class TestNSGA2(OptTest):
name = "quadratic"
optName = "NSGA2"
def objfunc(self, xdict):
x = xdict["x"]
y = xdict["y"]
funcs = {}
funcs["obj1"] = (x - 0.0) ** 2 + (y - 0.0) ** 2
funcs["obj2"] = (x - 1.0) ** 2 + (y - 1.0) ** 2
fail = False
return funcs, fail
def setup_optProb(self):
# Instantiate Optimization Problem
self.optProb = Optimization("quadratic", self.objfunc)
self.optProb.addVar("x", value=0, lower=-600, upper=600)
self.optProb.addVar("y", value=0, lower=-600, upper=600)
self.optProb.addObj("obj1")
self.optProb.addObj("obj2")
def test_opt(self):
self.setup_optProb()
# 300 generations will find x=(0,0), 200 or less will find x=(1,1)
optOptions = {"maxGen": 200}
sol = self.optimize(optOptions=optOptions)
tol = 1e-2
assert_allclose(sol.variables["x"][0].value, 1.0, atol=tol, rtol=tol)
assert_allclose(sol.variables["y"][0].value, 1.0, atol=tol, rtol=tol)
def optimize(self, optName, tol, optOptions={}, storeHistory=False):
# Optimization Object
optProb = Optimization("large and sparse", objfunc)
# Design Variables
optProb.addVar("x", lower=-100, upper=150, value=0)
optProb.addVarGroup("y", N, lower=-10 - arange(N), upper=arange(N), value=0)
optProb.addVarGroup("z", 2 * N, upper=arange(2 * N), lower=-100 - arange(2 * N), value=0)
# Constraints
optProb.addCon("con1", upper=100, wrt=["x"])
optProb.addCon("con2", upper=100)
optProb.addCon("con3", lower=4, wrt=["x", "z"])
optProb.addConGroup(
"lincon",
N,
lower=2 - 3 * arange(N),
linear=True,
wrt=["x", "y"],
jac={"x": np.ones((N, 1)), "y": sparse.spdiags(np.ones(N), 0, N, N)},
)
optProb.addObj("obj")
# Optimizer
try:
opt = OPT(optName, options=optOptions)
except Error:
raise unittest.SkipTest("Optimizer not available:", optName)
sol = opt(optProb, sens=sens)
# Check Solution
assert_allclose(sol.objectives["obj"].value, 10.0, atol=tol, rtol=tol)
assert_allclose(sol.variables["x"][0].value, 2.0, atol=tol, rtol=tol)
def test_opt(self):
# Instantiate Optimization Problem
optProb = Optimization("Rosenbrock function", objfunc)
optProb.addVar("x", "c", value=0, lower=-600, upper=600)
optProb.addVar("y", "c", value=0, lower=-600, upper=600)
optProb.addObj("obj1")
optProb.addObj("obj2")
# 300 generations will find x=(0,0), 200 or less will find x=(1,1)
options = {"maxGen": 200}
# Optimizer
try:
opt = NSGA2(options=options)
except Error:
raise unittest.SkipTest("Optimizer not available:", "NSGA2")
sol = opt(optProb)
# Check Solution
tol = 1e-2
assert_allclose(sol.variables["x"][0].value, 1.0, atol=tol, rtol=tol)
assert_allclose(sol.variables["y"][0].value, 1.0, atol=tol, rtol=tol)
def large_sparse(optimizer="SNOPT", optOptions=None):
opt_options = {} if optOptions is None else optOptions
# Optimization Object
optProb = Optimization("large and sparse", objfunc)
# Design Variables
optProb.addVar("x", lower=-100, upper=150, value=0)
optProb.addVarGroup("y", N, lower=-10 - arange(N), upper=arange(N), value=0)
optProb.addVarGroup("z", 2 * N, upper=arange(2 * N), lower=-100 - arange(2 * N), value=0)
# Constraints
optProb.addCon("con1", upper=100, wrt=["x"])
optProb.addCon("con2", upper=100)
optProb.addCon("con3", lower=4, wrt=["x", "z"])
optProb.addConGroup(
"lincon",
N,
lower=2 - 3 * arange(N),
linear=True,
wrt=["x", "y"],
