Multistart optimization

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

from __future__ import annotations

from gemseo import configure_logger
from gemseo import create_design_space
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo.disciplines.scenario_adapters.mdo_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],
    "DisciplinaryOpt",
    "obj",
    design_space,
)
scenario.default_inputs = {"algo": "SLSQP", "max_iter": 10}
scenario.add_constraint("cstr", constraint_type="ineq")

Create the scenario adapter

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

Create the DOE scenario

scenario_doe = create_scenario(
    adapter,
    "DisciplinaryOpt",
    "obj",
    design_space,
    scenario_type="DOE",
)
scenario_doe.add_constraint("cstr", constraint_type="ineq")
run_inputs = {"n_samples": 10, "algo": "fullfact"}
scenario_doe.execute(run_inputs)
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start DOEScenario execution ***
    INFO - 13:53:43: DOEScenario
    INFO - 13:53:43:    Disciplines: MDOScenario_adapter
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    |  1.5  |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm fullfact:
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    |  -1.5 |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 161.54 it/sec, obj=-0.875]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 190.59 it/sec, obj=-0.267]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 251.23 it/sec, obj=-0.809]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 295.26 it/sec, obj=-0.868]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 331.92 it/sec, obj=-0.872]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 339.78 it/sec, obj=-0.265]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 346.42 it/sec, obj=0.136]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 351.11 it/sec, obj=0.579]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 369.75 it/sec, obj=0.289]
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 371.87 it/sec, obj=1.25]
 WARNING - 13:53:43: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 12
    INFO - 13:53:43:    Solution:
 WARNING - 13:53:43:       The solution is not feasible.
    INFO - 13:53:43:       Objective: 0.2888129873625884
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = 0.1513713660745195
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | -1.252181466244097 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.040075) ***
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 21.98 it/sec, obj=0.289]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    | -1.166666666666667 |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 992.73 it/sec, obj=0.579]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 449.00 it/sec, obj=-0.875]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 437.15 it/sec, obj=-0.267]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 472.05 it/sec, obj=-0.809]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 500.16 it/sec, obj=-0.868]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 517.25 it/sec, obj=-0.874]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 495.02 it/sec, obj=-0.266]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 476.61 it/sec, obj=0.135]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 465.84 it/sec, obj=0.577]
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 475.68 it/sec, obj=0.288]
 WARNING - 13:53:43: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 12
    INFO - 13:53:43:    Solution:
 WARNING - 13:53:43:       The solution is not feasible.
    INFO - 13:53:43:       Objective: 0.28811314244670916
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = 0.15144075010172386
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | -1.252370379421043 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.033288) ***
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 24.96 it/sec, obj=0.288]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    | -0.8333333333333334 |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 920.01 it/sec, obj=1.25]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 446.08 it/sec, obj=-0.875]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 501.85 it/sec, obj=1.01]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 470.28 it/sec, obj=-0.875]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 496.85 it/sec, obj=0.819]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 478.30 it/sec, obj=-0.875]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 490.45 it/sec, obj=0.693]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 476.96 it/sec, obj=-0.875]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 489.39 it/sec, obj=0.584]
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 477.04 it/sec, obj=-0.875]
 WARNING - 13:53:43: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 12
    INFO - 13:53:43:    Solution:
 WARNING - 13:53:43:       The solution is not feasible.
    INFO - 13:53:43:       Objective: 0.5837798748832244
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = 0.19806414473664136
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | -1.165017254128868 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.032155) ***
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 26.25 it/sec, obj=0.584]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    |  -0.5 |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 924.67 it/sec, obj=1.38]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 439.47 it/sec, obj=2.88]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 498.53 it/sec, obj=1.23]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 464.01 it/sec, obj=2.87]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 491.09 it/sec, obj=0.848]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 464.67 it/sec, obj=0.658]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 440.78 it/sec, obj=0.643]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 426.27 it/sec, obj=0.616]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 417.42 it/sec, obj=0.615]
