gemseo.problems.multiobjective_optimization.binh_korn module#
Binh and Korn multi-objective problem.
This module implements the Binh and Korn multi-objective problem as defined in [BK97]:
\[\begin{split}\begin{aligned}
\text{minimize the objective function } & f_1(x, y) = 4x^2 + 4y^2 \\
& f_2(x, y) = (x-5)^2 + (y-5)^2 \\
\text{with respect to the design variables }&x,\,y \\
\text{subject to the general constraints }
& g_1(x,y) = (x-5)^2 + y^2 \leq 25.0\\
& g_2(x, y) = (x-8)^2 + (y+3)^2 \geq 7.7\\
\text{subject to the bound constraints }
& 0 \leq x \leq 5.0\\
& 0 \leq y \leq 3.0
\end{aligned}\end{split}\]
- class BinhKorn(initial_values=(1.0, 1.0))[source]#
Bases:
OptimizationProblemBinh and Korn optimization problem.
The constructor initializes the BinhKorn
OptimizationProblemby defining theDesignSpace, the objective function and the constraints.- Parameters:
initial_values (FigSizeType) --
Initial value of the design variables.
By default it is set to (1.0, 1.0).