def solveOpt(int_domain, J, a, model, u0, sign): ''' INPUT: int_domain = J = a = model = u0 = sign = OUTPUT: opt_prob = ''' def objfun(u, **kwargs): '''objfun defines optimization problem using the pyOpt sintax''' # 1) extract paraeters int_domain = kwargs['int_domain'] J = kwargs['J'] x = kwargs['a'] model = kwargs['model'] sign = kwargs['sign'] # 2) define objective function and constraints funz = np.trapz(x=int_domain, y=J * model.pf(int_domain, u, x)) g = [] fail = 0 return sign * funz, g, fail opt_prob = Optimization('ODAA problem', objfun) opt_prob.addObj('funz') solver = SLSQP() # choose the solver solver.setOption('IPRINT', -1) opt_prob.addVar('u', 'c', lower=-1, upper=1, value=u0) #print opt_prob # print optimization problem solver(opt_prob, int_domain=int_domain, J=J, a=a, model=model, sign=sign) #print opt_prob.solution(0) # print solution return opt_prob
def solveOpt(int_domain,J,x,model,u0): def objfun(u,**kwargs): # 1) extract paraeters int_domain = kwargs['int_domain'] J = kwargs['J'] x = kwargs['x'] model = kwargs['model'] # 2) define objective function f = np.trapz(int_domain,J * model.pf(int_domain,u,x)) g = [0]*2 # 3) budget constraint g[1] = u.sum() - 1 # 4) VaR constarint W = model.W sigmaMax = model.VaR / norm.ppf(1-model.alpha) g[0] = -sigmaMax + np.sqrt(W.dot(u).dot(u)) fail = 0 return f,g,fail opt_prob = Optimization('test problem',objfun) opt_prob.addObj('f') opt_prob.addCon('budget const','e') opt_prob.addCon('VaR const','i') opt_prob.addVarGroup('u',model.M,'c',lower=np.zeros(model.M), upper=np.ones(model.M),value=u0) print opt_prob slsqp = SLSQP() slsqp.setOption('IPRINT',-1) slsqp(opt_prob,sens_type='FD',int_domain=int_domain,J=J,x=x,model=model) print opt_prob.solution(0)
def solveOpt(int_domain, J, a, model, u0, sign): ''' INPUT: int_domain = J = a = model = u0 = sign = OUTPUT: opt_prob = ''' def objfun(u, **kwargs): '''objfun defines the objective function and the constraints (equality and inequality) of the optiization problem''' # 1) extract paraeters int_domain = kwargs['int_domain'] J = kwargs['J'] x = kwargs['a'] model = kwargs['model'] sign = kwargs['sign'] # 2) define objective function funz = np.trapz(x=int_domain, y=J * model.pf(int_domain, u, x)) g = [0] * 2 # 3) budget constraint g[0] = u.sum() - 1 # 4) VaR constarint W = model.W sigmaMax = model.VaR / norm.ppf(1 - model.alpha) g[1] = -sigmaMax + np.sqrt(W.dot(u).dot(u)) fail = 0 return sign * funz, g, fail opt_prob = Optimization('ODAA problem', objfun) opt_prob.addObj('funz') opt_prob.addCon('budget const', 'e') opt_prob.addCon('VaR const', 'i') slsqp = SLSQP() # instantiate Optimizer slsqp.setOption('IPRINT', -1) opt_prob.addVarGroup('u', model.M, 'c', lower=np.zeros(model.M), upper=np.ones(model.M), value=u0) #print opt_prob # print optimization problem slsqp(opt_prob, sens_type='FD', int_domain=int_domain, J=J, a=a, model=model, sign=sign) #print opt_prob.solution(0) # print solution return opt_prob
g[1] = 2 - x[1] fail = 0 return f,g,fail # ============================================================================= # # ============================================================================= # Instanciate Optimization Problem opt_prob = Optimization('TOY Constraint Problem',objfunc) opt_prob.addVar('x1','c',value=1.0,lower=0.0,upper=10.0) opt_prob.addVar('x2','c',value=1.0,lower=0.0,upper=10.0) opt_prob.addObj('f') opt_prob.addCon('g1','i') opt_prob.addCon('g2','i') print opt_prob # Instanciate Optimizer (ALPSO) & Solve Problem Storing History slsqp = SLSQP() slsqp.setOption('IFILE','slsqp1.out') slsqp(opt_prob,store_hst=True) print opt_prob.solution(0) # Solve Problem Using Stored History (Warm Start) slsqp.setOption('IFILE','slsqp2.out') slsqp(opt_prob, store_hst=True, hot_start='slsqp1') print opt_prob.solution(1)
