functions.opti_test_functions¶
Module provides common test functions for parameter estimation and optimisation algorithms such as Rosenbrock and Griewank functions.
- Current functions are:
ackley >=2 params: Ackley function, global optimum: 0.0 at origin
goldstein_price 2 params: Goldstein-Price function, global optimum: 3.0 (0.0,-1.0)
griewank 2 or 10 params: Griewank function, global optimum: 0 at origin
rastrigin 2 params: Rastrigin function, global optimum: -2 (0,0)
rosenbrock 2 params: Rosenbrock function, global optimum: 0 (1,1)
- six_hump_camelback 2 params: Six-hump Camelback function
True Optima: -1.031628453489877 (-0.08983,0.7126) and (0.08983,-0.7126)
This module was written by Matthias Cuntz while at Department of Computational Hydrosystems, Helmholtz Centre for Environmental Research - UFZ, Leipzig, Germany, and continued while at Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Nancy, France.
Copyright (c) 2013-2020 Matthias Cuntz - mc (at) macu (dot) de Released under the MIT License; see LICENSE file for details.
Written Oct 2013 by Matthias Cuntz (mc (at) macu (dot) de)
Rearrange function library, Mar 2015, Matthias Cuntz
Changed to Sphinx docstring and numpydoc, May 2020, Matthias Cuntz
The following functions are provided:
|
Ackley function (>= 2-D). |
|
Griewank function (2-D or 10-D). |
Goldstein-Price function (2-D). |
|
|
Rastrigin function (2-D). |
|
Rosenbrock function (2-D). |
Six-hump Camelback function (2-D). |
- ackley(x)[source]¶
Ackley function (>= 2-D).
Global Optimum: 0.0, at origin.
- Parameters
x (array) – multi-dimensional x-values (len(x) >= 2)
- Returns
Value of Ackley function.
- Return type
- goldstein_price(x)[source]¶
Goldstein-Price function (2-D).
Global Optimum: 3.0, at (0.0,-1.0).
- Parameters
x (array) –
2 x-values. len(x)=2.
x[i] bound to [-2,2] for i=1 and 2.
- Returns
Value of Goldstein-Price function.
- Return type
- griewank(x)[source]¶
Griewank function (2-D or 10-D).
Global Optimum: 0.0, at origin.
- Parameters
x (array) –
multi-dimensional x-values.
len(x)=2 or len(x)=10.
x[i] bound to [-600,600] for all i.
- Returns
Value of Griewank function.
- Return type
- rastrigin(x)[source]¶
Rastrigin function (2-D).
Global Optimum: -2.0, at origin.
- Parameters
x (array) –
2 x-values. len(x)=2.
x[i] bound to [-1,1] for i=1 and 2.
- Returns
Value of Rastrigin function.
- Return type