odatse.solver.analytical module#

class odatse.solver.analytical.Solver(info: Info)[source]#

Bases: Solver

Function Solver with pre-defined benchmark functions

Initialize the solver.

Parameters:: info (Info) – Information object containing solver configuration.

__init__(info: Info) → None[source]#

Initialize the solver.

Parameters:: info (Info) – Information object containing solver configuration.

odatse.solver.analytical.ackley(xs: ndarray) → float[source]#

Ackley’s function in arbitrary dimension

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of Ackley’s function.
Return type:: float

Notes

It has one global minimum f(xs)=0 at xs=[0,0,…,0]. It has many local minima.

odatse.solver.analytical.alpine(xs: ndarray) → float[source]#

Alpine function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the Alpine function.
Return type:: float

Notes

It has a global minimum f(x)=0 at x=[0,0,…,0].

odatse.solver.analytical.exponential(xs: ndarray) → float[source]#

Exponential function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the Exponential function.
Return type:: float

Notes

It has a global minimum f(x)=-1 at x=[0,0,…,0].

odatse.solver.analytical.griewank(xs: ndarray) → float[source]#

Griewank function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the Griewank function.
Return type:: float

Notes

It has a global minimum f(x)=0 at x=[0,0,…,0].

odatse.solver.analytical.himmelblau(xs: ndarray) → float[source]#

Himmelblau’s function.

Parameters:: xs (np.ndarray) – Input array of shape (2,).
Returns:: The calculated value of Himmelblau’s function.
Return type:: float

Notes

It has four global minima f(xs) = 0 at xs=[3,2], [-2.805118…, 3.131312…], [-3.779310…, -3.2831860], and [3.584428…, -1.848126…].

odatse.solver.analytical.linear_regression_test(xs: ndarray) → float[source]#

Negative log likelihood of linear regression with Gaussian noise N(0,sigma)

y = ax + b

trained by xdata = [1, 2, 3, 4, 5, 6] and ydata = [1, 3, 2, 4, 3, 5].

Model parameters (a, b, sigma) are corresponding to xs as the following, a = xs[0], b = xs[1], log(sigma**2) = xs[2]

It has a global minimum f(xs) = 1.005071.. at xs = [0.628571…, 0.8, -0.664976…].

Parameters:: xs (np.ndarray) – Input array of model parameters.
Returns:: The negative log likelihood of the linear regression model.
Return type:: float

odatse.solver.analytical.michalewicz(xs: ndarray) → float[source]#

Michalewicz function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the Michalewicz function.
Return type:: float

Notes

The global minimum value and location depend on the dimension. There are d! local minima. For d=2, it has a global minimum f(x)=-1.8013 at x=[2.2051, 1.5698]. For d=5, it has a global minimum f(x)=-4.6876. For d=10, it has a global minimum f(x)=-9.6602.

odatse.solver.analytical.qing(xs: ndarray) → float[source]#

Qing function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the Qing function.
Return type:: float

Notes

It has a global minimum f(x)=0 at x=[+/-sqrt(n), …], where n runs from 1 to d.

odatse.solver.analytical.quadratics(xs: ndarray) → float[source]#

Quadratic (sphere) function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the quadratic function.
Return type:: float

Notes

It has one global minimum f(xs)=0 at xs = [0,0,…,0].

odatse.solver.analytical.quartics(xs: ndarray) → float[source]#

Quartic function with two global minima.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the quartic function.
Return type:: float

Notes

It has two global minima f(xs)=0 at xs = [1,1,…,1] and [-1,-1,…,-1]. It has one saddle point f(0,0,…,0) = 1.0.

odatse.solver.analytical.rastrigin(xs: ndarray) → float[source]#

Rastrigin function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the Rastrigin function.
Return type:: float

Notes

It has a global minimum f(x)=0 at x=[0,0,…,0].

odatse.solver.analytical.rosenbrock(xs: ndarray) → float[source]#

Rosenbrock’s function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of Rosenbrock’s function.
Return type:: float

Notes

It has one global minimum f(xs) = 0 at xs=[1,1,…,1].

odatse.solver.analytical.schaffer(xs: ndarray) → float[source]#

Schaffer function (generalized).

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the Schaffer function.
Return type:: float

odatse.solver.analytical.schwefel(xs: ndarray) → float[source]#

Schwefel function.

Parameters:: xs (np.ndarray) – Input array.
Returns:: The calculated value of the Schwefel function.
Return type:: float

Notes

It has a global minimum f(x)=0 at x=[420.9687…, …].