f = a1 * (x[1] - x[0]**2.)**2. + (a2 - x[0])**2. g = [0.0] * 2 g[0] = x[0]**2. + x[1]**2.0 - a3 fail = 0 return f, g, fail # ============================================================================= # # ============================================================================= # Instantiate Optimization Problem opt_prob = Optimization('Rosenbrock Constrained Problem', objfunc) opt_prob.addVar('x1', 'c', lower=0.0, upper=1.0, value=0.5) opt_prob.addVar('x2', 'c', lower=0.0, upper=1.0, value=0.5) opt_prob.addObj('f') opt_prob.addCon('g1', 'i') print opt_prob # Arguments to pass into objfunc a1 = 100.0 a2 = 1.0 a3 = 1.0 # Instantiate Optimizer (SLSQP) & Solve Problem slsqp = SLSQP() slsqp.setOption('IPRINT', -1) slsqp(opt_prob, sens_type='FD', a12=[a1, a2], a3=a3) print opt_prob.solution(0)
def main(): ########################################### # Define some values ########################################### n_blades = 2 n_elements = 10 radius = unit_conversion.in2m(9.6) / 2 root_cutout = 0.1 * radius dy = float(radius - root_cutout) / n_elements dr = float(1) / n_elements y = root_cutout + dy * np.arange(1, n_elements + 1) r = y / radius pitch = 0.0 airfoils = (('SDA1075_494p', 0.0, 1.0), ) allowable_Re = [ 1000000., 500000., 250000., 100000., 90000., 80000., 70000., 60000., 50000., 40000., 30000., 20000., 10000. ] vehicle_weight = 12.455 max_chord = 0.3 max_chord_tip = 5. alt = 0 tip_loss = True mach_corr = False # Forward flight parameters v_inf = 4. # m/s alpha0 = 0.0454 # Starting guess for trimmed alpha in radians n_azi_elements = 5 # Mission times time_in_hover = 300. # Time in seconds time_in_ff = 500. mission_time = [time_in_hover, time_in_ff] Cl_tables = {} Cd_tables = {} Clmax = {} # Get lookup tables if any(airfoil[0] != 'simple' for airfoil in airfoils): for airfoil in airfoils: Cl_table, Cd_table, Clmax = aero_coeffs.create_Cl_Cd_table( airfoil[0]) Cl_tables[airfoil[0]] = Cl_table Cd_tables[airfoil[0]] = Cd_table Clmax[airfoil[0]] = Clmax # Create list of Cl functions. One for each Reynolds number. Cl_tables (and Cd_tables) will be empty for the # 'simple' case, therefore this will be skipped for the simple case. For the full table lookup case this will be # skipped because allowable_Re will be empty. Cl_funs = {} Cd_funs = {} lift_curve_info_dict = {} if Cl_tables and allowable_Re: Cl_funs = dict( zip(allowable_Re, [ aero_coeffs.get_Cl_fun(Re, Cl_tables[airfoils[0][0]], Clmax[airfoils[0][0]][Re]) for Re in allowable_Re ])) Cd_funs = dict( zip(allowable_Re, [ aero_coeffs.get_Cd_fun(Re, Cd_tables[airfoils[0][0]]) for Re in allowable_Re ])) lift_curve_info_dict = aero_coeffs.create_liftCurveInfoDict( allowable_Re, Cl_tables[airfoils[0][0]]) ########################################### # Set design variable bounds ########################################### # Hover opt 500 gen, 1000 pop, 12.455 N weight, 9.6 in prop chord = np.array([ 0.11923604, 0.2168746, 0.31540216, 0.39822882, 0.42919, 0.35039799, 0.3457828, 0.28567224, 0.23418368, 0.13502483 ]) twist = np.array([ 0.45316866, 0.38457724, 0.38225075, 0.34671967, 0.33151445, 0.28719111, 0.25679667, 0.25099005, 0.19400679, 0.10926302 ]) omega = 3811.03596674 * 2 * np.pi / 60 original = (omega, chord, twist) dtwist = np.array( [twist[i + 1] - twist[i] for i in xrange(len(twist) - 1)]) dchord = np.array( [chord[i + 1] - chord[i] for i in xrange(len(chord) - 1)]) twist0 = twist[0] chord0 = chord[0] omega_start = omega dtwist_start = dtwist dchord_start = dchord twist0_start = twist0 