需要缩放的抛物面优化
Paraboloid optimization requiring scaling
我想使用缩放器并最终使用 OpenMDAO 1.x 测试了您的 Paraboloid example from OpenMDAO 0.x 文档，但无论是否使用缩放器，我都会得到奇怪的结果。这是代码：
from __future__ import print_function
import sys
from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer
class Paraboloid(Component):
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
def solve_nonlinear(self, params, unknowns, resids):
x = params['x']
y = params['y']
#unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0
unknowns['f_xy'] = (1000.*x-3.)**2 + (1000.*x)*(0.01*y) + (0.01*y+4.)**2 - 3.
def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
#J['f_xy', 'x'] = 2.0*x - 6.0 + y
#J['f_xy', 'y'] = 2.0*y + 8.0 + x
J['f_xy', 'x'] = 2000000.0*x - 6000.0 + 10.0*y
J['f_xy', 'y'] = 0.0002*y + 0.08 + 10.0*x
return J
if __name__ == "__main__":
top = Problem()
root = top.root = Group()
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=0.001)
top.driver.add_desvar('p2.y', lower=-1000, upper=1000, scaler=1000.)
top.driver.add_objective('p.f_xy')
top.setup()
top.run()
print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
当我在我的系统上 运行 它时，它给出：
2.7.11 |Anaconda 2.5.0 (64-bit)| (default, Jan 29 2016, 14:26:21) [MSC v.1500 64 bit (AMD64)]
Python Type "help", "copyright", "credits" or "license" for more information.
[evaluate paraboloid_optimize_scaled.py]
##############################################
Setup: Checking for potential issues...
No recorders have been specified, so no data will be saved.
Setup: Check complete.
##############################################
Optimization terminated successfully. (Exit mode 0)
Current function value: [ 8981902.27846645]
Iterations: 1
Function evaluations: 12
Gradient evaluations: 1
Optimization Complete
-----------------------------------
Minimum of 8981902.278466 found at (3.000000, -4.000000)
我是不是漏掉了什么？
我无法直接复制您的问题。与您引用的 openmdao 0.x tutorial 相比，您的 solve_nonlinear 和 linearize 方法中有一些奇怪的缩放比例。但是当我清理它们时，我得到了正确的答案，对于合理的缩放器值，甚至对于一些不合理的值（你选择的值有点极端）。当您使用 add_desvar 中的 scaler/adder 时，您根本不需要修改您的模型。这些值只是修改优化器看到的有助于缩放的值，但在传递给您的模型之前会适当地转换回未缩放的值。
from __future__ import print_function
import sys
from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer
class Paraboloid(Component):
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
def solve_nonlinear(self, params, unknowns, resids):
x = params['x']
y = params['y']
unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0
def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = 2.0*x - 6.0 + y
J['f_xy', 'y'] = 2.0*y + 8.0 + x
return J
if __name__ == "__main__":
top = Problem()
root = top.root = Group()
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
# top.driver.add_desvar('p1.x', lower=-1000, upper=1000)
# top.driver.add_desvar('p2.y', lower=-1000, upper=1000)
top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=.001)
top.driver.add_desvar('p2.y', lower=-1000, upper=1000, scaler=1000.)
top.driver.add_objective('p.f_xy')
top.setup()
top.run()
print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
给出：
##############################################
Setup: Checking for potential issues...
No recorders have been specified, so no data will be saved.
Setup: Check complete.
##############################################
Optimization terminated successfully. (Exit mode 0)
Current function value: [-27.33333333]
Iterations: 12
Function evaluations: 15
Gradient evaluations: 12
Optimization Complete
-----------------------------------
缩放器在 OpenMDAO 1.x 中的定义与在 0.x 中的定义相反。在 1.x 中使用了以下比例关系。
driver_value = (model_value + adder)*scaler
因此，与旧教程中的缩放器相比，您需要更改缩放器。但是还有一个次要问题，您的分析导数中的错误也已在下面更正。
from __future__ import print_function
import sys
from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer
class Paraboloid(Component):
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
def solve_nonlinear(self, params, unknowns, resids):
x = params['x']
y = params['y']
#unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0
unknowns['f_xy'] = (1000.*x-3.)**2 + (1000.*x)*(0.01*y) + (0.01*y+4.)**2 - 3.
def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
#J['f_xy', 'x'] = 2.0*x - 6.0 + y
#J['f_xy', 'y'] = 2.0*y + 8.0 + x
J['f_xy', 'x'] = 2000000.0*x - 6000.0 + 10.0*y
J['f_xy', 'y'] = 0.0002*y + 0.08 + 10.0*x
return J
if __name__ == "__main__":
top = Problem()
root = top.root = Group()
root.fd_options['force_fd'] = True
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=1000.)
top.driver.add_desvar('p2.y', lower=-1000, upper=1000,scaler=.001)
top.driver.add_objective('p.f_xy')
top.setup()
top.run()
print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
给出：
Optimization terminated successfully. (Exit mode 0)
Current function value: [-27.333333]
Iterations: 3
Function evaluations: 6
Gradient evaluations: 3
Optimization Complete
-----------------------------------
Minimum of -27.333333 found at (0.006666, -733.299996)
我想使用缩放器并最终使用 OpenMDAO 1.x 测试了您的 Paraboloid example from OpenMDAO 0.x 文档，但无论是否使用缩放器，我都会得到奇怪的结果。这是代码：
from __future__ import print_function
import sys
from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer
class Paraboloid(Component):
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
def solve_nonlinear(self, params, unknowns, resids):
x = params['x']
y = params['y']
#unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0
unknowns['f_xy'] = (1000.*x-3.)**2 + (1000.*x)*(0.01*y) + (0.01*y+4.)**2 - 3.
