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Fig. 1. Process of building a classifier
which suggests the parameter configuration, different function features are computed.
These features are the basis of our training instances.
3
Computation of Function Features
Our computed features can be divided into three groups. Each group implies a dis-
tinct way of collecting information about the fitness topology of the objective function
from particles. The first group Random Probing describes features which are calculated
based on a random selection of fitness values and provides a general overview of the
fitness topology. Distance-based features are calculated for the second group Incremen-
tal Probing . They reflect the distribution of surrounding fitness values of some pivot
particles. The third group of features utilizes the dynamics of PSO to create features by
using the changes of the global best fitness within a small PSO instance. The features
are scale independent, i.e., that scaling the objective function by constants will not af-
fect the feature values. By this we imply that a configuration for PSO leads to the same
behavior on a function f as it shows for its scaled function f = αf + β,α > 0 .These
three groups are based on each other which means that the pivot particle for the second
group is taken from a particle of the first group to reduce the computing time. Important
for all these features are the number of evaluations of the objective function. The feature
computation should be only a small part of the whole optimization computation time.
3.1
Random Probing
Random Probing defines features that are calculated based on a set of k = 100 random
particle positions which are within the initialization range of the objective function (100
particles to get a short but adequate description about the function window). Probing
the objective function results in a distribution of fitness values which is used to extract
three features. Trivial characteristics like mean and standard deviation cannot be used as
features since they are not scale independent. That means, they will change their value
if the function is scaled by constants. In order to create reliable features, the fitness
values of all points are evaluated and three sets of particles (including their evaluation
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