def init_problem(self, n):
print(f"Solving Brachistochrone problem with n = {n}...")
self.n = n
self.x_arr = np.linspace(0, 1, n) # fixed
y_inner = np.linspace(1 - 1 / n, 1 / n,
n - 2) # initial guess of (inner) values
# Optimal/final y points
self.y_arr = np.zeros(n)
self.y_arr[0] = 1.0
# Optimization problem
opt_prob: pyop.Optimization = pyop.Optimization(
'brachistochrone', self.objfunc)
# Design variables
opt_prob.addVarGroup('y', nVars=n-2, type='c', value=y_inner, \
lower=None, upper=None)
# Assign the key value for the objective function
opt_prob.addObj('obj')
# Optimizer
optimizer = pyop.SNOPT()
# optimizer.setOption('iPrint',0)
path = '/home/seth/school/optimization/output/'
# optimizer.setOption('Print file', path+f'SNOPT_print-{n}.out')
# optimizer.setOption('Summary file', path+f'SNOPT_summary-{n}.out')
return opt_prob, optimizer
def init_problem(self):
# Optimization problem
self.opt_prob: pyop.Optimization = pyop.Optimization(
'trusty', self.objfunc)
# Design variables
self.opt_prob.addVarGroup('areas', nVars=10, type='c', value=self.areas, \
lower=0.1, upper=None)
# Constraints
# yield_compression, yield_tension, area_min
stress_yield = np.array([25e3] * 10)
stress_yield[8] = 75e3
self.opt_prob.addConGroup('stress_arr',
nCon=10,
lower=-stress_yield,
upper=stress_yield)
# Assign the key value for the objective function
self.opt_prob.addObj('mass')
self.optimizer = pyop.SNOPT()
self.optimizer.setOption('iPrint', 0)
path = '/home/seth/school/optimization/output/'
self.optimizer.setOption('Print file', path + f'SNOPT_print.out')
self.optimizer.setOption('Summary file', path + f'SNOPT_summary.out')
def optimize_farmcost(*args):
y0 = np.array([9, 10])
funcs, _ = obj_farmcost({"y": y0})
print(f'initial COE: {funcs["coe"]}')
# starting point and bounds
# objective
opt_prob: pyop.Optimization = pyop.Optimization('coe', obj_farmcost)
# linear constraint
# the constraint y3 > y2 can be formulated as a linear constraint.
opt_prob.addVarGroup('y', nVars=2, value=y0, lower=0, upper=10)
opt_prob.addConGroup('y3y2', nCon=1, lower=1e-5)
opt_prob.addObj('coe')
optimizer = pyop.SNOPT()
# deterministic optimization
sol: pyop.pyOpt_solution.Solution = optimizer(opt_prob, sens='FD')
print(f'{sol.fStar.item() = }')
print(f'{sol.xStar["y"] = }')
obj_farmcost(sol.xStar, plotit=False)
upper = [25e3] * 10
upper[8] = 75e3
# set_trace()
# Constraints
optProb.addConGroup('con', 10, lower=lower, upper=upper)
# Objective
optProb.addObj('obj')
# Check optimization problem:
print(optProb)
# Optimizer
optimizer = pyopt.SNOPT()
sol = optimizer(optProb, storeHistory=f"output/opt_histTruss.hst")
# Check Solution
print(sol)
# start = np.ones(10) * 0.1
#
# fit = minimize(solve,
# start,
# method="SLSQP",
# constraints=all_constraints,
# options={'disp':True},
# callback=callback)
#
# #### Output values for debugging
p = np.ones(12) * 1e-4
optProb = pyoptsparse.Optimization('Differential_Flatness', objective)
optProb.addVarGroup('xvars', 12, 'c', lower=None, upper=None, value=p)
eq_bnd = [0.0, 0.0, 0.0, 2.0, 10.0, 0.0, 0.0, 1.0]
optProb.addConGroup('eq_con', 8, lower=eq_bnd, upper=eq_bnd)
if use_gamma:
optProb.addConGroup(
'ineq_con', 400, lower=0.0, upper=None
) # I can get an answer but the constraints are violated and it runs into numerical difficulties
else:
optProb.addConGroup('ineq_con', 200, lower=0.0, upper=None)
optProb.addObj('obj')
opt = pyoptsparse.SNOPT()
sol = opt(optProb, sens='CS', storeHistory='constrained.txt')
data = {
'px': px_list,
'py': py_list,
'x': x_list,
'y': y_list,
'vx': vx_list,
'vy': vy_list,
'ax': ax_list,
'ay': ay_list,
'Jx': Jx_list,
'Jy': Jy_list,
'gam': gam_list,
'gam2': gam2_list,
def Pyoptsparse_Solve(problem,
solver='SNOPT',
FD='single',
sense_step=1.0E-6,
nonderivative_line_search=False):
""" This converts your SUAVE Nexus problem into a PyOptsparse optimization problem and solves it.
