Multistart optimization

Runs simple optimization problem with multiple starting points Nests a MDOScenario in a DOEScenario using a MDOScenarioAdapter.

from __future__ import annotations

from gemseo.api import configure_logger
from gemseo.api import create_design_space
from gemseo.api import create_discipline
from gemseo.api import create_scenario
from gemseo.disciplines.scenario_adapter import MDOScenarioAdapter

configure_logger()
<RootLogger root (INFO)>

Create the disciplines

objective = create_discipline("AnalyticDiscipline", expressions={"obj": "x**3-x+1"})
constraint = create_discipline(
    "AnalyticDiscipline", expressions={"cstr": "x**2+obj**2-1.5"}
)

Create the design space

design_space = create_design_space()
design_space.add_variable("x", l_b=-1.5, u_b=1.5, value=1.5)

Create the MDO scenario

scenario = create_scenario(
    [objective, constraint],
    formulation="DisciplinaryOpt",
    objective_name="obj",
    design_space=design_space,
)
scenario.default_inputs = {"algo": "SLSQP", "max_iter": 10}
scenario.add_constraint("cstr", "ineq")

Create the scenario adapter

dv_names = scenario.formulation.opt_problem.design_space.variables_names
adapter = MDOScenarioAdapter(
    scenario, dv_names, ["obj", "cstr"], set_x0_before_opt=True
)

