rastrigin module¶
The Rastrigin analytic problem¶

class
gemseo.problems.analytical.rastrigin.
Rastrigin
[source]¶ Bases:
gemseo.algos.opt_problem.OptimizationProblem
Rastrigin
OptimizationProblem
uses the Rastrigin objective function with theDesignSpace
\([0.1,0.1]^2\)From http://en.wikipedia.org/wiki/Rastrigin_function:
the Rastrigin function is a nonconvex function used as a performance test problem for optimization algorithms. It is a typical example of nonlinear multimodal function. It was first proposed by [Rastrigin] as a 2dimensional function and has been generalized by [MuhlenbeinEtAl]. Finding the minimum of this function is a fairly difficult problem due to its large search space and its large number of local minima. It has a global minimum at \(x=0\) where \(f(x)=0\). It can be extended to \(n>2\) dimensions:
\[f(x) = 10n + \sum_{i=1}^n [x_i^2  10\cos(2\pi x_i)]\][Rastrigin] Rastrigin, L. A. “Systems of extremal control.” Mir, Moscow (1974).
[MuhlenbeinEtAl] H. Mühlenbein, D. Schomisch and J. Born. “The Parallel Genetic Algorithm as Function Optimizer “. Parallel Computing, 17, pages 619–632, 1991.
The constructor initializes the Rastrigin
OptimizationProblem
by defining theDesignSpace
and the objective function.
static
get_solution
()[source]¶ Return theoretical optimal value of Rastrigin function.
 Returns
design variables values of optimized values, function value at optimum
 Return type
numpy array

static