A lookup table for minima

The following functions act as a lookup table for the minima of the mathamtical functions described in here. A minima for dimension n can be accesesed by calling the function with the dimension as the only argument.

test_functions.minima.minStyblinski_Tang(2) # returns the minimal value for n = 2
test_functions.minima.minStyblinski_Tangloc(2) # returns the location of the minimum

The min’func_name’loc functions returns the location of the minima, while the min’func_name’ functions returns the function value at the minima.

Note

Some functions are only valid for a certain amount of dimensions for these functions the parameter n is ignored.

Complete list of functions

All functions defined in this module are listed below.

dfmcontrol.Mathematical_functions.minima.minStyblinski_Tang(n: int)

This function has a global minimum at x = (-2.903534, -2.903534, …, -2.903534) with a value of -39.16616570377142 * n.

Parameters

n – Number of dimensions

Returns

Minimum value of the function at dimension n

dfmcontrol.Mathematical_functions.minima.minStyblinski_Tangloc(n: int)

Global minimum for Styblinski-Tang function.

Parameters

n – Number of dimensions

Returns

Global minimum location

dfmcontrol.Mathematical_functions.minima.minackley(n: int)

This function has a global minimum at x = (0, 0, …, 0) with a value of 0.

Parameters

n – Number of dimensions

Returns

Minimum value of the function at dimension n

dfmcontrol.Mathematical_functions.minima.minackleyloc(n: int)

Global minimum for Ackleys function.

Parameters

n – Number of dimensions

Returns

Global minimum location

dfmcontrol.Mathematical_functions.minima.minbooths_function(n: int = 2)

This function has a global minimum at x = (1, 3) with a value of 0. And is only defined for 2 dimensions.

Parameters

n – Number of dimensions (fixed at 2)

Returns

Minimum value of the function at dimension n

dfmcontrol.Mathematical_functions.minima.minbooths_functionloc(n: int = 2)

Global minimum for booths function.

Parameters

n – Number of dimensions (fixed at 2)

Returns

Global minimum location

dfmcontrol.Mathematical_functions.minima.minmichealewicz(n: int)

The global minima for this function can be approximated for n > 10 by the following formula: f(x) = -0.99864n + 0.30271 for dimensions 2 < n < 10 the global minima are defined in a lookup table.

Parameters

n – Number of dimensions

Returns

Minimum value of the function at dimension n

dfmcontrol.Mathematical_functions.minima.minmichealewiczloc(n: int)

The global minima for this function are defined between 1 <= n < 10 in a lookup table.

Parameters

n – Number of dimensions

Returns

Global minimum location

dfmcontrol.Mathematical_functions.minima.mintfx(x: float)

need to be implemented This function has a global minimum at x = 0 with a value of 0.

Parameters

x – Value of the function

Returns

Minimum value of the function at x

dfmcontrol.Mathematical_functions.minima.mintfxloc(x: float)

Global minimum for tfx function.

Parameters

x – Value of the function

Returns

Global minimum location

dfmcontrol.Mathematical_functions.minima.minwheelers_ridge(n: int = 2)

This function has a global minimum at x = (1, 3/2) with a value of -1. And is only defined for 2 dimensions.

Parameters

n – Number of dimensions (fixed at 2)

Returns

Minimum value of the function at dimension n

dfmcontrol.Mathematical_functions.minima.minwheelers_ridgeloc(n: int = 2)

Global minimum for wheelers ridge function.

Parameters

n – Number of dimensions (fixed at 2)

Returns

Global minimum location