gemseo.problems.multiobjective_optimization.viennet module#

Viennet multi-objective problem.

See [VFM96].

\[\begin{split}\begin{aligned} \text{minimize the objective function} & f_1(x, y) = (x^2 + y^2) / 2 + sin(x^2 + y^2) \\ & f_2(x, y) = (3x - 2y + 4)^2 / 8 + (x - y + 1)^2 / 27 + 15 \\ & f_3(x, y) = 1 / (x^2 + y^2 + 1) - 1.1 e^{-(x^2 + y^2)} \\ \text{with respect to the design variables}&x,\,y \\ \text{subject to the bound constraints} & -3.0 \leq x \leq 3.0\\ & -3.0 \leq y \leq 3.0 \end{aligned}\end{split}\]
class Viennet(l_b=-3.0, u_b=3.0, initial_guess=(0, 0))[source]#

Bases: OptimizationProblem

The Viennet optimization problem.

Parameters:
  • l_b (float) --

    The lower bound (common value to all variables).

    By default it is set to -3.0.

  • u_b (float) --

    The upper bound (common value to all variables).

    By default it is set to 3.0.

  • initial_guess (Iterable[float]) --

    The initial guess for the optimal solution.

    By default it is set to (0, 0).