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, (to appear in ACM Transactions on Mathematical Software, 29(4), 2003).

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 without changing the subject. The GKLS generator will be sent to you automatically.