jac={"x": np.ones((N, 1)), "y": sparse.spdiags(np.ones(N), 0, N, N)},
)
optProb.addObj("obj")
# Optimizer
opt = OPT(optimizer, options=opt_options)
optProb.printSparsity()
return opt, optProb
def optimize(self, optName, optOptions={}, storeHistory=False, places=5):
# Optimization Object
optProb = Optimization('large and sparse', objfunc)
# Design Variables
optProb.addVar('x', lower=-100, upper=150, value=0)
optProb.addVarGroup('y',
N,
lower=-10 - arange(N),
upper=arange(N),
value=0)
optProb.addVarGroup('z',
2 * N,
upper=arange(2 * N),
lower=-100 - arange(2 * N),
value=0)
# Constraints
optProb.addCon('con1', upper=100, wrt=['x'])
optProb.addCon('con2', upper=100)
optProb.addCon('con3', lower=4, wrt=['x', 'z'])
optProb.addConGroup('lincon',
N,
lower=2 - 3 * arange(N),
linear=True,
wrt=['x', 'y'],
jac={
'x': numpy.ones((N, 1)),
'y': sparse.spdiags(numpy.ones(N), 0, N, N)
})
optProb.addObj('obj')
# Optimizer
try:
opt = OPT(optName, options=optOptions)
except:
raise unittest.SkipTest('Optimizer not available:', optName)
sol = opt(optProb, sens=sens)
# Check Solution
self.assertAlmostEqual(sol.objectives['obj'].value,
10.0,
places=places)
self.assertAlmostEqual(sol.variables['x'][0].value, 2.0, places=places)
def optimize(self, x0, alg='IPOPT', options={}):
opt = {}
opt.update(options)
def objfun(xdict):
x, fail = self.set_vars(xdict)
funcs= {
'obj': self.obj(x),
'llcon': self.lifting_line_const(x),
"wcon": self.enough_lift_const(x)
}
return funcs, fail
optProb = Optimization('llOpt', objfun)
ub = self.get_vars(self.bounds.ub, dic=True)
lb = self.get_vars(self.bounds.lb, dic=True)
x0 = self.get_vars(x0, dic=True)
optProb.addVar('V', upper=ub['V'], lower=lb['V'], value=x0['V'])
optProb.addVar('b', upper=ub['b'], lower=lb['b'], value=x0['b'])
optProb.addVarGroup('c', self.N_th, upper=ub['c'], lower=lb['c'], value=x0['c'])
optProb.addVarGroup('al', self.N_th, upper=ub['al'], lower=lb['al'], value=x0['al'])
optProb.addVarGroup('A', self.N_A, upper=ub['A'], lower=lb['A'], value=x0['A'])
optProb.addObj('obj')
optProb.addConGroup('llcon', self.N_th, lower=0., upper=0.)
optProb.addCon('wcon', lower=0., upper=0.)
if alg== "IPOPT":
opt = OPT(alg, options=options)
sol = opt(optProb, sens='FD')
else:
raise NotImplementedError(f"No routine for algorithm {alg}")
D = dict(
al = [a.value for a in sol.variables['al']],
c = [a.value for a in sol.variables['c']],
A = [a.value for a in sol.variables['A']],
b = sol.variables['b'][0].value,
V = sol.variables['V'][0].value,
)
x = self.set_vars(D)[0]
return x, sol
def setUp(self):
# construct MP
self.MP = multiPointSparse(gcomm)
for setName in SET_NAMES:
comm_size = COMM_SIZES[setName]
self.MP.addProcessorSet(setName,
nMembers=len(comm_size),
memberSizes=comm_size)
self.comm, self.setComm, self.setFlags, self.groupFlags, self.ptID = self.MP.createCommunicators(
)
for setName in SET_NAMES:
self.MP.addProcSetObjFunc(setName, SET_FUNC_HANDLES[setName][0])
self.MP.addProcSetSensFunc(setName, SET_FUNC_HANDLES[setName][1])
# construct optProb
optProb = Optimization("multipoint test", self.MP.obj)
for dv in DVS:
optProb.addVar(dv)
optProb.addObj("total_drag")
self.MP.setObjCon(objCon)
self.MP.setOptProb(optProb)
