Note
Go to the end to download the full example code.
Multi-start optimization#
The optimization algorithm multistart
generates starting points using a DOE algorithm
and run a sub-optimization algorithm from each starting point.
from __future__ import annotations
from gemseo import create_design_space
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo import execute_post
from gemseo.algos.opt.multi_start.settings.multi_start_settings import (
MultiStart_Settings,
)
First, we 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"}
)
and the design space
design_space = create_design_space()
design_space.add_variable("x", lower_bound=-1.5, upper_bound=1.5, value=1.5)
Then, we define the MDO scenario
scenario = create_scenario(
[objective, constraint],
"obj",
design_space,
formulation_name="DisciplinaryOpt",
)
Note that the formulation settings passed to create_scenario() can be provided
via a Pydantic model. For more information, see Formulation Settings.
scenario.add_constraint("cstr", constraint_type="ineq")
and execute it with the MultiStart optimization algorithm
combining the local optimization algorithm SLSQP
and the full-factorial DOE algorithm:
multistart_settings = MultiStart_Settings(
max_iter=100,
opt_algo_name="SLSQP",
doe_algo_name="PYDOE_FULLFACT",
n_start=10,
# Set multistart_file_path to save the history of the local optima.
multistart_file_path="multistart.hdf5",
)
scenario.execute(multistart_settings)
INFO - 16:25:02: *** Start MDOScenario execution ***
INFO - 16:25:02: MDOScenario
INFO - 16:25:02: Disciplines: AnalyticDiscipline AnalyticDiscipline
INFO - 16:25:02: MDO formulation: DisciplinaryOpt
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 1.5 | 1.5 | float |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm MultiStart:
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -1.5 | 1.5 | float |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 610.44 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 913.89 it/sec, feas=False, obj=-0.267]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1133.09 it/sec, feas=False, obj=-0.809]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1259.36 it/sec, feas=False, obj=-0.868]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1236.16 it/sec, feas=False, obj=-0.872]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1220.69 it/sec, feas=False, obj=-0.265]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1214.23 it/sec, feas=False, obj=0.136]
INFO - 16:25:02: 80%|████████ | 8/10 [00:00<00:00, 1268.50 it/sec, feas=False, obj=0.579]
INFO - 16:25:02: 90%|█████████ | 9/10 [00:00<00:00, 1259.47 it/sec, feas=False, obj=0.289]
INFO - 16:25:02: 100%|██████████| 10/10 [00:00<00:00, 1304.40 it/sec, feas=False, obj=1.25]
WARNING - 16:25:02: Optimization found no feasible point; the least infeasible point is selected.
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
WARNING - 16:25:02: The solution is not feasible.
INFO - 16:25:02: Objective: 0.2888129873625884
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = 0.1513713660745195
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -1.252181466244097 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -1.166666666666667 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 862.49 it/sec, feas=False, obj=0.579]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 989.11 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1204.22 it/sec, feas=False, obj=-0.267]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1323.86 it/sec, feas=False, obj=-0.809]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1421.99 it/sec, feas=False, obj=-0.868]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1380.01 it/sec, feas=False, obj=-0.874]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1344.82 it/sec, feas=False, obj=-0.266]
INFO - 16:25:02: 80%|████████ | 8/10 [00:00<00:00, 1321.30 it/sec, feas=False, obj=0.135]
INFO - 16:25:02: 90%|█████████ | 9/10 [00:00<00:00, 1371.53 it/sec, feas=False, obj=0.577]
INFO - 16:25:02: 100%|██████████| 10/10 [00:00<00:00, 1353.79 it/sec, feas=False, obj=0.288]
WARNING - 16:25:02: Optimization found no feasible point; the least infeasible point is selected.
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
WARNING - 16:25:02: The solution is not feasible.
