def construct_krig(X, y, g, lb, ub):
# Define input for constraint Kriging
KrigConstInfo = initkriginfo()
KrigConstInfo['X'] = X
KrigConstInfo['y'] = g.reshape(-1,1) # should be in shape (n,1)
KrigConstInfo['problem'] = exp_const_eval
KrigConstInfo["nrestart"] = 5
KrigConstInfo["ub"] = ub
KrigConstInfo["lb"] = lb
KrigConstInfo["optimizer"] = "lbfgsb"
KrigConstInfo['limittype'] = '>=' # value of the expensive constraints should be more than equal 7.7
KrigConstInfo['limit'] = 7.7
# Define input for first objective Kriging
KrigInfo1 = initkriginfo()
KrigInfo1["X"] = X
KrigInfo1["y"] = y[:,0].reshape(-1,1)
KrigInfo1["problem"] = cust_func
KrigInfo1["nrestart"] = 5
KrigInfo1["ub"] = ub
KrigInfo1["lb"] = lb
KrigInfo1["optimizer"] = "lbfgsb"
# Define input for second objective Kriging
KrigInfo2 = deepcopy(KrigInfo1)
KrigInfo2['y'] = y[:,1].reshape(-1,1)
# Run Kriging
krigobj1 = Kriging(KrigInfo1, standardization=True, standtype='default', normy=False, trainvar=False)
krigobj1.train(parallel=False)
loocverr1, _ = krigobj1.loocvcalc()
krigobj2 = Kriging(KrigInfo2, standardization=True, standtype='default', normy=False, trainvar=False)
krigobj2.train(parallel=False)
loocverr2, _ = krigobj2.loocvcalc()
krigconst = Kriging(KrigConstInfo, standardization=True, standtype='default', normy=False, trainvar=False)
krigconst.train(parallel=False)
loocverrConst, _ = krigconst.loocvcalc()
print('LOOCV 1: ', loocverr1)
print('LOOCV 2: ', loocverr2)
print('LOOCV Constraint: ', loocverrConst)
# List of Kriging objects, objective and constraints should be separated
kriglist = [krigobj1, krigobj2]
expconstlist = [krigconst]
return kriglist, expconstlist
def generate_krig(lb, ub, n_krigsamp, nvar, problem, n_cpu):
init_krigsamp = mcpopgen(lb=lb, ub=ub, ndim=2, n_order=1, n_coeff=3)
print("Evaluating Kriging Sample")
ykrig = problem(init_krigsamp)
print(np.count_nonzero(ykrig <= 0))
# Set Kriging Info
KrigInfo = initkriginfo(1)
KrigInfo["X"] = init_krigsamp
KrigInfo["y"] = ykrig
KrigInfo["nvar"] = nvar
KrigInfo["nsamp"] = n_krigsamp
KrigInfo["nrestart"] = 5
KrigInfo["ub"] = ub
KrigInfo["lb"] = lb
KrigInfo["nkernel"] = len(KrigInfo["kernel"])
KrigInfo["optimizer"] = "lbfgsb"
#trainkrig
drm = None
t = time.time()
krigobj = Kriging(KrigInfo,
standardization=True,
standtype='default',
normy=False,
trainvar=False)
krigobj.train(n_cpu=n_cpu)
loocverr, _ = krigobj.loocvcalc()
elapsed = time.time() - t
print("elapsed time to train Kriging model: ", elapsed, "s")
print("LOOCV error of Kriging model: ", loocverr, "%")
return krigobj, loocverr, drm
def generate_kriging(n_cpu):
# Initialization
KrigInfo = dict()
kernel = ["gaussian"]
# Sampling
nsample = 40
nvar = 2
ub = np.array([5, 5])
lb = np.array([-5, -5])
nup = 3
sampoption = "halton"
samplenorm, sample = sampling(sampoption,
nvar,
nsample,
result="real",
upbound=ub,
lobound=lb)
X = sample
# Evaluate sample
y1 = evaluate(X, "styblinski")
# Initialize KrigInfo
KrigInfo = initkriginfo()
# Set KrigInfo
KrigInfo["X"] = X
KrigInfo["y"] = y1
KrigInfo["nvar"] = nvar
KrigInfo["problem"] = "styblinski"
KrigInfo["nsamp"] = nsample
KrigInfo["nrestart"] = 7
KrigInfo["ub"] = ub
KrigInfo["lb"] = lb
KrigInfo["kernel"] = kernel
