M. GAVIANO, D.E. KVASOV, D. LERA, and Ya.D. SERGEYEV,
Algorithm 829: Software for generation of classes of test functions with known
local and global minima for global optimization, ACM Transactions on
Mathematical Software, 2003, 29(4), 469-480.

Development of numerical algorithms for global
optimization is strongly connected to the problem of construction of test
functions for studying and verifying validity of these algorithms. Many of
global optimization tests are taken from real-life applications and for this
reason a complete information about them is not
available. It often happens that there are not known a
priori the number of local minima present in the problem, their locations,
regions of attraction, and even values (including that one of the global
minimum).

The GKLS generator is a procedure for generating three
types (non-differentiable, continuously differentiable, and twice continuously
differentiable) of classes of test functions with known local and global minima
for multiextremal multidimensional box-constrained
global optimization.

The procedure consists of defining a convex quadratic
function systematically distorted by polynomials in order to introduce local
minima. Each test class provided by the GKLS generator consists of 100
functions constructed randomly and is defined by the following parameters:

- problem dimension
- number of local
minima
- value of the global
minimum
- radius
of the attraction region of the global minimizer
- distance
from the global minimizer to the vertex of the
quadratic function

The other necessary parameters (i.e., locations of all
minimizers, their regions of attraction, and values
of minima) are chosen randomly by the generator. A special notebook with a
complete description of all the functions is supplied to the user. Partial
derivatives are also generated where it is possible.

Multiple generation of a class with the same
parameters produces the same 100 test functions.

**The GKLS generator
is free.**** You may get it by sending a message (that can be also empty) to yaro@si.deis.unical.it**** ****with the subject “GKLS”. The GKLS generator
will be sent to you automatically.**** **