of redundant function evaluations. See [HGSvBW01] for details of this method. In preliminary experiments, this method had more robust performance than the standardbasic_pattern
case in serial tests. This option supports a limited degree of parallelism. After successful iterations (where the step length is not contracted), a parallel search will be performed. After unsuccessful iterations (where the step length is contracted), only a single evaluation is performed.
The initial_delta
and variable_tolerance
specifications provide the
initial offset size and the threshold size at which to terminate the
algorithm. For any dimension that has both upper and lower bounds,
this step length will be internally rescaled to provide search steps
of length initial_delta
range 0.1. This rescaling does not
occur for other dimensions, so search steps in those directions have
length initial_delta
. Note that the factor of 0.1 in the rescaling
could result in an undesirably small initial step. This can be offset
by providing a large initial_delta
.
In general, pattern search methods can expand and contract their step
lengths. SCOLIB pattern search methods contract the step length by the
value contraction_factor
, and they expand the step length by the
value (1/contraction_factor). The expand_after_success
control
specifies how many successful objective function improvements must
occur with a specific step length prior to expansion of the step
length, whereas the no_expansion
flag instructs the algorithm to
forgo pattern expansion altogether.
Finally, constraint infeasibility can be managed in a somewhat more
sophisticated manner than the simple weighted penalty function. If the
constant_penalty
specification is used, then the simple weighted
penalty scheme described above is used. Otherwise, the constraint
penalty is adapted to the value constraint_penalty/L
, where L is
the the smallest step length used so far.
Expected HDF5 Output
If Dakota was built with HDF5 support and run with the
hdf5
keyword, this method
writes the following results to HDF5:
Best Objective Functions (when
objective_functions
) are specified)Calibration (when
calibration_terms
are specified)