Pyoptsparse has many algorithms, they can be switched out by using the solver input.
Assumptions:
None
Source:
N/A
Inputs:
problem [nexus()]
solver [str]
FD (parallel or single) [str]
sense_step [float]
nonderivative_line_search [bool]
Outputs:
outputs [list]
Properties Used:
None
"""
# Have the optimizer call the wrapper
mywrap = lambda x: PyOpt_Problem(problem, x)
inp = problem.optimization_problem.inputs
obj = problem.optimization_problem.objective
con = problem.optimization_problem.constraints
if FD == 'parallel':
from mpi4py import MPI
comm = MPI.COMM_WORLD
myrank = comm.Get_rank()
# Instantiate the problem and set objective
try:
import pyoptsparse as pyOpt
except:
raise ImportError('No version of pyOptsparse found')
opt_prob = pyOpt.Optimization('SUAVE', mywrap)
for ii in range(len(obj)):
opt_prob.addObj(obj[ii, 0])
# Set inputs
nam = inp[:, 0] # Names
ini = inp[:, 1] # Initials
bnd = inp[:, 2] # Bounds
scl = inp[:, 3] # Scale
typ = inp[:, 4] # Type
# Pull out the constraints and scale them
bnd_constraints = help_fun.scale_const_bnds(con)
scaled_constraints = help_fun.scale_const_values(con, bnd_constraints)
x = ini / scl
for ii in range(0, len(inp)):
lbd = (bnd[ii][0] / scl[ii])
ubd = (bnd[ii][1] / scl[ii])
#if typ[ii] == 'continuous':
vartype = 'c'
#if typ[ii] == 'integer':
#vartype = 'i'
opt_prob.addVar(nam[ii], vartype, lower=lbd, upper=ubd, value=x[ii])
# Setup constraints
for ii in range(0, len(con)):
name = con[ii][0]
edge = scaled_constraints[ii]
if con[ii][1] == '<':
opt_prob.addCon(name, upper=edge)
elif con[ii][1] == '>':
opt_prob.addCon(name, lower=edge)
elif con[ii][1] == '=':
opt_prob.addCon(name, lower=edge, upper=edge)
# Finalize problem statement and run
print(opt_prob)
if solver == 'SNOPT':
opt = pyOpt.SNOPT()
CD_step = (sense_step**2.)**(1. / 3.
) #based on SNOPT Manual Recommendations
opt.setOption('Function precision', sense_step**2.)
