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我正在尝试在具有 Sellar 问题的 OpenMDAO 上实现同时分析和设计 (SAND) 架构。我想到了以下方法-

class SellarDis1(Component):

    def __init__(self):
        super(SellarDis1, self).__init__()

        self.add_param('z', val=np.zeros(2))
        self.add_param('x', val=0.0)
        self.add_param('y2', val=1.0)
        self.add_output('y1', val=1.0)

    def solve_nonlinear(self, params, unknowns, resids):
        pass

    def apply_nonlinear(self, params, unknowns, resids):

        z1 = params['z'][0]
        z2 = params['z'][1]
        x1 = params['x']
        y2 = params['y2']
        y1 = unknowns['y1']

        resids['y1'] = z1**2 + z2 + x1 - 0.2*y2 - y1

    def linearize(self, params, unknowns, resids):
        J = {}

        J['y1','y1'] = 1.0
        J['y1','y2'] = -0.2
        J['y1','z'] = np.array([[2*params['z'][0], 1.0]])
        J['y1','x'] = 1.0

        return J


class SellarDis2(Component):

    def __init__(self):
        super(SellarDis2, self).__init__()

        self.add_param('z', val=np.zeros(2))
        self.add_param('y1', val=1.0)
        self.add_output('y2', val=1.0)

    def solve_nonlinear(self, params, unknowns, resids):
        pass

    def apply_nonlinear(self, params, unknowns, resids):

        z1 = params['z'][0]
        z2 = params['z'][1]
        y1 = params['y1']
        y1 = abs(y1)
        y2 = unknowns['y2']

        resids['y2'] = y1**.5 + z1 + z2 - y2

    def linearize(self, params, unknowns, resids):
        J = {}

        J['y2', 'y2'] = 1.0
        J['y2', 'y1'] = 0.5*params['y1']**-0.5
        J['y2', 'z'] = np.array([[1.0, 1.0]])

        return J

class SellarSAND(Group):

    def __init__(self):
        super(SellarSAND, self).__init__()

        self.add('px', IndepVarComp('x', 1.0), promotes=['*'])
        self.add('pz', IndepVarComp('z', np.array([5.0,2.0])), promotes=['*'])

        self.add('d1', SellarDis1(), promotes=['*'])
        self.add('d2', SellarDis2(), promotes=['*'])

        self.add('obj_cmp', ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)',
                                     z=np.array([0.0, 0.0]), x=0.0, y1=0.0, y2=0.0),
                 promotes=['*'])

        self.add('con_cmp1', ExecComp('con1 = 3.16 - y1'), promotes=['*'])
        self.add('con_cmp2', ExecComp('con2 = y2 - 24.0'), promotes=['*'])

        self.nl_solver = NLGaussSeidel()
        self.nl_solver.options['atol'] = 1.0e-12
        self.ln_solver = ScipyGMRES()


top = Problem()
top.root = SellarSAND()

top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.options['tol'] = 1.0e-12

top.driver.add_desvar('z', lower=np.array([-10.0, 0.0]),upper=np.array([10.0, 10.0]))
top.driver.add_desvar('x', lower=0.0, upper=10.0)

top.driver.add_objective('obj')
top.driver.add_constraint('con1', upper=0.0)
top.driver.add_constraint('con2', upper=0.0)

top.setup()
tt = time.time()
top.run()


print("\n")
print( "Minimum found at (z1,z2,x) = (%f, %f, %f)" % (top['z'][0], \
                                         top['z'][1], \
                                         top['x']))
print("Coupling vars: %f, %f" % (top['y1'], top['y2']))
print("Minimum objective: ", top['obj'])
print("Elapsed time: ", 1000*(time.time()-tt), "milliseconds")

但是在运行系统时，我得到了不正确的结果-

Iteration limit exceeded    (Exit mode 9)
            Current function value: [ 1.36787944]
            Iterations: 201
            Function evaluations: 2171
            Gradient evaluations: 201
Optimization Complete
-----------------------------------


Minimum found at (z1,z2,x) = (5.973519, 0.000000, 0.000000)
Coupling vars: 1.000000, 1.000000
Minimum objective:  1.36787944117
Elapsed time:  21578.5069466 milliseconds