def large_sparse(optimizer='SNOPT', optOptions=None):
opt_options = {} if optOptions is None else optOptions
# Optimization Object
optProb = Optimization('large and sparse', objfunc)
# Design Variables
optProb.addVar('x', lower=-100, upper=150, value=0)
optProb.addVarGroup('y',
N,
lower=-10 - arange(N),
upper=arange(N),
value=0)
optProb.addVarGroup('z',
2 * N,
upper=arange(2 * N),
lower=-100 - arange(2 * N),
value=0)
# Constraints
optProb.addCon('con1', upper=100, wrt=['x'])
optProb.addCon('con2', upper=100)
optProb.addCon('con3', lower=4, wrt=['x', 'z'])
optProb.addConGroup('lincon',
N,
lower=2 - 3 * arange(N),
linear=True,
wrt=['x', 'y'],
jac={
'x': numpy.ones((N, 1)),
'y': sparse.spdiags(numpy.ones(N), 0, N, N)
})
optProb.addObj('obj')
# Optimizer
opt = OPT(optimizer, options=opt_options)
optProb.printSparsity()
return opt, optProb
def optimize(self, x0, alg='IPOPT', options={}):
opt = {}
opt.update(options)
def objfun(xdict):
V = xdict['V']
b = xdict['b']
c = xdict['c']
al = xdict['al']
A, fail = self.ll(V, b, c, al)
funcs= {
'obj':10000. if fail else self.DoverL(V, b, c, al, A)
}
return funcs, fail
optProb = Optimization('llOpt', objfun)
ub = self.get_vars(self.bounds.ub, dic=True)
lb = self.get_vars(self.bounds.lb, dic=True)
x0 = self.get_vars(x0, dic=True)
optProb.addVar('V', upper=ub['V'], lower=lb['V'], value=x0['V'])
optProb.addVar('b', upper=ub['b'], lower=lb['b'], value=x0['b'])
optProb.addVarGroup('c', self.N_th, upper=ub['c'], lower=lb['c'], value=x0['c'])
optProb.addVarGroup('al', self.N_th, upper=ub['al'], lower=lb['al'], value=x0['al'])
optProb.addObj('obj')
if alg== "IPOPT":
opt = OPT(alg, options=options)
sol = opt(optProb, sens='FD')
else:
raise NotImplementedError(f"No routine for algorithm {alg}")
D = dict(
al = [a.value for a in sol.variables['al']],
c = [a.value for a in sol.variables['c']],
b = sol.variables['b'][0].value,
V = sol.variables['V'][0].value
)
x = self.set_vars(D)[0]
return x, sol
def test_opt(self):
# Instantiate Optimization Problem
optProb = Optimization('Rosenbrock function', objfunc)
optProb.addVar('x', 'c', value=0, lower=-600, upper=600)
optProb.addVar('y', 'c', value=0, lower=-600, upper=600)
optProb.addObj('obj1')
optProb.addObj('obj2')
#300 generations will find x=(0,0), 200 or less will find x=(1,1)
options = {'maxGen': 200}
# Optimizer
try:
opt = NSGA2(options=options)
except:
raise unittest.SkipTest('Optimizer not available:', optName)
sol = opt(optProb)
# Check Solution
self.assertAlmostEqual(sol.variables['x'][0].value, 1.0, places=2)
self.assertAlmostEqual(sol.variables['y'][0].value, 1.0, places=2)
from pyoptsparse import Optimization, NSGA2
def objfunc(xdict):
x = xdict['x']
y = xdict['y']
funcs = {}
funcs['obj1'] = (x - 0.0)**2 + (y - 0.0)**2
funcs['obj2'] = (x - 1.0)**2 + (y - 1.0)**2
fail = False
return funcs, fail
# Instantiate Optimization Problem
optProb = Optimization('Rosenbrock function', objfunc)
optProb.addVar('x', 'c', value=0, lower=-600, upper=600)
optProb.addVar('y', 'c', value=0, lower=-600, upper=600)
optProb.addObj('obj1')
optProb.addObj('obj2')
#300 generations will find x=(0,0), 200 or less will find x=(1,1)
options = {'maxGen': 200}
opt = NSGA2(options=options)
sol = opt(optProb)
print sol