opt.setOption('Difference interval', sense_step)
opt.setOption('Central difference interval', CD_step)
elif solver == 'SLSQP':
opt = pyOpt.SLSQP()
elif solver == 'FSQP':
opt = pyOpt.FSQP()
elif solver == 'PSQP':
opt = pyOpt.PSQP()
elif solver == 'NSGA2':
opt = pyOpt.NSGA2(pll_type='POA')
elif solver == 'ALPSO':
#opt = pyOpt.pyALPSO.ALPSO(pll_type='DPM') #this requires DPM, which is a parallel implementation
opt = pyOpt.ALPSO()
elif solver == 'CONMIN':
opt = pyOpt.CONMIN()
elif solver == 'IPOPT':
opt = pyOpt.IPOPT()
elif solver == 'NLPQLP':
opt = pyOpt.NLQPQLP()
elif solver == 'NLPY_AUGLAG':
opt = pyOpt.NLPY_AUGLAG()
if nonderivative_line_search == True:
opt.setOption('Nonderivative linesearch')
if FD == 'parallel':
outputs = opt(opt_prob, sens='FD', sensMode='pgc')
elif solver == 'SNOPT' or solver == 'SLSQP':
outputs = opt(opt_prob, sens='FD', sensStep=sense_step)
else:
outputs = opt(opt_prob)
return outputs
subject to mu_CL = 0.5
"""
uq_systemsize = 2
ndv = 5
UQObj = UQOASExample1Opt(uq_systemsize)
collocation_obj = StochasticCollocation(5, "Normal")
collocation_con = collocation_obj
collocation_grad_obj = StochasticCollocation(5,
"Normal",
QoI_dimensions=ndv)
collocation_grad_con = collocation_grad_obj
optProb = pyoptsparse.Optimization('UQ_OASExample1', objfunc)
optProb.addVarGroup('xvars', ndv, 'c', lower=-10., upper=15.)
optProb.addConGroup('con', 1, lower=0.5, upper=0.5)
optProb.addObj('obj')
opt = pyoptsparse.SNOPT(optOptions={'Major feasibility tolerance': 1e-10})
sol = opt(optProb, sens=sens)
# sol = opt(optProb, sens='FD')
# Error Calculation
full_integration_val = 0.03428059998452251
reduced_fval = sol.fStar
err = abs(full_integration_val - reduced_fval)
rel_err = abs((full_integration_val - reduced_fval) / full_integration_val)
print sol
print "integration val = ", sol.fStar
print "error val = ", err
print "rel_err val = ", rel_err
def init_problem(self):
px = np.zeros(6) + 1e-4
py = np.zeros(6) + 1e-4
self.n = 100
self.t = np.linspace(0, 15, self.n)
self.tpos_exp = self.t**np.arange(6).reshape(
6, 1) # exponents for trajectory equation
self.tvel_exp = self.t**np.array([0, 0, 1, 2, 3, 4]).reshape(
6, 1) # exponents for veloc terms
self.tacc_exp = self.t**np.array([0, 0, 0, 1, 2, 3]).reshape(
6, 1) # exponents for accel terms
self.tjerk_exp = self.t**np.array([0, 0, 0, 0, 1, 2]).reshape(
6, 1) # exponents for each jerk term
self.cvel = np.arange(
6, dtype=np.float64) # Constant mulipliers for each velocity term
self.cacc = np.array(
[0, 0, 2, 6, 12, 20],
dtype=np.float64) # Constant mulipliers for each acceleration term
self.cjerk = np.array(
[0, 0, 0, 6, 24, 60],
dtype=np.float64) # Constant multipliers for each jerk term
# Optimization problem
opt_prob: pyop.Optimization = pyop.Optimization(
'differential_flat', self.objfunc)
# Design variables
opt_prob.addVarGroup('px',
nVars=6,
type='c',
value=px,
lower=None,
upper=None)
opt_prob.addVarGroup('py',
nVars=6,
type='c',
value=py,
lower=None,
upper=None)
x0, y0, xf, yf = [0., 0., 10., 0.]
vx0, vy0, vxf, vyf = [0., 2., 0., 1.]
