gemseo / problems / multiobjective_optimization

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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 gemseo.problems.multiobjective_optimization.poloni.Poloni[source]

Bases: OptimizationProblem

Poloni multi-objective, bound constrained optimization problem.

Parameters:

  • design_space – The design space on which the functions are evaluated.

  • pb_type – The type of the optimization problem.

  • input_database – A database to initialize that of the optimization problem. If None, the optimization problem starts from an empty database.

  • differentiation_method – The default differentiation method to be applied to the functions of the optimization problem.

  • fd_step – The step to be used by the step-based differentiation methods.

  • parallel_differentiation – Whether to approximate the derivatives in

  • parallel. –

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

  • hdf_node_path – The path of the HDF node from which the database should be imported. If empty, the root node is considered.

  • **parallel_differentiation_options – The options to approximate the derivatives in parallel.

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.

Examples using Poloni

Multi-objective Poloni example with the mNBI algorithm

Multi-objective Poloni example with the mNBI algorithm