A derivation of the number of minima of the Griewank function

abstract

• The Griewank function is commonly used to test the ability of different solution procedures to find local optima. It is important to know the exact number of minima of the function to support its use as a test function. However, to the best of our knowledge, no attempts have been made to analytically derive the number of minima. Because of the complex nature of the function surface, a numerical method is developed to restrict domain spaces to hyperrectangles satisfying certain conditions. Within these domain spaces, an analytical method to count the number of minima is derived and proposed as a recursive functional form. The numbers of minima for two search spaces are provided as a reference. 2008 Elsevier Inc. All rights reserved.

authors

• Olivera, Francisco

published proceedings

• APPLIED MATHEMATICS AND COMPUTATION

author list (cited authors)

• Cho, H., Olivera, F., & Guikema, S. D.

citation count

• 17

complete list of authors

• Cho, Huidae||Olivera, Francisco||Guikema, Seth D

publication date

• January 2008

publisher

• Elsevier  Publisher

published in

• Applied Mathematics and Computation  Journal

keywords

• Griewank Function
• Local Minima
• Multi-modal Optimization
• Optimization

Digital Object Identifier (DOI)

• 10.1016/j.amc.2008.07.009

start page

• 694

end page

• 701

volume

• 204

issue

• 2

URL

• http://dx.doi.org/10.1016/j.amc.2008.07.009