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 410.06 it/sec, obj=0.615]
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 13
    INFO - 13:53:43:    Solution:
    INFO - 13:53:43:       The solution is feasible.
    INFO - 13:53:43:       Objective: 0.6150998219543254
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = -0.788285881879476
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | 0.5773788419679762 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.036542) ***
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 26.30 it/sec, obj=0.615]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    | -0.1666666666666667 |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 925.89 it/sec, obj=1.16]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 448.04 it/sec, obj=2.87]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 505.62 it/sec, obj=0.785]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 456.47 it/sec, obj=2.88]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 457.75 it/sec, obj=0.644]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 435.42 it/sec, obj=0.624]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 419.51 it/sec, obj=0.615]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 406.75 it/sec, obj=0.615]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 397.90 it/sec, obj=0.615]
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 392.93 it/sec, obj=0.615]
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 12
    INFO - 13:53:43:    Solution:
    INFO - 13:53:43:       The solution is feasible.
    INFO - 13:53:43:       Objective: 0.6150998205402495
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = -0.7883188793606977
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | 0.5773502675245377 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.038013) ***
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 26.14 it/sec, obj=0.615]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    | 0.1666666666666667 |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 988.52 it/sec, obj=0.838]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 439.42 it/sec, obj=2.88]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 499.14 it/sec, obj=0.656]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 450.56 it/sec, obj=0.639]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 424.15 it/sec, obj=0.616]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 409.23 it/sec, obj=0.615]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 396.11 it/sec, obj=0.615]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 390.03 it/sec, obj=0.615]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 385.06 it/sec, obj=0.615]
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 10
    INFO - 13:53:43:    Solution:
    INFO - 13:53:43:       The solution is feasible.
    INFO - 13:53:43:       Objective: 0.6150998205402508
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = -0.7883189092934597
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | 0.5773502416020033 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.033839) ***
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 26.41 it/sec, obj=0.615]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    |  0.5  |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 958.48 it/sec, obj=0.625]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 435.68 it/sec, obj=2.87]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 493.54 it/sec, obj=0.616]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 444.16 it/sec, obj=0.615]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 417.48 it/sec, obj=0.615]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 403.33 it/sec, obj=0.615]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 394.05 it/sec, obj=0.615]
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 8
    INFO - 13:53:43:    Solution:
    INFO - 13:53:43:       The solution is feasible.
    INFO - 13:53:43:       Objective: 0.6150998205402526
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = -0.7883188285028959
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | 0.5773503115686811 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.028595) ***
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 27.15 it/sec, obj=0.615]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    | 0.8333333333333335 |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 980.89 it/sec, obj=0.745]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 451.34 it/sec, obj=-0.875]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 440.16 it/sec, obj=-0.267]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 454.85 it/sec, obj=-0.809]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 484.60 it/sec, obj=-0.868]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 503.72 it/sec, obj=-0.874]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 485.93 it/sec, obj=-0.266]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 471.61 it/sec, obj=0.135]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 460.41 it/sec, obj=0.577]
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 473.30 it/sec, obj=0.288]
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 12
    INFO - 13:53:43:    Solution:
    INFO - 13:53:43:       The solution is feasible.
    INFO - 13:53:43:       Objective: 0.7453703703703706
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = -0.2499785665294918