KrigInfo["TrendOrder"] = 0
KrigInfo["nugget"] = -6
# KrigInfo["n_princomp"] = 1
KrigInfo["kernel"] = ["gaussian"]
KrigInfo["nkernel"] = len(KrigInfo["kernel"])
KrigInfo["optimizer"] = "lbfgsb"
# Run Kriging
t = time.time()
krigobj = Kriging(KrigInfo,
standardization=True,
standtype="default",
normy=False,
trainvar=False)
krigobj.train(n_cpu=n_cpu)
loocverr, _ = krigobj.loocvcalc()
elapsed = time.time() - t
print("elapsed time for train Kriging model: ", elapsed, "s")
print("LOOCV error of Kriging model: ", loocverr, "%")
return krigobj
def generate_kriging(n_cpu):
# Sampling
nsample = 20
nvar = 2
nobj = 2
lb = -1 * np.ones(shape=[nvar])
ub = 1 * np.ones(shape=[nvar])
sampoption = "halton"
samplenorm, sample = sampling(sampoption,
nvar,
nsample,
result="real",
upbound=ub,
lobound=lb)
X = sample
# Evaluate sample
global y
y = myproblem(X)
# Initialize KrigInfo
KrigInfo1 = initkriginfo()
# Set KrigInfo
KrigInfo1["X"] = X
KrigInfo1["y"] = y[:, 0].reshape(-1, 1)
KrigInfo1["problem"] = myproblem
KrigInfo1["nrestart"] = 5
KrigInfo1["ub"] = ub
KrigInfo1["lb"] = lb
KrigInfo1["optimizer"] = "lbfgsb"
# Initialize KrigInfo
KrigInfo2 = deepcopy(KrigInfo1)
KrigInfo2['y'] = y[:, 1].reshape(-1, 1)
# Run Kriging
krigobj1 = Kriging(KrigInfo1,
standardization=True,
standtype='default',
normy=False,
trainvar=False)
krigobj1.train(n_cpu=n_cpu)
loocverr1, _ = krigobj1.loocvcalc()
print("LOOCV error of Kriging model: ", loocverr1, "%")
krigobj2 = Kriging(KrigInfo2,
standardization=True,
standtype='default',
normy=False,
trainvar=False)
krigobj2.train(n_cpu=n_cpu)
loocverr2, _ = krigobj2.loocvcalc()
print("LOOCV error of Kriging model: ", loocverr2, "%")
return krigobj1, krigobj2
def generate_krig(init_samp, n_krigsamp, nvar, problem):
# Kriging Sample
t1 = time.time()
init_krigsamp = mcpopgen(type="lognormal",
ndim=nvar,
n_order=1,
n_coeff=5,
stddev=0.2,
mean=1)
ykrig = evaluate(init_krigsamp, type=problem)
t2 = time.time()
print("50 samp eval", t2 - t1)
# Evaluate Kriging Sample and calculate PoF real
init_samp_G = evaluate(init_samp, type=problem)
total_samp = np.hstack((init_samp, init_samp_G)).transpose()
positive_samp = total_samp[:, total_samp[nvar] >= 0]
positive_samp = positive_samp.transpose()
nsamp = np.size(init_samp, 0)
npos = np.size(positive_samp, 0)
Pfreal = 1 - npos / nsamp
lb = np.floor(np.min(init_samp)) * np.ones(shape=[nvar])
ub = np.ceil(np.max(init_samp)) * np.ones(shape=[nvar])
# Set Kriging Info
KrigInfo = initkriginfo("single")
KrigInfo["X"] = init_krigsamp
KrigInfo["y"] = ykrig
KrigInfo["nvar"] = nvar
KrigInfo["nsamp"] = n_krigsamp
KrigInfo["nrestart"] = 5
KrigInfo["ub"] = ub
KrigInfo["lb"] = lb
KrigInfo["nkernel"] = len(KrigInfo["kernel"])
KrigInfo["n_princomp"] = 4
KrigInfo["optimizer"] = "lbfgsb"
#trainkrig
t = time.time()
krigobj = KPLS(KrigInfo,
standardization=True,
standtype='default',
normy=False,
trainvar=False)
krigobj.train(parallel=False)
loocverr, _ = krigobj.loocvcalc()
elapsed = time.time() - t
print("elapsed time for train Kriging model: ", elapsed, "s")
print("LOOCV error of Kriging model: ", loocverr, "%")
return krigobj, Pfreal
def generate_krig(init_samp, krigsamp, nvar, problem):
