Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Specify the type of niching pressure
Alias: none
Argument(s): none
Default: No niche pressure
Required/Optional  Description of Group  Dakota Keyword  Dakota Keyword Description  

Required (Choose One)  Group 1  radial  Set niching distance to percentage of nondominated range  
distance  Enforce minimum Euclidean distance between designs  
max_designs  Limit number of solutions to remain in the population 
The purpose of niching is to encourage differentiation along the Pareto frontier and thus a more even and uniform sampling.
This is typically accomplished by discouraging clustering of design points in the performance space. In JEGA, the application of niche pressure occurs as a secondary selection operation. The nicher is given a chance to perform a preselection operation prior to the operation of the selection (replacement) operator, and is then called to perform niching on the set of designs that were selected by the selection operator.
The radial nicher takes information input from the user to compute a minimum allowable distance between designs in the performance space and acts as a secondary selection operator whereby it enforces this minimum distance. The distance nicher requires that solutions must be separated from other solutions by a minimum distance in each dimension (vs. Euclidean distance for the radial niching). After niching is complete, all designs in the population will be at least the minimum distance from one another in all directions.
The radial
niche pressure applicator works by enforcing a minimum Euclidean distance between designs in the performance space at each generation. The algorithm proceeds by starting at the (or one of the) extreme designs along objective dimension 0 and marching through the population removing all designs that are too close to the current design. One exception to the rule is that the algorithm will never remove an extreme design which is defined as a design that is maximal or minimal in all but 1 objective dimension (for a classical 2 objective problem, the extreme designs are those at the tips of the nondominated frontier). The distance
nicher enforces a minimimum distance in each dimension.
The designs that are removed by the nicher are not discarded. They are buffered and reinserted into the population during the next preselection operation. This way, the selector is still the only operator that discards designs and the algorithm will not waste time "refilling" gaps created by the nicher.
The radial
nicher requires as input a vector of fractions with length equal to the number of objectives. The elements of the vector are interpreted as percentages of the nondominated range for each objective defining a minimum distance to all other designs. All values should be in the range (0, 1). The minimum allowable distance between any two designs in the performance space is the Euclidian (simple squarerootsumofsquares calculation) distance defined by these percentages. The distance
nicher has a similar input vector requirement, only the distance is the minimum distance in each dimension.
The max_designs
niche pressure applicator is designed to choose a limited number of solutions to remain in the population. That number is specified by num_designs
. It does so in order to balance the tendency for populations to grow very large and thus consuming too many computer resources. It operates by ranking designs according to their fitness standing and a computed count of how many other designs are too close to them. Too close is a function of the supplied niche_vector, which specifies the minimum distance between any two points in the performance space along each dimension individually. Once the designs are all ranked, the top c\ num_designs designs are kept in the population and the remaining ones are bufferred or discarded. Note that like other niching operators, this one will not discard an extreme design.