# The Ackley test case¶

## Introduction¶

The Ackley test case is a real function defined in dimension where is an integer.

The Ackley function is defined by the equation:

for any . However, we consider the smaller interval in this example, for visual purposes.

We use the dimension with the parameters , , .

The solution is

where

## References¶

• Adorio, E. P., & Diliman, U. P. MVF - Multivariate Test Functions Library in C for Unconstrained Global Optimization (2005). Retrieved June 2013, from http://http://www.geocities.ws/eadorio/mvf.pdf.

• Molga, M., & Smutnicki, C. Test functions for optimization needs (2005). Retrieved June 2013, from http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf.

• Back, T. (1996). Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press on Demand.

>>> from openturns.usecases import ackley_function as ackley_function