INFO - 16:25:02: Objective: 0.28811314244670916
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = 0.15144075010172386
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -1.252370379421043 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+---------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+---------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -0.8333333333333334 | 1.5 | float |
INFO - 16:25:02: +------+-------------+---------------------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 864.09 it/sec, feas=False, obj=1.25]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 1192.24 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1199.63 it/sec, feas=False, obj=1.01]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1319.07 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1286.99 it/sec, feas=False, obj=0.819]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1354.97 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1330.32 it/sec, feas=False, obj=0.693]
INFO - 16:25:02: 80%|████████ | 8/10 [00:00<00:00, 1385.52 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 90%|█████████ | 9/10 [00:00<00:00, 1361.35 it/sec, feas=False, obj=0.584]
INFO - 16:25:02: 100%|██████████| 10/10 [00:00<00:00, 1403.48 it/sec, feas=False, obj=-0.875]
WARNING - 16:25:02: Optimization found no feasible point; the least infeasible point is selected.
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
WARNING - 16:25:02: The solution is not feasible.
INFO - 16:25:02: Objective: 0.5837798748832244
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = 0.19806414473664136
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -1.165017254128868 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -0.5 | 1.5 | float |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 870.73 it/sec, feas=False, obj=1.38]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 1218.21 it/sec, feas=False, obj=2.88]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1217.86 it/sec, feas=False, obj=1.23]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1328.68 it/sec, feas=False, obj=2.87]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1282.19 it/sec, feas=True, obj=0.848]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1208.21 it/sec, feas=True, obj=0.658]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1167.54 it/sec, feas=True, obj=0.643]
INFO - 16:25:02: 80%|████████ | 8/10 [00:00<00:00, 1138.48 it/sec, feas=True, obj=0.616]
INFO - 16:25:02: 90%|█████████ | 9/10 [00:00<00:00, 1116.40 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 100%|██████████| 10/10 [00:00<00:00, 1102.84 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
INFO - 16:25:02: The solution is feasible.
INFO - 16:25:02: Objective: 0.6150998219543254
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = -0.788285881879476
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 0.5773788419679762 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+---------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+---------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -0.1666666666666667 | 1.5 | float |
INFO - 16:25:02: +------+-------------+---------------------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 878.94 it/sec, feas=True, obj=1.16]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 1220.69 it/sec, feas=False, obj=2.87]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1174.66 it/sec, feas=True, obj=0.785]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1223.01 it/sec, feas=False, obj=2.88]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1157.24 it/sec, feas=True, obj=0.644]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1125.13 it/sec, feas=True, obj=0.624]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1100.17 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 80%|████████ | 8/10 [00:00<00:00, 1081.56 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 90%|█████████ | 9/10 [00:00<00:00, 1070.76 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 100%|██████████| 10/10 [00:00<00:00, 1060.99 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
INFO - 16:25:02: The solution is feasible.
INFO - 16:25:02: Objective: 0.6150998205402495
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = -0.7883188793606977
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 0.5773502675245377 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 0.1666666666666667 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 867.67 it/sec, feas=True, obj=0.838]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 1192.92 it/sec, feas=False, obj=2.88]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1206.99 it/sec, feas=True, obj=0.656]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1130.08 it/sec, feas=True, obj=0.639]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1088.36 it/sec, feas=True, obj=0.616]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1068.48 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1058.06 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 80%|████████ | 8/10 [00:00<00:00, 1050.12 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 90%|█████████ | 9/10 [00:00<00:00, 1041.66 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
INFO - 16:25:02: The solution is feasible.
INFO - 16:25:02: Objective: 0.6150998205402495
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = -0.7883188774386114
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 0.5773502691891133 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 0.5 | 1.5 | float |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 870.73 it/sec, feas=True, obj=0.625]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 1199.57 it/sec, feas=False, obj=2.87]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1212.93 it/sec, feas=True, obj=0.616]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1141.07 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1096.89 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1071.75 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1059.32 it/sec, feas=True, obj=0.615]
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Successive iterates of the objective function are closer than ftol_rel or ftol_abs. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
INFO - 16:25:02: The solution is feasible.