from pyoptsparse import Optimization, NSGA2
def objfunc(xdict):
x = xdict["x"]
y = xdict["y"]
funcs = {}
funcs["obj1"] = (x - 0.0)**2 + (y - 0.0)**2
funcs["obj2"] = (x - 1.0)**2 + (y - 1.0)**2
fail = False
return funcs, fail
# Instantiate Optimization Problem
optProb = Optimization("Rosenbrock function", objfunc)
optProb.addVar("x", "c", value=0, lower=-600, upper=600)
optProb.addVar("y", "c", value=0, lower=-600, upper=600)
optProb.addObj("obj1")
optProb.addObj("obj2")
# 300 generations will find x=(0,0), 200 or less will find x=(1,1)
options = {"maxGen": 200}
opt = NSGA2(options=options)
sol = opt(optProb)
print(sol)
# CL_star
funcs['cl_con_' + fc] = funcs['cl_' + fc] - CL_star[fc]
# end for
return funcs
# =====================================================
# Set-up Optimization Problem
# =====================================================
opt_prob = Optimization('opt', MP.obj, use_groups=True)
# Add Aero Variables
for fc in flowCases:
opt_prob.addVar('alpha_' + fc, value=1.6, lower=0., upper=10., scale=.1)
# Add Geo variables
opt_prob = DVGeo.addVariablesPyOpt(opt_prob)
# Constraints:
for fc in flowCases:
opt_prob.addCon('cl_con_' + fc,
type='i',
lower=0.0,
upper=0.0,
scale=10,
wrt=['geo', 'alpha_' + fc])
# Geometric Constraints
DVCon.addConstraintsPyOpt(opt_prob)
Mach = 0.45
Cl_i = np.array([0.5])
Cl_req = np.asscalar(normalize_y(Cl_i, 0))
x0_t = np.zeros(16)
x0_t[14] = Mach
x0_t = normalize_x(x0_t)
Mach_n = x0_t[0, 14]
low_alpha = None
up_alpha = None
optProb = Optimization('naca4412', objfunc)
optProb.addVarGroup('modes', 14, 'c', lower=None, upper=None, value=.5)
optProb.addVar('alpha', 'c', lower=low_alpha, upper=up_alpha, value=.5)
optProb.addCon('thick_0.1', lower=thickness_constraint[0], upper=None)
optProb.addCon('thick_0.3', lower=thickness_constraint[1], upper=None)
optProb.addCon('thick_0.5', lower=thickness_constraint[2], upper=None)
optProb.addCon('thick_0.7', lower=thickness_constraint[3], upper=None)
optProb.addCon('thick_0.9', lower=thickness_constraint[4], upper=None)
optProb.addCon('Cl', lower=Cl_req, upper=Cl_req)
optProb.addObj('obj')
print(optProb)
#%%
opt = pyoptsparse.SLSQP()
sol = opt(optProb, sens=sens)
print(sol)
class TestOptProb(unittest.TestCase):
tol = 1e-12
def objfunc(self, xdict):
"""
This is a simple quadratic test function with linear constraints.
The actual problem doesn't really matter, since we are not testing optimization,
but just optProb. However, we need to initialize and run an optimization
in order to have optimizer-specific fields in optProb populated, such as
jacIndices.
This problem is probably not feasible, but that's okay.
"""
funcs = {}
funcs["obj_0"] = 0
for x in xdict.keys():
funcs["obj_0"] += np.sum(np.power(xdict[x], 2))
for iCon, nc in enumerate(self.nCon):
conName = "con_{}".format(iCon)
funcs[conName] = np.zeros(nc)
for x in xdict.keys():
for j in range(nc):
funcs[conName][j] = (iCon + 1) * np.sum(xdict[x])
return funcs, False
def setup_optProb(self, nObj=1, nDV=[4], nCon=[2], xScale=[1.0], objScale=[1.0], conScale=[1.0], offset=[0.0]):
"""
This function sets up a general optimization problem, with arbitrary
DVs, constraints and objectives.
Arbitrary scaling for the various parameters can also be specified.