# Monte Carlo Sampling
t1 = time.time()
init_krigsamp = krigsamp
n_krigsamp = np.size(krigsamp, 0)
ykrig = evaluate(init_krigsamp, type=problem)
t2 = time.time()
init_samp_G = evaluate(init_samp, type=problem)
total_samp = np.hstack((init_samp, init_samp_G)).transpose()
positive_samp = total_samp[:, total_samp[nvar] >= 0]
positive_samp = positive_samp.transpose()
nsamp = np.size(init_samp, 0)
npos = np.size(positive_samp, 0)
Pfreal = 1 - npos / nsamp
lb = np.floor(np.min(init_samp)) * np.ones(shape=[nvar])
ub = np.ceil(np.max(init_samp)) * np.ones(shape=[nvar])
# Set Kriging Info
KrigInfo = initkriginfo("single")
KrigInfo["X"] = init_krigsamp
KrigInfo["y"] = ykrig
KrigInfo["nvar"] = nvar
KrigInfo["nsamp"] = n_krigsamp
KrigInfo["nrestart"] = 5
KrigInfo["ub"] = ub
KrigInfo["lb"] = lb
KrigInfo["nkernel"] = len(KrigInfo["kernel"])
KrigInfo["optimizer"] = "lbfgsb"
#trainkrig
t = time.time()
krigobj = Kriging(KrigInfo,
standardization=True,
standtype='default',
normy=False,
trainvar=False)
krigobj.train(parallel=False)
loocverr, _ = krigobj.loocvcalc()
elapsed = time.time() - t
print("elapsed time for train Kriging model: ", elapsed, "s")
print("LOOCV error of Kriging model: ", loocverr, "%")
return krigobj, Pfreal
def generate_krig(init_samp, n_krigsamp, nvar, problem, n_cpu):
init_krigsamp = mcpopgen(type="lognormal",
ndim=nvar,
n_order=1,
n_coeff=5,
stddev=0.2,
mean=1)
print("Evaluating Kriging Sample")
ykrig = evaluate(init_krigsamp, type=problem)
print(np.count_nonzero(ykrig <= 0))
lb = (np.min(init_samp, axis=0))
ub = (np.max(init_samp, axis=0))
Pfreal = None
# Set Kriging Info
KrigInfo = initkriginfo(1)
KrigInfo["X"] = init_krigsamp
KrigInfo["y"] = ykrig
KrigInfo["nvar"] = nvar
KrigInfo["nsamp"] = n_krigsamp
KrigInfo["nrestart"] = 5
KrigInfo["ub"] = ub
KrigInfo["lb"] = lb
KrigInfo["nkernel"] = len(KrigInfo["kernel"])
KrigInfo["n_princomp"] = 4
KrigInfo["optimizer"] = "lbfgsb"
#trainkrig
drm = None
t = time.time()
krigobj = KPLS(KrigInfo,
standardization=True,
standtype='default',
normy=False,
trainvar=False)
krigobj.train(n_cpu=n_cpu)
loocverr, _ = krigobj.loocvcalc()
elapsed = time.time() - t
print("elapsed time to train Kriging model: ", elapsed, "s")
print("LOOCV error of Kriging model: ", loocverr, "%")
return krigobj, loocverr, drm
def generate_kriging(n_cpu):
# Sampling
nsample = 10
nvar = 2
lb = np.array([-5, -5])
ub = np.array([5, 5])
sampoption = "halton"
samplenorm, sample = sampling(sampoption,
nvar,
nsample,
result="real",
upbound=ub,
lobound=lb)
X = sample
# Evaluate sample
# global y
y = evaluate(X, "styblinski")
# Initialize KrigInfo
# global KrigInfo
KrigInfo = initkriginfo()
# Set KrigInfo
KrigInfo["X"] = X
KrigInfo["y"] = y
KrigInfo["problem"] = "styblinski"
KrigInfo["nrestart"] = 5
KrigInfo["ub"] = ub
KrigInfo["lb"] = lb
KrigInfo["optimizer"] = "lbfgsb"
# Run Kriging
krigobj = Kriging(KrigInfo,
standardization=True,
standtype='default',
normy=False,
trainvar=False)
krigobj.train(n_cpu=n_cpu)
loocverr, _ = krigobj.loocvcalc()
print("LOOCV error of Kriging model: ", loocverr, "%")
return krigobj
def create_krig(self, obj_krig_map=None, con_krig_map=None, n_cpu=1):
"""Initialise and train Kriging models.