self.L = 1.5 # length of car
gam_max = np.pi / 4
self.vmax_square = 10**2 # vmax = 10 m/s
self.amax_square = 2**2 # amax = 2 m/s**2
#### CONSTRAINTS ####
# start and finish constraints
opt_prob.addConGroup('initial pos',
nCon=2,
lower=[x0, y0],
upper=[x0, y0])
opt_prob.addConGroup('initial vel',
nCon=2,
lower=[vx0, vy0],
upper=[vx0, vy0])
opt_prob.addConGroup('final pos',
nCon=2,
lower=[xf, yf],
upper=[xf, yf])
opt_prob.addConGroup('final vel',
nCon=2,
lower=[vxf, vyf],
upper=[vxf, vyf])
# constraints over entire trajectory
opt_prob.addConGroup('v', nCon=self.n, lower=0, upper=self.vmax_square)
opt_prob.addConGroup('a', nCon=self.n, lower=0, upper=self.amax_square)
# opt_prob.addConGroup('gam_max', nCon=self.n, lower=-gam_max, upper=gam_max)
opt_prob.addConGroup('gam_plus', nCon=self.n, lower=0, upper=None)
opt_prob.addConGroup('gam_minus', nCon=self.n, lower=0, upper=None)
# Assign the key value for the objective function
opt_prob.addObj('obj-min-jerk')
# Optimizer
optimizer = pyop.SNOPT()
# optimizer.setOption('iPrint',0)
# optimizer.setOption('iSumm', 0)
# path = '/home/seth/school/optimization/output/'
# optimizer.setOption('Print file', path+f'SNOPT_print-{n}.out')
# optimizer.setOption('Summary file', path+f'SNOPT_summary-{n}.out')
return opt_prob, optimizer
def __init__(self):
# Plotting histories
p0 = np.zeros(6) + 1e-4
self.n = 100
self.t = np.linspace(0, 15, self.n)
self.tpos_exp = self.t**np.arange(6).reshape(
6, 1) # exponents for trajectory equation
self.tvel_exp = self.t**np.array([0, 0, 1, 2, 3, 4]).reshape(
6, 1) # exponents for veloc terms
self.tacc_exp = self.t**np.array([0, 0, 0, 1, 2, 3]).reshape(
6, 1) # exponents for accel terms
self.tjerk_exp = self.t**np.array([0, 0, 0, 0, 1, 2]).reshape(
6, 1) # exponents for each jerk term
self.cvel = np.arange(
6, dtype=np.float64) # Constant mulipliers for each velocity term
self.cacc = np.array(
[0, 0, 2, 6, 12, 20],
dtype=np.float64) # Constant mulipliers for each acceleration term
self.cjerk = np.array(
[0, 0, 0, 6, 24, 60],
dtype=np.float64) # Constant multipliers for each jerk term
# Optimization problem
opt_prob: pyop.Optimization = pyop.Optimization(
'differential_flat_quad', self.objfunc)
# Design variables
opt_prob.addVarGroup('px',
nVars=6,
type='c',
value=p0,
lower=None,
upper=None)
opt_prob.addVarGroup('py',
nVars=6,
type='c',
value=p0,
lower=None,
upper=None)
opt_prob.addVarGroup('pz',
nVars=6,
type='c',
value=p0,
lower=None,
upper=None)
opt_prob.addVarGroup('ps',
nVars=6,
type='c',
value=p0,
lower=None,
upper=None)
# ENU
# [ x, y, z, psi ]
pos0 = np.array([0., 0., 0., 0.])
posf = np.array([0., 10., 10., 0.])
vel0 = np.array([0., 2., 2., 0.])
velf = np.array([0., 2., 0., 0.])
