gemseo.problems.optimization.rastrigin module#
The Rastrigin analytic problem.
- class Rastrigin[source]#
Bases:
OptimizationProblem
The Rastrigin optimization problem.
It uses the Rastrigin objective function with the
DesignSpace
\([-0.1,0.1]^2\)From http://en.wikipedia.org/wiki/Rastrigin_function: the Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms. It is a typical example of non-linear multimodal function. It was first proposed by [Rastrigin] as a 2-dimensional 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.
- Parameters:
pb_type -- The type of the optimization problem.
use_standardized_objective -- Whether to use standardized objective for logging and post-processing.
- static get_solution()[source]#
Return theoretical optimal value of Rastrigin function.
- Returns:
The design variable and objective function at optimum.