Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Pattern search, derivative free optimization method
This keyword is related to the topics:
Alias: none
Argument(s): none
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Optional  constant_penalty  Use a simple weighted penalty to manage feasibility  
Optional  no_expansion  Don't allow expansion of the search pattern  
Optional  expand_after_success  Set the factor by which a search pattern can be expanded  
Optional  pattern_basis  Pattern basis selection  
Optional  stochastic  Generate trial points in random order  
Optional  total_pattern_size  Total number of points in search pattern  
Optional  exploratory_moves  Exploratory moves selection  
Optional  synchronization  Select how Dakota schedules function evaluations in a pattern search  
Optional  contraction_factor  Amount by which step length is rescaled  
Optional  constraint_penalty  Multiplier for the penalty function  
Optional  initial_delta  Initial step size for nongradient based optimizers  
Optional  threshold_delta  Stopping criteria based on step length or pattern size  
Optional  solution_target  Stopping criteria based on objective function value  
Optional  seed  Seed of the random number generator  
Optional  show_misc_options  Show algorithm parameters not exposed in Dakota input  
Optional  misc_options  Set method options not available through Dakota spec  
Optional  max_iterations  Stopping criterion based on number of iterations  
Optional  convergence_tolerance  Stopping criterion based on convergence of the objective function or statistics  
Optional  max_function_evaluations  Stopping criteria based on number of function evaluations  
Optional  scaling  Turn on scaling for variables, responses, and constraints  
Optional  model_pointer  Identifier for model block to be used by a method 
Pattern search techniques are nongradientbased optimization methods which use a set of offsets from the current iterate to locate improved points in the design space.
See the page 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 reenabled 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.
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:
basic_pattern
case is the simple pattern search approach, which uses the same pattern in each iteration.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.adaptive_pattern
case invokes a pattern search technique that adaptively rescales the different search directions to maximize the number of redundant function evaluations. See[44] for details of this method. In preliminary experiments, this method had more robust performance than the standard basic_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 threshold_delta
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.
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