# x0, y0, z0, psi0 = [0., 0., 0., 0.]
# xf, yf, zf, psif = [0., 10., 10., 0.]
# vx0, vy0, vz0, w0 = [0., 2., 2., 0.]
# vxf, vyf, vzf, wf = [0., 2., 0., 0.]
self.L = 1.5 # length of car
gam_max = np.pi / 4
self.vmax_square = 10**2 # vmax = 10 m/s
self.amax_square = 2**2 # amax = 2 m/s**2
#### CONSTRAINTS ####
# start and finish constraints
opt_prob.addConGroup('initial pos', nCon=4, lower=pos0, upper=pos0)
opt_prob.addConGroup('initial vel', nCon=4, lower=vel0, upper=vel0)
opt_prob.addConGroup('final pos', nCon=4, lower=posf, upper=posf)
opt_prob.addConGroup('final vel', nCon=4, lower=velf, upper=velf)
# constraints over entire trajectory
# opt_prob.addConGroup('v', nCon=self.n, lower=0, upper=self.vmax_square)
# opt_prob.addConGroup('a', nCon=self.n, lower=0, upper=self.amax_square)
# opt_prob.addConGroup('gam_max', nCon=self.n, lower=-gam_max, upper=gam_max)
# opt_prob.addConGroup('gam_plus', nCon=self.n, lower=0, upper=None)
# opt_prob.addConGroup('gam_minus', nCon=self.n, lower=0, upper=None)
# Assign the key value for the objective function
opt_prob.addObj('obj-min-jerk')
# Optimizer
optimizer = pyop.SNOPT()
# optimizer.setOption('iPrint',0)
# optimizer.setOption('iSumm', 0)
path = '/home/seth/school/optimization/output/'
optimizer.setOption('Print file', path + f'SNOPT-hw5.out')
optimizer.setOption('Summary file', path + f'SNOPT-hw5-summary.out')
self.opt_prob: pyop.Optimization = opt_prob
self.optimizer: pyop.SNOPT = optimizer
upper=0.01, scale=1.e3, value=sc_sol_dict[dict_val]['thickness_cp'])
optProb.addVar('sweep', lower=10., upper=30., value=sc_sol_dict[dict_val]['sweep'])
optProb.addVar('alpha', lower=-10., upper=10., value=sc_sol_dict[dict_val]['alpha'])
# Constraints
optProb.addConGroup('con_failure', 1, upper=0.)
optProb.addConGroup('con_L_equals_W', 1, lower=0., upper=0.)
optProb.addConGroup('con_thickness_intersects', n_thickness_intersects,
upper=0., wrt=['thickness_cp'])
optProb.addConGroup('con_CM', n_CM, lower=-0.001, upper=0.001)
optProb.addConGroup('con_twist_cp', 3, lower=np.array([-1e20, -1e20, 5.]),
upper=np.array([1e20, 1e20, 5.]), wrt=['twist_cp'])
# Objective
optProb.addObj('obj', scale=1.e-1)
opt = pyoptsparse.SNOPT(options = {'Major feasibility tolerance' : 1e-9,
'Verify level' : -1})
sol = opt(optProb, sens=sens_uq)
end_time = time.time()
elapsed_time = end_time - start_time
print(sol)
print(sol.fStar)
print()
print("twist = ", UQObj.QoI.p['oas_scaneagle.wing.geometry.twist'])
print("thickness =", UQObj.QoI.p['oas_scaneagle.wing.thickness'])
print('\nthickness_cp = ', UQObj.QoI.p['oas_scaneagle.wing.thickness_cp'])
print('twist_cp = ', UQObj.QoI.p['oas_scaneagle.wing.twist_cp'])
print("sweep = ", UQObj.QoI.p['oas_scaneagle.wing.sweep'])
print("aoa = ", UQObj.QoI.p['oas_scaneagle.alpha'])
print()
conval = [0] * 2
conval[0] = x[0] + 2. * x[1] + 2. * x[2] - 72.0
conval[1] = -x[0] - 2. * x[1] - 2. * x[2]
funcs['con'] = conval
fail = False
return funcs, fail
optProb: pyop.Optimization = pyop.Optimization('TP037', objfunc)
# Design variables - can be created individually or as a group
optProb.addVarGroup('xvars',
nVars=3,
type='c',
lower=[0, 0, 0],
upper=[42, 42, 42],
value=10)
# Constraints - also individually or group
optProb.addConGroup('con', nCon=2, lower=None, upper=0.0)
optProb.addObj('obj')
print(optProb)
opt = pyop.SNOPT()
opt.setOption('iPrint', 0)
opt.setOption('iSumm', 0)
sol = opt(optProb, sens='FD')
print(sol)