Create the DOE scenario

scenario_doe = create_scenario(
    adapter,
    formulation="DisciplinaryOpt",
    objective_name="obj",
    design_space=design_space,
    scenario_type="DOE",
)
scenario_doe.add_constraint("cstr", "ineq")
run_inputs = {"n_samples": 10, "algo": "fullfact"}
scenario_doe.execute(run_inputs)
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start DOEScenario execution ***
    INFO - 15:59:54: DOEScenario
    INFO - 15:59:54:    Disciplines: MDOScenario_adapter
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound | value | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    |  1.5  |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm fullfact:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound | value | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    |  -1.5 |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 133.64 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 168.60 it/sec, obj=-.267]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 223.01 it/sec, obj=-.809]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 264.42 it/sec, obj=-.868]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 298.20 it/sec, obj=-.872]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 307.94 it/sec, obj=-.265]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 315.36 it/sec, obj=0.136]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 321.97 it/sec, obj=0.579]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 339.25 it/sec, obj=0.289]
    INFO - 15:59:54:
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 342.64 it/sec, obj=1.25]
    INFO - 15:59:54:
 WARNING - 15:59:54: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 12
    INFO - 15:59:54:    Solution:
 WARNING - 15:59:54:       The solution is not feasible.
    INFO - 15:59:54:       Objective: 0.2888129873625884
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = 0.1513713660745195
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | -1.252181466244097 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.040088) ***
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 21.65 it/sec, obj=0.289]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    | -1.166666666666667 |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 1002.46 it/sec, obj=0.579]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 423.97 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 415.28 it/sec, obj=-.267]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 448.86 it/sec, obj=-.809]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 471.41 it/sec, obj=-.868]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 487.64 it/sec, obj=-.874]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 467.17 it/sec, obj=-.266]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 452.51 it/sec, obj=0.135]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 441.41 it/sec, obj=0.577]
    INFO - 15:59:54:
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 453.22 it/sec, obj=0.288]
    INFO - 15:59:54:
 WARNING - 15:59:54: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 12
    INFO - 15:59:54:    Solution:
 WARNING - 15:59:54:       The solution is not feasible.
    INFO - 15:59:54:       Objective: 0.28811314244670916
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = 0.15144075010172386
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | -1.252370379421043 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.027871) ***
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 26.54 it/sec, obj=0.288]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound |        value        | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    | -0.8333333333333334 |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 1011.89 it/sec, obj=1.25]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 443.65 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 498.69 it/sec, obj=1.01]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 457.46 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 479.28 it/sec, obj=0.819]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 458.54 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 473.91 it/sec, obj=0.693]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 458.61 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 470.61 it/sec, obj=0.584]
    INFO - 15:59:54:
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 458.94 it/sec, obj=-.875]
    INFO - 15:59:54:
 WARNING - 15:59:54: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 12
    INFO - 15:59:54:    Solution:
 WARNING - 15:59:54:       The solution is not feasible.
    INFO - 15:59:54:       Objective: 0.5837798748832244
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = 0.19806414473664136
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | -1.165017254128868 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.026518) ***
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 28.87 it/sec, obj=0.584]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound | value | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    |  -0.5 |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 1015.32 it/sec, obj=1.38]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 442.27 it/sec, obj=2.88]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 493.47 it/sec, obj=1.23]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 457.38 it/sec, obj=2.87]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 480.28 it/sec, obj=0.848]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 446.67 it/sec, obj=0.658]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 424.86 it/sec, obj=0.643]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 410.28 it/sec, obj=0.616]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 398.90 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 385.94 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 13
    INFO - 15:59:54:    Solution:
    INFO - 15:59:54:       The solution is feasible.
    INFO - 15:59:54:       Objective: 0.6150998219543254
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = -0.788285881879476
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | 0.5773788419679762 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.031880) ***
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 29.19 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound |        value        | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    | -0.1666666666666667 |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 984.12 it/sec, obj=1.16]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 446.20 it/sec, obj=2.87]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 495.55 it/sec, obj=0.785]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 442.39 it/sec, obj=2.88]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 451.65 it/sec, obj=0.644]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 426.08 it/sec, obj=0.624]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 408.50 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 397.70 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 384.16 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 377.51 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 12
    INFO - 15:59:54:    Solution:
    INFO - 15:59:54:       The solution is feasible.
    INFO - 15:59:54:       Objective: 0.6150998205402495
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = -0.7883188793606977
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | 0.5773502675245377 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.032140) ***
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 29.34 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    | 0.1666666666666667 |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 993.44 it/sec, obj=0.838]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 439.75 it/sec, obj=2.88]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 494.55 it/sec, obj=0.656]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 437.24 it/sec, obj=0.639]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 409.98 it/sec, obj=0.616]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 394.29 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 384.88 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 373.10 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 368.24 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 10
    INFO - 15:59:54:    Solution:
    INFO - 15:59:54:       The solution is feasible.
    INFO - 15:59:54:       Objective: 0.6150998205402508
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = -0.7883189092934597