我在这里做错了什么？此外，组件类中定义的残差是否被 Solver 或 Driver 减少了？

4

1 回答 1

2

编辑——我最初实现了 All-At-Once，所以我重写了这个。现在应该是沙子了。

因此，在我对 SAND 的理解中，优化器通过同时改变设计变量和耦合变量来最小化问题，以实现可行性并将残差约束驱动为零。这意味着残差需要明确表示，因此我们不需要任何隐式组件或求解器——优化器完成所有工作。我修改了你的代码如下：

import time

import numpy as np

from openmdao.api import Component, Group, Problem, IndepVarComp, ExecComp, NLGaussSeidel, ScipyGMRES, \
     ScipyOptimizer, pyOptSparseDriver


class SellarDis1(Component):

    def __init__(self):
        super(SellarDis1, self).__init__()

        self.add_param('z', val=np.zeros(2))
        self.add_param('x', val=0.0)
        self.add_param('y2', val=1.0)
        self.add_param('y1', val=1.0)

        self.add_output('resid1', val=1.0)

    def solve_nonlinear(self, params, unknowns, resids):

        z1 = params['z'][0]
        z2 = params['z'][1]
        x1 = params['x']
        y2 = params['y2']
        y1 = params['y1']

        unknowns['resid1'] = z1**2 + z2 + x1 - 0.2*y2 - y1

    def linearize(self, params, unknowns, resids):
        J = {}

        J['resid1','y1'] = -1.0
        J['resid1','y2'] = -0.2
        J['resid1','z'] = np.array([[2*params['z'][0], 1.0]])
        J['resid1','x'] = 1.0

        return J


class SellarDis2(Component):

    def __init__(self):
        super(SellarDis2, self).__init__()

        self.add_param('z', val=np.zeros(2))
        self.add_param('y1', val=1.0)
        self.add_param('y2', val=1.0)

        self.add_output('resid2', val=1.0)

    def solve_nonlinear(self, params, unknowns, resids):

        z1 = params['z'][0]
        z2 = params['z'][1]
        y1 = params['y1']
        y1 = abs(y1)
        y2 = params['y2']

        unknowns['resid2'] = y1**.5 + z1 + z2 - y2

    def linearize(self, params, unknowns, resids):
        J = {}

        J['resid2', 'y2'] = -1.0
        J['resid2', 'y1'] = 0.5*params['y1']**-0.5
        J['resid2', 'z'] = np.array([[1.0, 1.0]])

        return J

class SellarSAND(Group):

    def __init__(self):
        super(SellarSAND, self).__init__()

        self.add('px', IndepVarComp('x', 1.0), promotes=['*'])
        self.add('pz', IndepVarComp('z', np.array([5.0, 2.0])), promotes=['*'])
        self.add('py1', IndepVarComp('y1', 1.0), promotes=['*'])
        self.add('py2', IndepVarComp('y2', 1.0), promotes=['*'])

        self.add('d1', SellarDis1(), promotes=['*'])
        self.add('d2', SellarDis2(), promotes=['*'])

        self.add('obj_cmp', ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)',
                                     z=np.array([0.0, 0.0]), x=0.0, y1=0.0, y2=0.0),
                 promotes=['*'])

        self.add('con_cmp1', ExecComp('con1 = 3.16 - y1'), promotes=['*'])
        self.add('con_cmp2', ExecComp('con2 = y2 - 24.0'), promotes=['*'])


top = Problem()
top.root = SellarSAND()

top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.options['tol'] = 1.0e-12

top.driver.add_desvar('z', lower=np.array([-10.0, 0.0]),upper=np.array([10.0, 10.0]))
top.driver.add_desvar('x', lower=0.0, upper=10.0)
top.driver.add_desvar('y1', lower=-10.0, upper=10.0)
top.driver.add_desvar('y2', lower=-10.0, upper=10.0)

top.driver.add_objective('obj')
top.driver.add_constraint('con1', upper=0.0)
top.driver.add_constraint('con2', upper=0.0)
top.driver.add_constraint('resid1', equals=0.0)
top.driver.add_constraint('resid2', equals=0.0)

top.setup()
tt = time.time()
top.run()


print("\n")
print( "Minimum found at (z1,z2,x) = (%f, %f, %f)" % (top['z'][0], \
                                         top['z'][1], \
                                         top['x']))
print("Coupling vars: %f, %f" % (top['d1.y1'], top['d1.y2']))
print("Minimum objective: ", top['obj'])
print("Elapsed time: ", 1000*(time.time()-tt), "milliseconds")

你走在正确的轨道上；我的主要更改是使其全部明确并将 y1 和 y2 声明为 des vars。

这样做，我得到

Minimum found at (z1,z2,x) = (1.977639, -0.000000, -0.000000)
Coupling vars: 3.160000, 3.755278
('Minimum objective: ', 3.1833939516406136)
('Elapsed time: ', 22.55988121032715, 'milliseconds')
于 2016-02-05T14:56:36.047 回答