chord0_start = chord0 omega_lower = 2000 * 2 * np.pi / 60 omega_upper = 8000.0 * 2 * np.pi / 60 twist0_lower = 0. * 2 * np.pi / 360 twist0_upper = 60. * 2 * np.pi / 360 chord0_upper = 0.1198 chord0_lower = 0.05 dtwist_lower = -10.0 * 2 * np.pi / 360 dtwist_upper = 10.0 * 2 * np.pi / 360 dchord_lower = -0.1 dchord_upper = 0.1 opt_prob = Optimization('Mission Simulator', objfun) opt_prob.addVar('omega_h', 'c', value=omega_start, lower=omega_lower, upper=omega_upper) opt_prob.addVar('twist0', 'c', value=twist0_start, lower=twist0_lower, upper=twist0_upper) opt_prob.addVar('chord0', 'c', value=chord0_start, lower=chord0_lower, upper=chord0_upper) opt_prob.addVarGroup('dtwist', n_elements - 1, 'c', value=dtwist_start, lower=dtwist_lower, upper=dtwist_upper) opt_prob.addVarGroup('dchord', n_elements - 1, 'c', value=dchord_start, lower=dchord_lower, upper=dchord_upper) opt_prob.addObj('f') opt_prob.addCon('thrust', 'i') opt_prob.addCon('c_tip', 'i') opt_prob.addConGroup('c_lower', n_elements, 'i') opt_prob.addConGroup('c_upper', n_elements, 'i') print opt_prob slsqp = SLSQP() slsqp.setOption('IPRINT', 1) slsqp.setOption('MAXIT', 1000) slsqp.setOption('ACC', 1e-8) fstr, xstr, inform = slsqp(opt_prob, sens_type='FD', n_blades=n_blades, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch, airfoils=airfoils, vehicle_weight=vehicle_weight, max_chord=max_chord, tip_loss=tip_loss, mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs, Cl_tables=Cl_tables, Cd_tables=Cd_tables, allowable_Re=allowable_Re, alt=alt, v_inf=v_inf, alpha0=alpha0, mission_time=mission_time, n_azi_elements=n_azi_elements, lift_curve_info_dict=lift_curve_info_dict, max_chord_tip=max_chord_tip) print opt_prob.solution(0) # pop_size = 300 # max_gen = 500 # opt_method = 'nograd' # nsga2 = NSGA2() # nsga2.setOption('PrintOut', 2) # nsga2.setOption('PopSize', pop_size) # nsga2.setOption('maxGen', max_gen) # nsga2.setOption('pCross_real', 0.85) # nsga2.setOption('xinit', 1) # fstr, xstr, inform = nsga2(opt_prob, n_blades=n_blades, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch, # airfoils=airfoils, vehicle_weight=vehicle_weight, max_chord=max_chord, tip_loss=tip_loss, # mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs, Cl_tables=Cl_tables, # Cd_tables=Cd_tables, allowable_Re=allowable_Re, opt_method=opt_method, alt=alt, # v_inf=v_inf, alpha0=alpha0, mission_time=mission_time, n_azi_elements=n_azi_elements, # pop_size=pop_size, max_gen=max_gen, lift_curve_info_dict=lift_curve_info_dict, # max_chord_tip=max_chord_tip) # print opt_prob.solution(0) # opt_method = 'nograd' # xstart_alpso = np.concatenate((np.array([omega_start, twist0_start, chord0_start]), dtwist_start, dchord_start)) # alpso = ALPSO() # alpso.setOption('xinit', 0) # alpso.setOption('SwarmSize', 200) # alpso.setOption('maxOuterIter', 100) # alpso.setOption('stopCriteria', 0) # fstr, xstr, inform = alpso(opt_prob, xstart=xstart_alpso, n_blades=n_blades, n_elements=n_elements, # root_cutout=root_cutout, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch, # airfoils=airfoils, thrust=thrust, max_chord=max_chord, tip_loss=tip_loss, # mach_corr=mach_corr, Cl_funs=Cl_funs, Cd_funs=Cd_funs, Cl_tables=Cl_tables, # Cd_tables=Cd_tables, allowable_Re=allowable_Re, opt_method=opt_method) # print opt_prob.solution(0) def get_performance(o, c, t): chord_meters = c * radius prop = propeller.Propeller(t, chord_meters, radius, n_blades, r, y, dr, dy, airfoils=airfoils, Cl_tables=Cl_tables, Cd_tables=Cd_tables) quad = quadrotor.Quadrotor(prop, vehicle_weight) ff_kwargs = { 'propeller': prop, 'pitch': pitch, 'n_azi_elements': n_azi_elements, 'allowable_Re': allowable_Re, 