INFO - 16:25:02: Objective: 0.6150998205402495
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = -0.78831887743932
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 0.5773502691884995 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 0.8333333333333335 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 861.78 it/sec, feas=True, obj=0.745]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 998.29 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1216.09 it/sec, feas=False, obj=-0.267]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1260.69 it/sec, feas=False, obj=-0.809]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1357.12 it/sec, feas=False, obj=-0.868]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1321.04 it/sec, feas=False, obj=-0.874]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1303.27 it/sec, feas=False, obj=-0.266]
INFO - 16:25:02: 80%|████████ | 8/10 [00:00<00:00, 1288.52 it/sec, feas=False, obj=0.135]
INFO - 16:25:02: 90%|█████████ | 9/10 [00:00<00:00, 1336.66 it/sec, feas=False, obj=0.577]
INFO - 16:25:02: 100%|██████████| 10/10 [00:00<00:00, 1325.13 it/sec, feas=False, obj=0.288]
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
INFO - 16:25:02: The solution is feasible.
INFO - 16:25:02: Objective: 0.7453703703703706
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = -0.2499785665294918
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 0.8333333333333335 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+-------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+-------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 1.166666666666667 | 1.5 | float |
INFO - 16:25:02: +------+-------------+-------------------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 10%|█ | 1/10 [00:00<00:00, 862.85 it/sec, feas=False, obj=1.42]
INFO - 16:25:02: 20%|██ | 2/10 [00:00<00:00, 1012.87 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 30%|███ | 3/10 [00:00<00:00, 1218.33 it/sec, feas=False, obj=-0.267]
INFO - 16:25:02: 40%|████ | 4/10 [00:00<00:00, 1347.35 it/sec, feas=False, obj=-0.809]
INFO - 16:25:02: 50%|█████ | 5/10 [00:00<00:00, 1436.01 it/sec, feas=False, obj=-0.868]
INFO - 16:25:02: 60%|██████ | 6/10 [00:00<00:00, 1386.78 it/sec, feas=False, obj=-0.874]
INFO - 16:25:02: 70%|███████ | 7/10 [00:00<00:00, 1357.25 it/sec, feas=False, obj=-0.266]
INFO - 16:25:02: 80%|████████ | 8/10 [00:00<00:00, 1343.47 it/sec, feas=False, obj=0.135]
INFO - 16:25:02: 90%|█████████ | 9/10 [00:00<00:00, 1388.03 it/sec, feas=False, obj=0.577]
INFO - 16:25:02: 100%|██████████| 10/10 [00:00<00:00, 1365.07 it/sec, feas=False, obj=0.288]
WARNING - 16:25:02: Optimization found no feasible point; the least infeasible point is selected.
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
WARNING - 16:25:02: The solution is not feasible.
