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
# load parameter name and range
pf = util.read_param_file('%s.txt' % modelname)
bd = np.array(pf['bounds'])
nInput = pf['num_vars']
nOutput = 2
xlb = bd[:, 0]
xub = bd[:, 1]
# parameters for NSGA2
pop = 100
gen = 100
# run NSGA2
bestx, besty, x, y = \
NSGA2.optimization(model, nInput, nOutput, xlb, xub, pop, gen)
# plot results
plt.plot(y[:, 0], y[:, 1], 'b.', label='evaluated points')
plt.plot(besty[:, 0], besty[:, 1], 'r.', label='NSGA2 optimal')
model_true = __import__(modelname + '_true')
y_true = model_true.pareto()
plt.plot(y_true[:, 0], y_true[:, 1], 'k-', label='True Pareto')
plt.xlabel('y1')
plt.ylabel('y2')
plt.legend()
# save figure
plt.savefig('%s/ZDT1_NSGA2.png' % respath)