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | 0.8333333333333335 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.033092) ***
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 27.31 it/sec, obj=0.745]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+-------------------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound |       Value       | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+-------------------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    | 1.166666666666667 |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+-------------------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 954.34 it/sec, obj=1.42]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 447.18 it/sec, obj=-0.875]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 438.67 it/sec, obj=-0.267]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 474.75 it/sec, obj=-0.809]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 501.33 it/sec, obj=-0.868]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 520.48 it/sec, obj=-0.874]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 496.49 it/sec, obj=-0.266]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 446.39 it/sec, obj=0.135]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 439.97 it/sec, obj=0.577]
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 455.25 it/sec, obj=0.288]
 WARNING - 13:53:43: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 12
    INFO - 13:53:43:    Solution:
 WARNING - 13:53:43:       The solution is not feasible.
    INFO - 13:53:43:       Objective: 0.28811314244698893
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = 0.1514407501016959
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | -1.252370379420967 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.034341) ***
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 27.40 it/sec, obj=0.288]
    INFO - 13:53:43:
    INFO - 13:53:43: *** Start MDOScenario execution ***
    INFO - 13:53:43: MDOScenario
    INFO - 13:53:43:    Disciplines: AnalyticDiscipline AnalyticDiscipline
    INFO - 13:53:43:    MDO formulation: DisciplinaryOpt
    INFO - 13:53:43: Optimization problem:
    INFO - 13:53:43:    minimize obj(x)
    INFO - 13:53:43:    with respect to x
    INFO - 13:53:43:    subject to constraints:
    INFO - 13:53:43:       cstr(x) <= 0.0
    INFO - 13:53:43:    over the design space:
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | Name | Lower bound | Value | Upper bound | Type  |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43:       | x    |     -1.5    |  1.5  |     1.5     | float |
    INFO - 13:53:43:       +------+-------------+-------+-------------+-------+
    INFO - 13:53:43: Solving optimization problem with algorithm SLSQP:
    INFO - 13:53:43:     10%|█         | 1/10 [00:00<00:00, 916.99 it/sec, obj=2.88]
    INFO - 13:53:43:     20%|██        | 2/10 [00:00<00:00, 441.60 it/sec, obj=-0.875]
    INFO - 13:53:43:     30%|███       | 3/10 [00:00<00:00, 429.85 it/sec, obj=-0.267]
    INFO - 13:53:43:     40%|████      | 4/10 [00:00<00:00, 468.35 it/sec, obj=-0.809]
    INFO - 13:53:43:     50%|█████     | 5/10 [00:00<00:00, 493.91 it/sec, obj=-0.868]
    INFO - 13:53:43:     60%|██████    | 6/10 [00:00<00:00, 514.14 it/sec, obj=-0.874]
    INFO - 13:53:43:     70%|███████   | 7/10 [00:00<00:00, 491.82 it/sec, obj=-0.266]
    INFO - 13:53:43:     80%|████████  | 8/10 [00:00<00:00, 477.72 it/sec, obj=0.135]
    INFO - 13:53:43:     90%|█████████ | 9/10 [00:00<00:00, 467.37 it/sec, obj=0.577]
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 479.39 it/sec, obj=0.288]
 WARNING - 13:53:43: Optimization found no feasible point !  The least infeasible point is selected.
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: Maximum number of iterations reached. GEMSEO Stopped the driver
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 12
    INFO - 13:53:43:    Solution:
 WARNING - 13:53:43:       The solution is not feasible.
    INFO - 13:53:43:       Objective: 0.28811314244587316
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = 0.15144075010180735
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |       Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | -1.252370379421268 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+--------------------+-------------+-------+
    INFO - 13:53:43: *** End MDOScenario execution (time: 0:00:00.033064) ***
    INFO - 13:53:43:    100%|██████████| 10/10 [00:00<00:00, 27.57 it/sec, obj=0.288]
    INFO - 13:53:43: Optimization result:
    INFO - 13:53:43:    Optimizer info:
    INFO - 13:53:43:       Status: None
    INFO - 13:53:43:       Message: None
    INFO - 13:53:43:       Number of calls to the objective function by the optimizer: 10
    INFO - 13:53:43:    Solution:
    INFO - 13:53:43:       The solution is feasible.
    INFO - 13:53:43:       Objective: 0.6150998205402495
    INFO - 13:53:43:       Standardized constraints:
    INFO - 13:53:43:          cstr = -0.7883188793606977
    INFO - 13:53:43:       Design space:
    INFO - 13:53:43:          +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43:          | Name | Lower bound |        Value        | Upper bound | Type  |
    INFO - 13:53:43:          +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43:          | x    |     -1.5    | -0.1666666666666667 |     1.5     | float |
    INFO - 13:53:43:          +------+-------------+---------------------+-------------+-------+
    INFO - 13:53:43: *** End DOEScenario execution (time: 0:00:00.374752) ***

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

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 0x7f2d1c192ee0>

Total running time of the script: (0 minutes 0.577 seconds)

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