def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
#J['f_xy', 'x'] = 2.0*x - 6.0 + y
#J['f_xy', 'y'] = 2.0*y + 8.0 + x
J['f_xy', 'x'] = 2000000.0*x - 6000.0 + 10.0*y
J['f_xy', 'y'] = 0.0002*y + 0.08 + 10.0*x
return J
if __name__ == "__main__":
top = Problem()
root = top.root = Group()
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=0.001)
top.driver.add_desvar('p2.y', lower=-1000, upper=1000, scaler=1000.)
top.driver.add_objective('p.f_xy')
top.setup()
top.run()
print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
当我在我的系统上 运行 它时，它给出：
2.7.11 |Anaconda 2.5.0 (64-bit)| (default, Jan 29 2016, 14:26:21) [MSC v.1500 64 bit (AMD64)]
Python Type "help", "copyright", "credits" or "license" for more information.
[evaluate paraboloid_optimize_scaled.py]
##############################################
Setup: Checking for potential issues...
No recorders have been specified, so no data will be saved.
Setup: Check complete.
##############################################
Optimization terminated successfully. (Exit mode 0)
Current function value: [ 8981902.27846645]
Iterations: 1
Function evaluations: 12
Gradient evaluations: 1
Optimization Complete
-----------------------------------
Minimum of 8981902.278466 found at (3.000000, -4.000000)
我是不是漏掉了什么？
我无法直接复制您的问题。与您引用的 openmdao 0.x tutorial 相比，您的 solve_nonlinear 和 linearize 方法中有一些奇怪的缩放比例。但是当我清理它们时，我得到了正确的答案，对于合理的缩放器值，甚至对于一些不合理的值（你选择的值有点极端）。当您使用 add_desvar 中的 scaler/adder 时，您根本不需要修改您的模型。这些值只是修改优化器看到的有助于缩放的值，但在传递给您的模型之前会适当地转换回未缩放的值。
from __future__ import print_function
import sys
from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer
class Paraboloid(Component):
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
def solve_nonlinear(self, params, unknowns, resids):
x = params['x']
y = params['y']
unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0
def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = 2.0*x - 6.0 + y
J['f_xy', 'y'] = 2.0*y + 8.0 + x
return J
if __name__ == "__main__":
top = Problem()
root = top.root = Group()
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
# top.driver.add_desvar('p1.x', lower=-1000, upper=1000)
# top.driver.add_desvar('p2.y', lower=-1000, upper=1000)
top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=.001)
top.driver.add_desvar('p2.y', lower=-1000, upper=1000, scaler=1000.)
top.driver.add_objective('p.f_xy')
top.setup()
top.run()
print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
给出：
##############################################
Setup: Checking for potential issues...
No recorders have been specified, so no data will be saved.
Setup: Check complete.
##############################################
Optimization terminated successfully. (Exit mode 0)
Current function value: [-27.33333333]
Iterations: 12
Function evaluations: 15
Gradient evaluations: 12
Optimization Complete
-----------------------------------
缩放器在 OpenMDAO 1.x 中的定义与在 0.x 中的定义相反。在 1.x 中使用了以下比例关系。
driver_value = (model_value + adder)*scaler
因此，与旧教程中的缩放器相比，您需要更改缩放器。但是还有一个次要问题，您的分析导数中的错误也已在下面更正。
from __future__ import print_function
import sys
from openmdao.api import IndepVarComp, Component, Problem, Group, ScipyOptimizer
class Paraboloid(Component):
def __init__(self):
super(Paraboloid, self).__init__()
self.add_param('x', val=0.0)
self.add_param('y', val=0.0)
self.add_output('f_xy', val=0.0)
def solve_nonlinear(self, params, unknowns, resids):
x = params['x']
y = params['y']
#unknowns['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0
unknowns['f_xy'] = (1000.*x-3.)**2 + (1000.*x)*(0.01*y) + (0.01*y+4.)**2 - 3.
def linearize(self, params, unknowns, resids):
""" Jacobian for our paraboloid."""
x = params['x']
y = params['y']
J = {}
#J['f_xy', 'x'] = 2.0*x - 6.0 + y
#J['f_xy', 'y'] = 2.0*y + 8.0 + x
J['f_xy', 'x'] = 2000000.0*x - 6000.0 + 10.0*y
J['f_xy', 'y'] = 0.0002*y + 0.08 + 10.0*x
return J
if __name__ == "__main__":
top = Problem()
root = top.root = Group()
root.fd_options['force_fd'] = True
root.add('p1', IndepVarComp('x', 3.0))
root.add('p2', IndepVarComp('y', -4.0))
root.add('p', Paraboloid())
root.connect('p1.x', 'p.x')
root.connect('p2.y', 'p.y')
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.add_desvar('p1.x', lower=-1000, upper=1000, scaler=1000.)
top.driver.add_desvar('p2.y', lower=-1000, upper=1000,scaler=.001)
top.driver.add_objective('p.f_xy')
top.setup()
top.run()
print('\n')
print('Minimum of %f found at (%f, %f)' % (top['p.f_xy'], top['p.x'], top['p.y']))
给出：
Optimization terminated successfully. (Exit mode 0)
Current function value: [-27.333333]
Iterations: 3
Function evaluations: 6
Gradient evaluations: 3
Optimization Complete
-----------------------------------
Minimum of -27.333333 found at (0.006666, -733.299996)