"""
self.nObj = nObj
self.nDV = nDV
self.nCon = nCon
self.xScale = xScale
self.objScale = objScale
self.conScale = conScale
self.offset = offset
# Optimization Object
self.optProb = Optimization("Configurable Test Problem", self.objfunc)
self.x0 = {}
# Design Variables
for iDV in range(len(nDV)):
n = nDV[iDV]
lower = np.random.uniform(-5, 2, n)
upper = np.random.uniform(5, 20, n)
x0 = np.random.uniform(lower, upper)
dvName = "x{}".format(iDV)
self.x0[dvName] = x0
self.optProb.addVarGroup(
dvName,
n,
lower=lower,
upper=upper,
value=x0,
scale=xScale[iDV],
offset=offset[iDV],
)
# Constraints
for iCon in range(len(nCon)):
nc = nCon[iCon]
lower = np.random.uniform(-5, 2, nc)
upper = np.random.uniform(5, 6, nc)
self.optProb.addConGroup(
"con_{}".format(iCon),
nc,
lower=lower,
upper=upper,
scale=conScale[iCon],
)
# Objective
for iObj in range(nObj):
self.optProb.addObj("obj_{}".format(iObj), scale=objScale[iObj])
# Finalize
self.optProb.printSparsity()
# run optimization
# we don't care about outputs, but this performs optimizer-specific re-ordering
# of constraints so we need this to test mappings
opt = OPT("slsqp", options={"IFILE": "optProb_SLSQP.out"})
opt(self.optProb, "FD")
def test_setDV_getDV(self):
"""
We just test that setDV and getDV work, even with scaling
"""
self.setup_optProb(
nObj=1,
nDV=[4, 8],
nCon=[2, 3],
xScale=[4, 1],
objScale=[0.3],
conScale=[0.1, 8],
offset=[3, 7],
)
# test getDV first
x0 = self.optProb.getDVs()
assert_dict_allclose(x0, self.x0)
# now set, get, and compare
newDV = {"x0": np.arange(4), "x1": np.arange(8)}
self.optProb.setDVs(newDV)
outDV = self.optProb.getDVs()
assert_dict_allclose(newDV, outDV)
def test_setDV_VarGroup(self):
"""
Test that setDV works with a subset of VarGroups
"""
self.setup_optProb(
nObj=1,
nDV=[4, 8],
nCon=[2, 3],
xScale=[4, 1],
objScale=[0.3],
conScale=[0.1, 8],
offset=[3, 7],
)
oldDV = self.optProb.getDVs()
# set values for only one VarGroup
newDV = {"x0": np.arange(4)}
self.optProb.setDVs(newDV)
outDV = self.optProb.getDVs()
# check x0 changed
assert_allclose(newDV["x0"], outDV["x0"])
# check x1 is the same
assert_allclose(oldDV["x1"], outDV["x1"])
def test_mappings(self):
"""
This test checks the various mapping and process helper functions
in pyOpt_optimization. In this function we just set up an optimization problem,
and the actual test is done in `map_check_value`.
"""
nDV = [4, 8, 1]
nCon = [2, 3, 1, 1]
self.setup_optProb(
nObj=1,
nDV=nDV,
nCon=nCon,
xScale=[np.random.rand(i) for i in nDV],
objScale=[0.3],
conScale=[np.random.rand(i) for i in nCon],
offset=[np.random.rand(i) * np.arange(i) for i in nDV],
)
# first test X
x = self.optProb.getDVs()
self.map_check_value("X", x)
# next we check the objective
funcs, _ = self.objfunc(x)
obj_funcs = {}
for key in funcs.keys():
if "obj" in key:
obj_funcs[key] = funcs[key]
self.map_check_value("Obj", obj_funcs)
# lastly we check the constraints
funcs, _ = self.objfunc(x)
con_funcs = {}
for key in funcs.keys():
if "con" in key:
con_funcs[key] = funcs[key]
self.map_check_value("Con", con_funcs)
def map_check_value(self, key, val):
"""
This function checks all the mapping and process functions
in both directions, for a given key = {'X', 'Con', 'Obj'}
and val in dictionary format.