'Cl_funs': Cl_funs, 'Cd_funs': Cd_funs, 'tip_loss': tip_loss, 'mach_corr': mach_corr, 'alt': alt, 'lift_curve_info_dict': lift_curve_info_dict } trim0 = np.array([alpha0, o]) alpha_trim, omega_trim, converged = trim.trim(quad, v_inf, trim0, ff_kwargs) T_ff, H_ff, P_ff = bemt.bemt_forward_flight( quad, pitch, omega_trim, alpha_trim, v_inf, n_azi_elements, alt=alt, tip_loss=tip_loss, mach_corr=mach_corr, allowable_Re=allowable_Re, Cl_funs=Cl_funs, Cd_funs=Cd_funs, lift_curve_info_dict=lift_curve_info_dict) dT_h, P_h = bemt.bemt_axial(prop, pitch, o, allowable_Re=allowable_Re, Cl_funs=Cl_funs, Cd_funs=Cd_funs, tip_loss=tip_loss, mach_corr=mach_corr, alt=alt) return sum(dT_h), P_h, T_ff, P_ff, alpha_trim, omega_trim omega = xstr[0] twist0 = xstr[1] chord0 = xstr[2] dtwist = xstr[3:3 + len(r) - 1] dchord = xstr[3 + len(r) - 1:] twist = calc_twist_dist(twist0, dtwist) chord = calc_chord_dist(chord0, dchord) print "chord = " + repr(chord) print "twist = " + repr(twist) # twist_base = calc_twist_dist(twist0_base, dtwist_base) # chord_base = calc_chord_dist(chord0_base, dchord_base) perf_opt = get_performance(omega, chord, twist) perf_orig = get_performance(original[0], original[1], original[2]) print "omega_orig = " + str(original[0]) print "Hover Thrust of original = " + str(perf_orig[0]) print "Hover Power of original = " + str(perf_orig[1]) print "FF Thrust of original = " + str(perf_orig[2]) print "FF Power of original = " + str(perf_orig[3]) print "Trim original (alpha, omega) = (%f, %f)" % (perf_orig[4], perf_orig[5]) print "omega = " + str(omega * 60 / 2 / np.pi) print "Hover Thrust of optimized = " + str(perf_opt[0]) print "Hover Power of optimized = " + str(perf_opt[1]) print "FF Thrust of optimized = " + str(perf_opt[2]) print "FF Power of optimized = " + str(perf_opt[3]) print "Trim optimized (alpha, omega) = (%f, %f)" % (perf_opt[4], perf_opt[5]) # print "Omega base = " + str(omega_start*60/2/np.pi) # print "Thrust of base = " + str(sum(perf_base[0])) # print "Power of base = " + str(sum(perf_base[1])) # plt.figure(1) plt.plot(r, original[1], '-b') plt.plot(r, chord, '-r') plt.xlabel('radial location') plt.ylabel('c/R') plt.legend(['start', 'opt']) plt.figure(2) plt.plot(r, original[2] * 180 / np.pi, '-b') plt.plot(r, twist * 180 / np.pi, '-r') plt.xlabel('radial location') plt.ylabel('twist') plt.legend(['start', 'opt']) plt.show()
g[1] = 2 - x[1] fail = 0 return f,g,fail # ============================================================================= # # ============================================================================= # Instanciate Optimization Problem opt_prob = Optimization('TOY Constrained Problem',objfunc) opt_prob.addVar('x1','c',value=1.0,lower=0.0,upper=10.0) opt_prob.addVar('x2','c',value=1.0,lower=0.0,upper=10.0) opt_prob.addObj('f') opt_prob.addCon('g1','i') opt_prob.addCon('g2','i') print(opt_prob) # Instanciate Optimizer (SLSQP) & Solve Problem Storing History slsqp = SLSQP() slsqp.setOption('IFILE','slsqp1.out') slsqp(opt_prob,store_hst=True) print(opt_prob.solution(0)) # Solve Problem Using Stored History (Warm Start) slsqp.setOption('IFILE','slsqp2.out') slsqp(opt_prob, store_hst=True, hot_start='slsqp1') print(opt_prob.solution(1))