INFO - 16:25:02: Objective: 0.28811314244698893
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = 0.1514407501016959
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -1.252370379420967 | 1.5 | float |
INFO - 16:25:02: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:02: Optimization problem:
INFO - 16:25:02: minimize obj(x)
INFO - 16:25:02: with respect to x
INFO - 16:25:02: under the inequality constraints
INFO - 16:25:02: cstr(x) <= 0
INFO - 16:25:02: over the design space:
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | 1.5 | 1.5 | float |
INFO - 16:25:02: +------+-------------+-------+-------------+-------+
INFO - 16:25:02: Solving optimization problem with algorithm SLSQP:
INFO - 16:25:02: 11%|█ | 1/9 [00:00<00:00, 858.43 it/sec, feas=False, obj=2.88]
INFO - 16:25:02: 22%|██▏ | 2/9 [00:00<00:00, 994.62 it/sec, feas=False, obj=-0.875]
INFO - 16:25:02: 33%|███▎ | 3/9 [00:00<00:00, 1211.64 it/sec, feas=False, obj=-0.267]
INFO - 16:25:02: 44%|████▍ | 4/9 [00:00<00:00, 1332.90 it/sec, feas=False, obj=-0.809]
INFO - 16:25:02: 56%|█████▌ | 5/9 [00:00<00:00, 1431.50 it/sec, feas=False, obj=-0.868]
INFO - 16:25:02: 67%|██████▋ | 6/9 [00:00<00:00, 1389.15 it/sec, feas=False, obj=-0.874]
INFO - 16:25:02: 78%|███████▊ | 7/9 [00:00<00:00, 1353.25 it/sec, feas=False, obj=-0.266]
INFO - 16:25:02: 89%|████████▉ | 8/9 [00:00<00:00, 1329.31 it/sec, feas=False, obj=0.135]
INFO - 16:25:02: 100%|██████████| 9/9 [00:00<00:00, 1378.55 it/sec, feas=False, obj=0.577]
WARNING - 16:25:02: Optimization found no feasible point; the least infeasible point is selected.
INFO - 16:25:02: Optimization result:
INFO - 16:25:02: Optimizer info:
INFO - 16:25:02: Status: None
INFO - 16:25:02: Message: Maximum number of iterations reached. GEMSEO stopped the driver.
INFO - 16:25:02: Solution:
WARNING - 16:25:02: The solution is not feasible.
INFO - 16:25:02: Objective: 0.13490034433852438
INFO - 16:25:02: Standardized constraints:
INFO - 16:25:02: cstr = 0.1877267982258064
INFO - 16:25:02: Design space:
INFO - 16:25:02: +------+-------------+-------------------+-------------+-------+
INFO - 16:25:02: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:02: +------+-------------+-------------------+-------------+-------+
INFO - 16:25:02: | x | -1.5 | -1.29210243221006 | 1.5 | float |
INFO - 16:25:02: +------+-------------+-------------------+-------------+-------+
WARNING - 16:25:02: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 16:25:02: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 16:25:02: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 16:25:03: Optimization found no feasible point; the least infeasible point is selected.
WARNING - 16:25:03: Optimization found no feasible point; the least infeasible point is selected.
INFO - 16:25:03: Exporting the optimization problem to the file multistart.hdf5
INFO - 16:25:03: 1%| | 1/100 [00:00<00:11, 8.50 it/sec, feas=False, obj=0.577]
INFO - 16:25:03: Optimization result:
INFO - 16:25:03: Optimizer info:
INFO - 16:25:03: Status: None
INFO - 16:25:03: Message: None
INFO - 16:25:03: Solution:
INFO - 16:25:03: The solution is feasible.
INFO - 16:25:03: Objective: 0.6150998205402495
INFO - 16:25:03: Standardized constraints:
INFO - 16:25:03: cstr = -0.7883188793606977
INFO - 16:25:03: Design space:
INFO - 16:25:03: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:03: | Name | Lower bound | Value | Upper bound | Type |
INFO - 16:25:03: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:03: | x | -1.5 | 0.5773502675245377 | 1.5 | float |
INFO - 16:25:03: +------+-------------+--------------------+-------------+-------+
INFO - 16:25:03: *** End MDOScenario execution ***
Lastly, we can plot the history of the objective, either by concatenating the 10 sub-optimization histories:
execute_post(
scenario, post_name="BasicHistory", variable_names=["obj"], save=False, show=True
)
<gemseo.post.basic_history.BasicHistory object at 0x72a4f23a9790>
or by filtering the local optima (one per starting point):
execute_post(
"multistart.hdf5",
post_name="BasicHistory",
variable_names=["obj"],
save=False,
show=True,
)
INFO - 16:25:03: Importing the optimization problem from the file multistart.hdf5
<gemseo.post.basic_history.BasicHistory object at 0x72a4d5866fc0>
Total running time of the script: (0 minutes 0.352 seconds)