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | 0.5773502416020033 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.028462) ***
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 29.86 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound | value | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    |  0.5  |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 990.86 it/sec, obj=0.625]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 443.16 it/sec, obj=2.87]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 491.67 it/sec, obj=0.616]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 439.50 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 412.24 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 396.24 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 385.96 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 8
    INFO - 15:59:54:    Solution:
    INFO - 15:59:54:       The solution is feasible.
    INFO - 15:59:54:       Objective: 0.6150998205402526
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = -0.7883188285028959
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | 0.5773503115686811 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.022080) ***
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 31.10 it/sec, obj=0.615]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    | 0.8333333333333335 |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 990.62 it/sec, obj=0.745]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 441.27 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 423.87 it/sec, obj=-.267]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 438.84 it/sec, obj=-.809]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 463.28 it/sec, obj=-.868]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 481.97 it/sec, obj=-.874]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 461.70 it/sec, obj=-.266]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 440.57 it/sec, obj=0.135]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 431.86 it/sec, obj=0.577]
    INFO - 15:59:54:
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 444.39 it/sec, obj=0.288]
    INFO - 15:59:54:
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 12
    INFO - 15:59:54:    Solution:
    INFO - 15:59:54:       The solution is feasible.
    INFO - 15:59:54:       Objective: 0.7453703703703706
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = -0.2499785665294918
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | 0.8333333333333335 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.027817) ***
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 31.38 it/sec, obj=0.745]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+-------------------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound |       value       | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+-------------------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    | 1.166666666666667 |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+-------------------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 855.46 it/sec, obj=1.42]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 424.16 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 412.60 it/sec, obj=-.267]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 447.24 it/sec, obj=-.809]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 471.12 it/sec, obj=-.868]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 488.32 it/sec, obj=-.874]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 464.88 it/sec, obj=-.266]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 451.16 it/sec, obj=0.135]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 440.44 it/sec, obj=0.577]
    INFO - 15:59:54:
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 452.89 it/sec, obj=0.288]
    INFO - 15:59:54:
 WARNING - 15:59:54: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 12
    INFO - 15:59:54:    Solution:
 WARNING - 15:59:54:       The solution is not feasible.
    INFO - 15:59:54:       Objective: 0.28811314244698893
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = 0.1514407501016959
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | -1.252370379420967 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.027895) ***
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 31.68 it/sec, obj=0.288]
    INFO - 15:59:54:
    INFO - 15:59:54: *** Start MDOScenario execution ***
    INFO - 15:59:54: MDOScenario
    INFO - 15:59:54:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 15:59:54:    MDO formulation: DisciplinaryOpt
    INFO - 15:59:54: Optimization problem:
    INFO - 15:59:54:    minimize obj(x)
    INFO - 15:59:54:    with respect to x
    INFO - 15:59:54:    subject to constraints:
    INFO - 15:59:54:       cstr(x) <= 0.0
    INFO - 15:59:54:    over the design space:
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | name | lower_bound | value | upper_bound | type  |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54:    | x    |     -1.5    |  1.5  |     1.5     | float |
    INFO - 15:59:54:    +------+-------------+-------+-------------+-------+
    INFO - 15:59:54: Solving optimization problem with algorithm SLSQP:
    INFO - 15:59:54: ...   0%|          | 0/10 [00:00<?, ?it]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  10%|█         | 1/10 [00:00<00:00, 1015.32 it/sec, obj=2.88]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  20%|██        | 2/10 [00:00<00:00, 440.37 it/sec, obj=-.875]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  30%|███       | 3/10 [00:00<00:00, 417.58 it/sec, obj=-.267]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  40%|████      | 4/10 [00:00<00:00, 452.25 it/sec, obj=-.809]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  50%|█████     | 5/10 [00:00<00:00, 474.75 it/sec, obj=-.868]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  60%|██████    | 6/10 [00:00<00:00, 491.80 it/sec, obj=-.874]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  70%|███████   | 7/10 [00:00<00:00, 469.28 it/sec, obj=-.266]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  80%|████████  | 8/10 [00:00<00:00, 454.49 it/sec, obj=0.135]
    INFO - 15:59:54:
    INFO - 15:59:54: ...  90%|█████████ | 9/10 [00:00<00:00, 443.81 it/sec, obj=0.577]
    INFO - 15:59:54:
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 455.16 it/sec, obj=0.288]
    INFO - 15:59:54:
 WARNING - 15:59:54: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 15:59:54:
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 12
    INFO - 15:59:54:    Solution:
 WARNING - 15:59:54:       The solution is not feasible.
    INFO - 15:59:54:       Objective: 0.28811314244587316
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = 0.15144075010180735
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |       value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | -1.252370379421268 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+--------------------+-------------+-------+
    INFO - 15:59:54: *** End MDOScenario execution (time: 0:00:00.027693) ***
    INFO - 15:59:54: ... 100%|██████████| 10/10 [00:00<00:00, 31.94 it/sec, obj=0.288]
    INFO - 15:59:54: Optimization result:
    INFO - 15:59:54:    Optimizer info:
    INFO - 15:59:54:       Status: None
    INFO - 15:59:54:       Message: None
    INFO - 15:59:54:       Number of calls to the objective function by the optimizer: 10
    INFO - 15:59:54:    Solution:
    INFO - 15:59:54:       The solution is feasible.
    INFO - 15:59:54:       Objective: 0.6150998205402495
    INFO - 15:59:54:       Standardized constraints:
    INFO - 15:59:54:          cstr = -0.7883188793606977
    INFO - 15:59:54:       Design space:
    INFO - 15:59:54:       +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54:       | name | lower_bound |        value        | upper_bound | type  |
    INFO - 15:59:54:       +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54:       | x    |     -1.5    | -0.1666666666666667 |     1.5     | float |
    INFO - 15:59:54:       +------+-------------+---------------------+-------------+-------+
    INFO - 15:59:54: *** End DOEScenario execution (time: 0:00:00.322461) ***

{'eval_jac': False, 'algo': 'fullfact', 'n_samples': 10}

Plot the optimum objective for different x0

scenario_doe.post_process("BasicHistory", variable_names=["obj"], save=False, show=True)
History plot
<gemseo.post.basic_history.BasicHistory object at 0x7ff196307d00>

Total running time of the script: ( 0 minutes 0.514 seconds)

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