def onestep(nInput,
xlb,
xub,
Xinit,
Yinit,
ngs=None,
maxn=3000,
kstop=10,
pcento=0.1,
peps=0.001):
"""
Adaptive Surrogate Modelling-based Optimization
One-step mode for offline optimization
Do NOT call the model evaluation function
nInput: number of model input
xlb: lower bound of input
xub: upper bound of input
Xinit/Yinit: initial samplers for surrogate model construction
ngs: number of complexes (sub-populations)
kstop: maximum number of evolution loops before convergency
pcento: the percentage change allowed in kstop loops before convergency
peps: minimum range of parameter
maxn: number of maximum model runs - surrogate model
"""
x = Xinit.copy()
y = Yinit.copy()
sm = gp.GPR_Matern(x, y, nInput, 1, x.shape[0], xlb, xub)
bestx_sm, bestf_sm, icall_sm, nloop_sm, \
bestx_list_sm, bestf_list_sm, icall_list_sm = \
SCEUA.optimization(sm, nInput, xlb, xub,
ngs, maxn, kstop, pcento, peps, verbose = False)
x_resample = bestx_sm.copy()
return x_resample
def onestep(nInput, nOutput, xlb, xub, dft, pct, \
Xinit, Yinit, pop = 100, gen = 100, \
crossover_rate = 0.9, mu = 20, mum = 20, weight = 0.001):
''' Weighted Multi-Objective Adaptive Surrogate Modelling-based Optimization
One-step mode for offline optimization
Do NOT call the model evaluation function
nInput: number of model input
nOutput: number of output objectives
xlb: lower bound of input
xub: upper bound of input
dft: default point to constrained the objective space,
objective value simulated by default parameters
(dimension equals to nOutput, this is the reference point in MO-ASMO paper)
pct: percentage of resampled points in each iteration
Xinit and Yinit: initial samplers for surrogate model construction
### options for the embedded WNSGA-II of WMO-ASMO
pop: number of population
gen: number of generation
crossover_rate: ratio of crossover in each generation
mu: distribution index for crossover
mum: distribution index for mutation
weight: assign weight factor if one objective is worse than the dft point
'''
N_resample = int(pop*pct)
Ninit = Xinit.shape[0]
x = Xinit.copy()
y = Yinit.copy()
sm = gp.GPR_Matern(x, y, nInput, nOutput, x.shape[0], xlb, xub)
bestx_sm, besty_sm, x_sm, y_sm = \
WNSGA2.optimization(sm, nInput, nOutput, xlb, xub, dft, \
pop, gen, crossover_rate, mu, mum, weight)
D = WNSGA2.weighted_crowding_distance(besty_sm, dft, weight)
idxr = D.argsort()[::-1][:N_resample]
x_resample = bestx_sm[idxr,:]
return x_resample
def onestep(nInput, nOutput, xlb, xub, pct, \
Xinit, Yinit, pop = 100, gen = 100, \
crossover_rate = 0.9, mu = 20, mum = 20):
"""
Multi-Objective Adaptive Surrogate Modelling-based Optimization
One-step mode for offline optimization
Do NOT call the model evaluation function
nInput: number of model input
nOutput: number of output objectives
xlb: lower bound of input
xub: upper bound of input
pct: percentage of resampled points in each iteration
Xinit and Yinit: initial samplers for surrogate model construction
### options for the embedded NSGA-II of MO-ASMO
pop: number of population
gen: number of generation
crossover_rate: ratio of crossover in each generation
mu: distribution index for crossover
mum: distribution index for mutation
"""
N_resample = int(pop * pct)
x = Xinit.copy()
y = Yinit.copy()
sm = gp.GPR_Matern(x, y, nInput, nOutput, x.shape[0], xlb, xub)
bestx_sm, besty_sm, x_sm, y_sm = \
NSGA2.optimization(sm, nInput, nOutput, xlb, xub, \
pop, gen, crossover_rate, mu, mum)
D = NSGA2.crowding_distance(besty_sm)
idxr = D.argsort()[::-1][:N_resample]
x_resample = bestx_sm[idxr, :]
return x_resample
def optimization(model, nInput, nOutput, xlb, xub, niter, pct, \
Xinit = None, Yinit = None, pop = 100, gen = 100, \
crossover_rate = 0.9, mu = 20, mum = 20):
"""
Multi-Objective Adaptive Surrogate Modelling-based Optimization
model: the evaluated model function
nInput: number of model input
nOutput: number of output objectives
xlb: lower bound of input
xub: upper bound of input
niter: number of iteration
pct: percentage of resampled points in each iteration
Xinit and Yinit: initial samplers for surrogate model construction
### options for the embedded NSGA-II of MO-ASMO
pop: number of population
gen: number of generation
crossover_rate: ratio of crossover in each generation
mu: distribution index for crossover
mum: distribution index for mutation
"""
N_resample = int(pop * pct)
if (Xinit is None and Yinit is None):
Ninit = nInput * 10
Xinit = sampling.glp(Ninit, nInput)
for i in range(Ninit):
Xinit[i, :] = Xinit[i, :] * (xub - xlb) + xlb
Yinit = np.zeros((Ninit, nOutput))
for i in range(Ninit):
Yinit[i, :] = model.evaluate(Xinit[i, :])
else:
Ninit = Xinit.shape[0]
icall = Ninit
x = Xinit.copy()
y = Yinit.copy()
