gemseo.problems.multiobjective_optimization.poloni module

Poloni's bi-objective optimization problem.

See [PGOP00].

\[\begin{split}\begin{aligned} &a1 = 0.5 * sin(1) - 2 * cos(1) + sin(2) - 1.5 * cos(2)\\ &a2 = 1.5 * sin(1) - cos(1) + 2 * sin(2) - 0.5 * cos(2)\\ &b1(x, y) = 0.5 * sin(x) - 2 * cos(x) + sin(y) - 1.5 * cos(y)\\ &b2(x, y) = 1.5 * sin(x) - cos(x) + 2 * sin(y) - 0.5 * cos(y)\\ \text{minimize the objective function}\\ & f_1(x, y) = 1 + (a1 - b1(x,y)^2 + (a2 - b2(x,y))^2 \\ & f_2(x, y) = (x + 3)^2 + (y + 1)^2 \\ \text{with respect to the design variables}\\ &x \\ \text{subject to the bound constraints}\\ & -\pi \leq x \leq \pi\\ & -\pi \leq y \leq \pi \end{aligned}\end{split}\]

class Poloni

Bases: OptimizationProblem

Poloni multi-objective, bound constrained optimization problem.

Parameters:

• pb_type -- The type of the optimization problem.

• use_standardized_objective -- Whether to use standardized objective for logging and post-processing.