The objective function for the Branin problem.

The Branin (or Branin-Hoo) function is defined as

f(x,y) = a(y-bx^2+cx-r)^2 + s(1-t)cos(x)+s

Recommended values for the parameters are: a = 1 b = 5.1/(4*pi^2) c = 5/pi r = 6 s = 10 t = 1/(8*pi)

Domain: x = [-5, 10] y = [0, 15]

The Branin function has three global minima at

(x,y) = (-pi, 12.275), (pi, 2.275), (9.42478, 2.475)

with a function value of

f(x,y) = 0.397887

Public members¶

BraninObjective(problem, ana_deriv=False, name='f')[source]

Constructor

f(x, y)[source]

The Branin function f(x, y)

g(var, x, y, components=None)[source]

The derivative of the Branin function

property has_ana_derivs

Returns analyical derivatives flag

maximize()[source]

Returns flag for maximization of each component.

n_components()[source]

Returns the number of components of the function.

calc_individual(vars_int, vars_float, problem_results, ...)[source]

Calculate values for a single individual of the underlying problem.

calc_population(vars_int, vars_float, problem_results, ...)[source]

Calculate values for all individuals of a population.

ana_deriv(vars_int, vars_float, var, components=None)[source]

Calculates the analytic derivative, if possible.

classmethod new(objective_type, *args, **kwargs)[source]

Run-time objective function factory.

initialize(verbosity=0)[source]

Initialize the object.

property component_names

The names of the components

property var_names_int

The names of the integer variables

property n_vars_int

The number of int variables

property var_names_float

The names of the float variables

property n_vars_float

The number of float variables

vardeps_int()[source]

Gets the dependencies of all components on the function int variables

vardeps_float()[source]

Gets the dependencies of all components on the function float variables

rename_vars_int(varmap)[source]

Rename integer variables.

rename_vars_float(varmap)[source]

Rename float variables.

finalize_individual(vars_int, vars_float, problem_results, ...)[source]

Finalization, given the champion data.

finalize_population(vars_int, vars_float, problem_results, ...)[source]

Finalization, given the final population data.

__str__()[source]

Get info string

property initialized

Flag for finished initialization

finalize(verbosity=0)[source]

Finalize the object.