for i in range(niter):
print('Surrogate Opt loop: %d' % i)
sm = gp.GPR_Matern(x, y, nInput, nOutput, x.shape[0], xlb, xub)
bestx_sm, besty_sm, x_sm, y_sm = \
NSGA2.optimization(sm, nInput, nOutput, xlb, xub, \
pop, gen, crossover_rate, mu, mum)
D = NSGA2.crowding_distance(besty_sm)
idxr = D.argsort()[::-1][:N_resample]
x_resample = bestx_sm[idxr, :]
y_resample = np.zeros((N_resample, nOutput))
for j in range(N_resample):
y_resample[j, :] = model.evaluate(x_resample[j, :])
icall += N_resample
x = np.vstack((x, x_resample))
y = np.vstack((y, y_resample))
xtmp = x.copy()
ytmp = y.copy()
xtmp, ytmp, rank, crowd = NSGA2.sortMO(xtmp, ytmp, nInput, nOutput)
idxp = (rank == 0)
bestx = xtmp[idxp, :]
besty = ytmp[idxp, :]
return bestx, besty, x, y
def optimization(model,
nInput,
xlb,
xub,
niter,
Xinit=None,
Yinit=None,
ngs=None,
maxn=3000,
kstop=10,
pcento=0.1,
peps=0.001):
"""
Adaptive Surrogate Modelling-based Optimization
model: the evaluated model function
nInput: number of model input
xlb: lower bound of input
xub: upper bound of input
niter: number of total iteration
Xinit/Yinit: initial samplers for surrogate model construction
ngs: number of complexes (sub-populations)
kstop: maximum number of evolution loops before convergency
pcento: the percentage change allowed in kstop loops before convergency
peps: minimum range of parameter
maxn: number of maximum model runs - surrogate model
"""
if (Xinit is None and Yinit is None):
Ninit = nInput * 10
Xinit = sampling.glp(Ninit, nInput)
for i in range(Ninit):
Xinit[i, :] = Xinit[i, :] * (xub - xlb) + xlb
Yinit = np.zeros(Ninit)
for i in range(Ninit):
Yinit[i] = model.evaluate(Xinit[i, :])
else:
Ninit = Xinit.shape[0]
icall = Ninit
x = Xinit.copy()
y = Yinit.copy()
bestf = np.inf
for i in range(niter):
print('Surrogate Opt loop: %d' % i)
sm = gp.GPR_Matern(x, y, nInput, 1, x.shape[0], xlb, xub)
bestx_sm, bestf_sm, icall_sm, nloop_sm, \
bestx_list_sm, bestf_list_sm, icall_list_sm = \
SCEUA.optimization(sm, nInput, xlb, xub,
ngs, maxn, kstop, pcento, peps, verbose = False)
bestx_tmp = bestx_sm.copy()
bestf_tmp = model.evaluate(bestx_tmp)
icall += 1
x = np.vstack((x, bestx_tmp))
y = np.append(y, bestf_tmp)
if bestf_tmp < bestf:
bestf = bestf_tmp
bestx = bestx_tmp
return bestx, bestf, x, y
def optimization(model, nInput, nOutput, xlb, xub, dft, niter, pct, \
Xinit = None, Yinit = None, pop = 100, gen = 100, \
crossover_rate = 0.9, mu = 20, mum = 20, weight = 0.001):
''' Weighted Multi-Objective Adaptive Surrogate Modelling-based Optimization
model: the evaluated model function
nInput: number of model input
nOutput: number of output objectives
xlb: lower bound of input
xub: upper bound of input
dft: default point to constrained the objective space,
objective value simulated by default parameters
(dimension equals to nOutput, this is the reference point in MO-ASMO paper)
niter: number of iteration
pct: percentage of resampled points in each iteration
Xinit and Yinit: initial samplers for surrogate model construction
### options for the embedded WNSGA-II of WMO-ASMO
pop: number of population
gen: number of generation
crossover_rate: ratio of crossover in each generation
mu: distribution index for crossover
mum: distribution index for mutation
weight: assign weight factor if one objective is worse than the dft point
'''
N_resample = int(pop*pct)
if (Xinit is None and Yinit is None):
Ninit = nInput * 10
Xinit = sampling.glp(Ninit, nInput)
for i in range(Ninit):
Xinit[i,:] = Xinit[i,:] * (xub - xlb) + xlb
Yinit = np.zeros((Ninit, nOutput))
for i in range(Ninit):
Yinit[i,:] = model.evaluate(Xinit[i,:])
else:
Ninit = Xinit.shape[0]
icall = Ninit
x = Xinit.copy()
y = Yinit.copy()
for i in range(niter):
print('Surrogate Opt loop: %d' % i)
sm = gp.GPR_Matern(x, y, nInput, nOutput, x.shape[0], xlb, xub)
bestx_sm, besty_sm, x_sm, y_sm = \
WNSGA2.optimization(sm, nInput, nOutput, xlb, xub, dft, \
pop, gen, crossover_rate, mu, mum, weight)
D = WNSGA2.weighted_crowding_distance(besty_sm, dft, weight)
idxr = D.argsort()[::-1][:N_resample]
x_resample = bestx_sm[idxr,:]
y_resample = np.zeros((N_resample,nOutput))
for j in range(N_resample):
y_resample[j,:] = model.evaluate(x_resample[j,:])
icall += N_resample
x = np.vstack((x, x_resample))
y = np.vstack((y, y_resample))
xtmp = x.copy()
ytmp = y.copy()
xtmp, ytmp, rank, crowd = WNSGA2.sortMO_W(xtmp, ytmp, nInput, nOutput, dft, weight)
bestx = []
besty = []
for i in range(ytmp.shape[0]):
if rank[i] == 0 and sum(ytmp[i,:] < dft) == nOutput:
bestx.append(xtmp[i,:])
besty.append(ytmp[i,:])
bestx = np.array(bestx)
besty = np.array(besty)
#idxp = (rank == 0)
#bestx = xtmp[idxp,:]
#besty = ytmp[idxp,:]
return bestx, besty, x, y