Introduction - Self-Adaptive Heuristics for Evolutionary Computation - page 6

Experiments
Many results of this work are based on experiments. Each proposed heuristic or
self-adaptive modification is experimentally evaluated. The blocks experimen-
tal settings show the setup of each experimental series. Our benchmark set of
problems, see appendix A, contains a variety of problem types: Typical con-
tinuous unimodal functions like sphere and double sum, as well as continuous
multimodal functions like griewank and rastrigin have been selected. Hence, the
reader can compare our results to own results. We tested most of these problems
with N = 10 dimensions. For the sake of comparability typical problems in bit
string representation, e.g. onemax or ackley, have been chosen. Problems with
certain properties like ridge functions or functions with noise in fitness reveal
the algorithm's properties on special problem classes. For constrained contin-
uous search domains we have chosen our benchmark functions from the g -test
suite [83]. The latter is a typical test suite of constrained problems in the EA
community. For combinatorial representations we have tested traveling salesman
problems of various sizes from the TSPlib [117].
Most of the experiments of this work show the behavior of 25 runs. This, as
well as other settings, e.g. initialization interval and termination condition, are
oriented to the recommendations of the CEC special sessions on real-parameter
optimization 2005 [149] and the session on constrained real-parameter optimiza-
tion 2006 [83]. Differing termination conditions, i.e. fitness stagnation, have been
chosen for problems which suffer from premature step size reduction, see the ex-
periments in chapter 7.
The results are presented in various forms. Tables show the best , median ,
worst , mean and the corresponding standard deviation of all runs, i.e. of the
best solution in the last generation. Figures show the development of the best
solution in the course of generations. Figures with typical runs ought to show
local properties like cracks or smoothness, which may be lost when averaging.
Other figures show the more generalized fitness development on average. With
exception of the SA-PMX experiments of chapter 5, fitness in the figures means
distance to optimum . The Wilcoxon rank-sum test proves statistical relevance of
many parts of this work. It tests the null hypothesis that the probability distri-
butions of two sample sets are equal. The Wilcoxon rank-sum test is applicable,
if the distribution of the data is not known. But it is necessary to point out the
following statement.
All experimental results only show the behavior on the problem classes exemplarily.
We are aware that generalization is cautious and due to the no free lunch theorem
almost impossible.