2
In the past two decades, different kinds of nature-inspired optimization algorithms have been
designed and applied to solve optimization problems, e.g., simulated annealing (SA),
evolutionary algorithms (EAs), differential evolution (DE), particle swarm optimization (PSO),
Ant Colony Optimisation (ACO), Estimation of Distribution Algorithms (EDA), etc. Although
these approaches have shown excellent search abilities when applying to some 30-100
dimensional problems, many of them suffer from the "curse of dimensionality", which implies
that their performance deteriorates quickly as the dimensionality of search space increases. The
reasons appear to be two-fold. First, complexity of the problem usually increases with the size of
problem, and a previously successful search strategy may no longer be capable of finding the
optimal solution. Second, the solution space of the problem increases exponentially with the
problem size, and a more efficient search strategy is required to explore all the promising regions
in a given time budget.
Historically, scaling EAs to large size problems have attracted much interest, including both
theoretical and practical studies. The earliest practical approach might be the parallelism of an
existing EA. Later, cooperative coevolution appears to be another promising method. However,
existing work on this topic are often limited to the test problems used in individual studies, and a
systematic evaluation platform is not available in the literature for comparing the scalability of
different EAs.
In this report, 6 benchmark functions are given based on [1] and [2] for high-dimensional
optimization. All of them are scalable for any size of dimension. The codes in Matlab and C for
them are available at http://nical.ustc.edu.cn/cec08ss.php
. The other benchmark function
(Function 7 - FastFractal "DoubleDip") is generated based on [3] [4]. The C code for function 7
has been contributed by Ales Zamuda from the University of Maribor, Slovenia. It uses the GJC
/ CNI interface to run the Java code from C++. In the package, C code is provided in a separate
zip file, named “cec08-f7-cpp.zip”.
The mathematical formulas and properties of these functions are described in Section 2, and
the evaluation criteria are given in Section 3.
1. Summary of the 7 CEC’08 Test Functions
z Unimodal Functions (2):
¾ F
1
: Shifted Sphere Function
¾ F
2
: Shifted Schwefel’s Problem 2.21
z Multimodal Functions (5):
¾ F
3
: Shifted Rosenbrock’s Function
¾ F
4
: Shifted Rastrigin’s Function
¾ F
5
: Shifted Griewank’s Function
¾ F
6
: Shifted Ackley’s Function
¾ F
7
: FastFractal “DoubleDip” Function
#完美解决问题 #运行顺畅 #内容详尽 #全网独家 #注释完整