def optimizeTrajectory(self, plot_func=None): # use non-linear optimization to find parameters for minimal # condition number trajectory self.plot_func = plot_func if self.config['showOptimizationGraph']: self.initGraph() ## describe optimization problem with pyOpt classes from pyOpt import Optimization from pyOpt import ALPSO, SLSQP # Instanciate Optimization Problem opt_prob = Optimization('Trajectory optimization', self.objective_func) opt_prob.addObj('f') # add variables, define bounds # w_f - pulsation opt_prob.addVar('wf', 'c', value=self.wf_init, lower=self.wf_min, upper=self.wf_max) # q - offsets for i in range(self.dofs): opt_prob.addVar('q_%d'%i,'c', value=self.qinit[i], lower=self.qmin[i], upper=self.qmax[i]) # a, b - sin/cos params for i in range(self.dofs): for j in range(self.nf[0]): opt_prob.addVar('a{}_{}'.format(i,j), 'c', value=self.ainit[i][j], lower=self.amin, upper=self.amax) for i in range(self.dofs): for j in range(self.nf[0]): opt_prob.addVar('b{}_{}'.format(i,j), 'c', value=self.binit[i][j], lower=self.bmin, upper=self.bmax) # add constraint vars (constraint functions are in obfunc) if self.config['minVelocityConstraint']: opt_prob.addConGroup('g', self.dofs*5, 'i') else: opt_prob.addConGroup('g', self.dofs*4, 'i') #print opt_prob initial = [v.value for v in list(opt_prob._variables.values())] if self.config['useGlobalOptimization']: ### optimize using pyOpt (global) opt = ALPSO() #augmented lagrange particle swarm optimization opt.setOption('stopCriteria', 0) opt.setOption('maxInnerIter', 3) opt.setOption('maxOuterIter', self.config['globalOptIterations']) opt.setOption('printInnerIters', 1) opt.setOption('printOuterIters', 1) opt.setOption('SwarmSize', 30) opt.setOption('xinit', 1) #TODO: how to properly limit max number of function calls? # no. func calls = (SwarmSize * inner) * outer + SwarmSize self.iter_max = opt.getOption('SwarmSize') * opt.getOption('maxInnerIter') * opt.getOption('maxOuterIter') + opt.getOption('SwarmSize') # run fist (global) optimization try: #reuse history opt(opt_prob, store_hst=False, hot_start=True, xstart=initial) except NameError: opt(opt_prob, store_hst=False, xstart=initial) print(opt_prob.solution(0)) ### pyOpt local # after using global optimization, get more exact solution with # gradient based method init optimizer (only local) opt2 = SLSQP() #sequential least squares opt2.setOption('MAXIT', self.config['localOptIterations']) if self.config['verbose']: opt2.setOption('IPRINT', 0) # TODO: amount of function calls depends on amount of variables and iterations to approximate gradient # iterations are probably steps along the gradient. How to get proper no. of func calls? self.iter_max = "(unknown)" if self.config['useGlobalOptimization']: if self.last_best_sol is not None: #use best constrained solution for i in range(len(opt_prob._variables)): opt_prob._variables[i].value = self.last_best_sol[i] else: #reuse previous solution for i in range(len(opt_prob._variables)): opt_prob._variables[i].value = opt_prob.solution(0).getVar(i).value opt2(opt_prob, store_hst=False, sens_step=0.1) else: try: #reuse history opt2(opt_prob, store_hst=True, hot_start=True, sens_step=0.1) except NameError: opt2(opt_prob, store_hst=True, sens_step=0.1) local_sol = opt_prob.solution(0) if not self.config['useGlobalOptimization']: print(local_sol) local_sol_vec = np.array([local_sol.getVar(x).value for x in range(0,len(local_sol._variables))]) if self.last_best_sol is not None: local_sol_vec = self.last_best_sol print("using last best constrained solution instead of given solver solution.") sol_wf, sol_q, sol_a, sol_b = self.vecToParams(local_sol_vec) print("testing final solution") self.iter_cnt = 0 self.objective_func(local_sol_vec) print("\n") self.trajectory.initWithParams(sol_a, sol_b, sol_q, self.nf, sol_wf) if self.config['showOptimizationGraph']: plt.ioff() return self.trajectory
