gemseo / problems / multiobjective_optimization

fonseca_fleming module¶

Fonseca-Fleming bi-objective optimization problem.

See [FF95].

\[\begin{split}\begin{aligned} \text{minimize the objective function} & f_1(x) = 1 - exp(-\sum_{i=1}^{d}((x_i - 1 / sqrt(d)) ^ 2)) \\ & f_2(x) = 1 + exp(-\sum_{i=1}^{d}((x_i + 1 / sqrt(d)) ^ 2)) \\ \text{with respect to the design variables}&x\\ \text{subject to the bound constraints} & x\in[-4,4]^d \end{aligned}\end{split}\]

class gemseo.problems.multiobjective_optimization.fonseca_fleming.FonsecaFleming(dimension=3)[source]

Bases: OptimizationProblem

Fonseca-Fleming multi-objective, bound constrained optimization problem.

Parameters:

dimension (int) –

The design vector size.

By default it is set to 3.

constraints: list[MDOFunction]: The constraints.

current_iter: int: The current iteration.

database: Database: The database to store the optimization problem data.

design_space: DesignSpace: The design space on which the optimization problem is solved.

eq_tolerance: float: The tolerance for the equality constraints.

fd_step: float: The finite differences step.

ineq_tolerance: float: The tolerance for the inequality constraints.

max_iter: int: The maximum iteration.

new_iter_observables: list[MDOFunction]: The observables to be called at each new iterate.

nonproc_constraints: list[MDOFunction]: The non-processed constraints.

nonproc_new_iter_observables: list[MDOFunction]: The non-processed observables to be called at each new iterate.

nonproc_objective: MDOFunction: The non-processed objective function.

nonproc_observables: list[MDOFunction]: The non-processed observables.

observables: list[MDOFunction]: The observables.

pb_type: ProblemType: The type of optimization problem.

preprocess_options: dict: The options to pre-process the functions.

solution: OptimizationResult | None: The solution of the optimization problem if solved; otherwise None.

stop_if_nan: bool: Whether the optimization stops when a function returns NaN.

use_standardized_objective: bool

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

The standardized objective corresponds to the original one expressed as a cost function to minimize. A DriverLibrary works with this standardized objective and the Database stores its values. However, for convenience, it may be more relevant to log the expression and the values of the original objective.