"""
# dictionary of function handles to test
map_funcs = {
"X": [self.optProb._mapXtoOpt, self.optProb._mapXtoUser],
"X_Dict": [self.optProb._mapXtoOpt_Dict, self.optProb._mapXtoUser_Dict],
"Con": [self.optProb._mapContoOpt, self.optProb._mapContoUser],
"Con_Dict": [self.optProb._mapContoOpt_Dict, self.optProb._mapContoUser_Dict],
"Obj": [self.optProb._mapObjtoOpt, self.optProb._mapObjtoUser],
"Obj_Dict": [self.optProb._mapObjtoOpt_Dict, self.optProb._mapObjtoUser_Dict],
}
process_funcs = {
"X": {"vec": self.optProb.processXtoVec, "dict": self.optProb.processXtoDict},
"Con": {"vec": self.optProb.processContoVec, "dict": self.optProb.processContoDict},
"Obj": {"vec": self.optProb.processObjtoVec, "dict": self.optProb.processObjtoDict},
}
def processValue(key, val, output):
"""helper function since some functions have optional arguments that are needed"""
if key == "Con":
return process_funcs[key][output](val, scaled=False, natural=True)
elif key == "Obj":
return process_funcs[key][output](val, scaled=False)
else:
return process_funcs[key][output](val)
# test dict to vec mappings
vec = processValue(key, val, "vec")
dictionary = processValue(key, vec, "dict")
assert_dict_allclose(val, dictionary)
# test mappings using dictionaries
val_opt = map_funcs[key + "_Dict"][0](val)
val_user = map_funcs[key + "_Dict"][1](val_opt)
assert_dict_allclose(val_user, val)
assert_dict_not_allclose(val_user, val_opt)
# test mappings using vectors
val = processValue(key, val, "vec")
val_opt = map_funcs[key][0](val)
val_user = map_funcs[key][1](val_opt)
assert_allclose(val_user, val, atol=self.tol, rtol=self.tol)
assert_not_allclose(val_user, val_opt)
# check that the scaling was actually done correctly
# we only check this for the array version because
# it's much simpler
if key == "X":
scale = np.hstack(self.xScale)
offset = np.hstack(self.offset)
assert_allclose(val_opt, (val_user - offset) * scale)
else:
if key == "Obj":
scale = np.hstack(self.objScale)
else:
scale = np.hstack(self.conScale)
assert_allclose(val_opt, val_user * scale)
def test_finalize(self):
"""
Check that multiple finalize calls don't mess up the optProb
"""
self.setup_optProb(nObj=1, nDV=[4, 8], nCon=[2, 3], xScale=[1.0, 1.0], conScale=[1.0, 1.0], offset=[0, 0])
assert_optProb_size(self.optProb, 1, 12, 5)
self.optProb.addObj("obj2")
assert_optProb_size(self.optProb, 2, 12, 5)
self.optProb.addVar("DV2")
assert_optProb_size(self.optProb, 2, 13, 5)
self.optProb.addCon("CON2")
assert_optProb_size(self.optProb, 2, 13, 6)
class TestLarge(OptTest):
name = "large_sparse"
DVs = {"x", "y", "z"}
objs = {"obj"}
cons = {"con1", "con2", "con3"}
xStar = {"x": 2}
fStar = 10.0
def objfunc(self, xdict):
x = xdict["x"]
y = xdict["y"]
z = xdict["z"]
funcs = {}
funcs["obj"] = x**2 + 2 * np.sum(y**2) + 3 * np.sum(z)
funcs["con1"] = x + 1e-3 * abs(x) ** 2.05
funcs["con2"] = x**4 + np.sum(y) + np.sum(z**2)
funcs["con3"] = x + np.sum(z)
return funcs, False
def sens(self, xdict, funcs):
x = xdict["x"]
y = xdict["y"]
z = xdict["z"]
funcsSens = {
"obj": {
"x": 2 * x,
"y": 4 * y,
"z": 3 * np.ones(2 * self.N),
},
"con1": {
"x": 2.05 * x * (x * x) ** 0.025,
},
"con2": {
"x": 4 * x**3,
"y": np.ones(self.N),
"z": 2 * z,
},
"con3": {
"x": 1.0,
"z": np.ones(2 * self.N),
},
}
return funcsSens, False
def setup_optProb(self, sparse=True):
# set N
if sparse:
self.N = 10000
else:
self.N = 500
# Optimization Object
self.optProb = Optimization("large and sparse", self.objfunc, sens=self.sens)
# Design Variables
self.optProb.addVar("x", lower=-100, upper=150, value=0)
self.optProb.addVarGroup("y", self.N, lower=-10 - np.arange(self.N), upper=np.arange(self.N), value=0)
self.optProb.addVarGroup(
"z", 2 * self.N, upper=np.arange(2 * self.N), lower=-100 - np.arange(2 * self.N), value=0
)
# Constraints
self.optProb.addCon("con1", upper=100, wrt=["x"])
self.optProb.addCon("con2", upper=100)
self.optProb.addCon("con3", lower=4, wrt=["x", "z"])
xJac = np.ones((self.N, 1))
if sparse:
rows_cols = np.array([i for i in range(0, self.N)]).astype(int)
yJac = {"coo": [rows_cols, rows_cols, np.ones(self.N)], "shape": [self.N, self.N]}
else:
yJac = np.eye(self.N)
self.optProb.addConGroup(
"lincon",
self.N,
lower=2 - 3 * np.arange(self.N),
linear=True,
wrt=["x", "y"],
jac={"x": xJac, "y": yJac},
)
self.optProb.addObj("obj")
@parameterized.expand(
[
("SNOPT", True),
("IPOPT", True),
("SNOPT", False),
]
)
def test_opt(self, optName, sparse):
self.optName = optName
self.setup_optProb(sparse=sparse)
sol = self.optimize()
self.assert_solution_allclose(sol, 1e-5, partial_x=True)
def test_dense_workspace_too_small(self):
self.optName = "SNOPT"
self.setup_optProb(sparse=False)
optOptions = {"Total real workspace": 401300} # 500 + 200 * (503 + 1501)
sol = self.optimize(optOptions=optOptions)
# Check that the workspace is too small without overwriting the lengths
self.assert_inform_equal(sol, 84)