Default settings for the objective or constraint Krigings can
be overidden by setting the obj_krig_map or con_krig_map dict.
The dictionary should take the form:
e.g.
map = {'default': {'nrestart': 5,
'optimizer': 'lbfgsb',
},
'CD': {'optimizer': 'cobyla',
},
'CL': {'nrestart': 10,
'limittype': '>=',
'limit': 0.15},
},
}
-where the dict key is used to identify the objective or
constraint by label (int, if no explicit x_label and y_label set
previously). The subdict key-value pairs are set in each
surrogate_models.supports.initinfo.initkriginfo('single'). The
'default' dict is applied first and can be overridden by the
following dictionaries.
Args:
obj_krig_map (dict(dict()), optional): Map specific settings
onto objective Kriging models via the labels.
con_krig_map (dict(dict()), optional): Map specific settings
onto constraint Kriging models via the labels.
n_cpu (int, optional): If > 1, uses parallel processing.
Defaults to 1.
"""
def apply_krig_map(krig_info, map, label):
"""Helper func. Apply 'default' dict, then labeled dict"""
if 'default' in map:
for k, v in map['default'].items():
print(f"Setting {label} Kriging defaults '{k}': {v}")
krig_info[k] = v
if label in map:
for k, v in map[label].items():
print(f"Setting {label} Kriging '{k}': {v}")
krig_info[k] = v
# Set up Kriging for each objective
obj_infos = []
for i in range(self.n_obj):
krig_multi_info = initkriginfo()
krig_multi_info["X"] = self.X
krig_multi_info["y"] = self.y[:, i].reshape(-1, 1)
krig_multi_info["ub"] = self.ub
krig_multi_info["lb"] = self.lb
label = self.y_labels[i]
if obj_krig_map is not None:
apply_krig_map(krig_multi_info, obj_krig_map, label)
obj_infos.append(krig_multi_info)
# Set up Kriging for each constraint
con_infos = []
for i in range(self.n_con):
krig_multi_info = initkriginfo()
krig_multi_info["X"] = self.X
krig_multi_info["y"] = self.g[:, i].reshape(-1, 1)
krig_multi_info["ub"] = self.ub
krig_multi_info["lb"] = self.lb
label = self.g_labels[i]
if con_krig_map is not None:
apply_krig_map(krig_multi_info, con_krig_map, label)
con_infos.append(krig_multi_info)
# Train Kriging models
start_total_train = time.time()
for i, krig_info in enumerate(obj_infos):
krig_obj = Kriging(krig_info, standardization=True,
standtype='default', normy=False,
trainvar=False)
start_train = time.time()
krig_obj.train(n_cpu=n_cpu)
t = time.time() - start_train
print(f'{self.y_labels[i]} training time: {t:.2f} seconds')
loocve, _ = krig_obj.loocvcalc()
print(f'Objective {self.y_labels[i]} LOOCVE: {loocve}')
self.obj_krig.append(krig_obj)
self.obj_loocve.append(loocve)
self.obj_time.append(t)
for i, krig_info in enumerate(con_infos):
krig_con = Kriging(krig_info, standardization=True,
standtype='default', normy=False,
trainvar=False)
start_train = time.time()
t = time.time() - start_train
print(f'{self.y_labels[i]} training time: {t:.2f} seconds')
krig_con.train(n_cpu=n_cpu)
loocve, _ = krig_con.loocvcalc()
print(f'Constraint {self.g_labels[i]} LOOCVE: {loocve}')
self.con_krig.append(krig_con)
self.con_loocve.append(loocve)
self.con_time.append(t)
elapsed = time.time() - start_total_train
print(f'Total training time: {elapsed:.2f} seconds')
# Save data for summary
self.total_train_time = elapsed
self.obj_krig_map = obj_krig_map
self.con_krig_map = con_krig_map