.. _use-case-ackley: The Ackley test case ==================== Introduction ------------ The Ackley test case is a real function defined in dimension :math:d where :math:d is an integer. The Ackley function is defined by the equation: .. math:: f(\mathbf{x}) = -a \exp\left(-b\sqrt{\frac{1}{d}\sum_{i=1}^d}x_i^2\right)-\exp\left(\frac{1}{d}\sum_{i=1}^d \cos(c x_i)\right)+a+\exp(1) for any :math:\mathbf{x} \in [-15,15]^d. However, we consider the smaller interval :math:[-4,4]^d in this example, for visual purposes. We use the dimension :math:d=2 with the parameters :math:a=20, :math:b=0.2, :math:c=2\pi. The solution is .. math:: \mathbf{x}^\star=(0,0,...,0) where .. math:: f_{min} = f(\mathbf{x}^\star) = 0. 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. Load the use case ----------------- We can load this model from the use cases module as follows : .. code-block:: python >>> from openturns.usecases import ackley_function >>> # Load the Ackley model >>> am = ackley_function.AckleyModel() API documentation ----------------- See :class:~openturns.usecases.ackley_function.AckleyModel. Examples based on this use case ------------------------------- .. raw:: html
.. only:: html .. figure:: /auto_numerical_methods/optimization/images/thumb/sphx_glr_plot_ego_thumb.png :alt: :ref:sphx_glr_auto_numerical_methods_optimization_plot_ego.py .. raw:: html
.. toctree:: :hidden: /auto_numerical_methods/optimization/plot_ego