# dy = float(np.random.rand(1))*dy_start+200.
# offset = float(np.random.rand(1))*25.+10.
# rotate = float(np.random.rand(1))*30.-15.
dx = dx_start
dy = dy_start
offset = offset_start
rotate = rotate_start
input = {'dx':dx,'dy':dy,'offset':offset,'rotate':rotate}
funcs,_ = obj_func_grid(input)
AEPstart = funcs['obj']
print AEPstart
nCalls = 0
"""Optimization"""
optProb = Optimization('Wind_Farm_AEP', obj_func_grid)
optProb.addObj('obj')
optProb.addVar('dx', type='c', lower=0., upper=None, value=dx)
optProb.addVar('dy', type='c', lower=0., upper=None, value=dy)
optProb.addVar('offset', type='c', lower=None, upper=None, value=offset)
optProb.addVar('rotate', type='c', lower=None, upper=None, value=rotate)
num_cons_sep = (nTurbs-1)*nTurbs/2
optProb.addConGroup('sep', num_cons_sep, lower=0., upper=None)
optProb.addConGroup('bound', nTurbs, lower=0., upper=None)
opt = SNOPT()
opt.setOption('Scale option',0)
opt.setOption('Iterations limit',1000000)
opt.setOption('Summary file','summary_grid.out')
opt.setOption('Major optimality tolerance',1.e-5)
opt.setOption('Major feasibility tolerance',1.e-6)
res = opt(optProb)
dx_f = res.xStar['dx']
dy_f = res.xStar['dy']
def optimize(self,
sparse=True,
tol=None,
optOptions={},
storeHistory=False):
# set N
if sparse:
self.N = 50000
else:
self.N = 500
# Optimization Object
optProb = Optimization("large and sparse", self.objfunc)
# Design Variables
optProb.addVar("x", lower=-100, upper=150, value=0)
optProb.addVarGroup("y",
self.N,
lower=-10 - np.arange(self.N),
upper=np.arange(self.N),
value=0)
optProb.addVarGroup("z",
2 * self.N,
upper=np.arange(2 * self.N),
lower=-100 - np.arange(2 * self.N),
value=0)
# Constraints
optProb.addCon("con1", upper=100, wrt=["x"])
optProb.addCon("con2", upper=100)
optProb.addCon("con3", lower=4, wrt=["x", "z"])
xJac = np.ones((self.N, 1))
if sparse:
yJac = scipy.sparse.spdiags(np.ones(self.N), 0, self.N, self.N)
else:
yJac = np.eye(self.N)
optProb.addConGroup(
"lincon",
self.N,
lower=2 - 3 * np.arange(self.N),
linear=True,
wrt=["x", "y"],
jac={
"x": xJac,
"y": yJac
},
)
optProb.addObj("obj")
# Optimizer
try:
opt = SNOPT(options=optOptions)
except Error:
raise unittest.SkipTest("Optimizer not available: SNOPT")
sol = opt(optProb, sens=self.sens)
# Check Solution
if tol is not None:
if opt.version != "7.7.7":
assert_allclose(sol.objectives["obj"].value,
10.0,
atol=tol,
rtol=tol)
else:
assert_allclose(sol.fStar, 10.0, atol=tol, rtol=tol)
assert_allclose(sol.variables["x"][0].value,
2.0,
atol=tol,
rtol=tol)
return sol