fail = 0 return f,g, fail # ============================================================================= # # ============================================================================= # Instantiate Optimization Problem opt_prob = Optimization('TP37 Constraint Problem',objfunc) opt_prob.addVar('x1','c',lower=0.0,upper=42.0,value=10.0) opt_prob.addVar('x2','c',lower=0.0,upper=42.0,value=10.0) opt_prob.addVar('x3','c',lower=0.0,upper=42.0,value=10.0) opt_prob.addObj('f') opt_prob.addCon('g1','i') opt_prob.addCon('g2','i') # Instantiate Optimizer (SLSQP) slsqp = SLSQP() slsqp.setOption('IPRINT',-1) # Solve Problem (Without Parallel Gradient) slsqp(opt_prob,sens_type='CS') if myrank == 0: print opt_prob.solution(0) #end # Solve Problem (With Parallel Gradient) slsqp(opt_prob,sens_type='CS',sens_mode='pgc') print opt_prob.solution(1)
for i in range(1, len(CONS_LHS_MIN_1_php) + 1): x_value = 'x' + str(i) opt_prob.addVar(x_value, 'c', lower=float(CONS_LHS_MIN_1_php[i - 1]), upper=float(CONS_RHS_MAX_1_php[i - 1]), value=1) opt_prob.addObj('f') for i in range(1, len(NUTRIENTS_php) * 2 + 1): g_value = 'g' + str(i) opt_prob.addCon(g_value, 'i') # Instantiate Optimizer (SLSQP) slsqp = SLSQP() slsqp.setOption('IPRINT', 2) # Solve Problem (Without Parallel Gradient) [fstr, xstr, inform] = slsqp(opt_prob, sens_type='CS') if myrank == 0: sol = opt_prob.solution(0) #end xstr_array = [] for element in xstr: element = decimal.Decimal(element) xstr_array.append(round(element, 4)) results_vector = [] results_vector.append(xstr_array)
design_problem = PyOptOptimization(dp.comm, dp.eval_objcon, dp.eval_objcon_grad, number_of_steps=3) opt_prob = Optimization('crm_togw', design_problem.eval_obj_con) opt_prob.addObj('TOGW') opt_prob.addCon('cruise_lift', type='e') opt_prob.addCon('maneuver_lift', type='e') opt_prob.addCon('area', type='e') opt_prob.addCon('ksfailure', type='i') for i in range(187 - 3): opt_prob.addCon('Smoothness %i a' % i, type='i') opt_prob.addCon('Smoothness %i b' % i, type='i') variables = dp.model.get_variables() for i, var in enumerate(variables): print('i', i) opt_prob.addVar(var.name, type='c', value=var.value / dp.var_scale[i], lower=var.lower / dp.var_scale[i], upper=var.upper / dp.var_scale[i]) opt = SLSQP(pll_type='POA') opt.setOption('MAXIT', 999) opt(opt_prob, sens_type=design_problem.eval_obj_con_grad, disp_opts=True)
opt_prob = Optimization('Aerothermoelasticity', design_problem.eval_obj_con) opt_prob.addObj('Average Temperature') opt_prob.addVar('x1', type='c', value=t0, lower=0.1, upper=1.0) opt_prob.addVar('x2', type='c', value=t0, lower=0.1, upper=1.0) opt_prob.addVar('x3', type='c', value=t0, lower=0.1, upper=1.0) opt_prob.addCon('maximum mass', type='i', lower=-np.inf, upper=np.inf, equal=0.0) if 'verify' in sys.argv: x0 = np.array([t], TransferScheme.dtype) f0, c0, fail = dp.eval_obj(x0) g, A, fail = dp.eval_obj_grad(x0, f0, c0) for dh in [1e-6, 5e-7, 1e-7, 5e-8, 1e-8]: x = x0 + dh f1, c1, fail = dp.eval_obj(x) fd = (c1[0] - c0[0])/dh rel_err = (fd - A[0,0])/fd print('Finite-difference interval: %25.15e'%(dh)) print('Finite-difference value: %25.15e'%(fd)) print('Gradient value: %25.15e'%(A[0,0])) print('Relative error: %25.15e'%(rel_err)) else: opt = SLSQP(pll_type='POA') opt.setOption('ACC',1e-10) # Set optimization tolerance to 1e-5 (default 1e-6) opt.setOption('MAXIT', 999) opt(opt_prob, sens_type=design_problem.eval_obj_con_grad, disp_opts=True) print('FINISHED')
def optimize_twist(**k): omega = k['omega'] omega_lower = k['omega_lower'] omega_upper = k['omega_upper'] twist0 = k['twist0'] twist0_lower = k['twist0_lower'] twist0_upper = k['twist0_upper'] n_elements = k['n_elements'] dtwist = k['dtwist'] dtwist_lower = k['dtwist_lower'] dtwist_upper = k['dtwist_upper'] opt_prob_fc = Optimization('Rotor in Hover w/ Fixed Chord', objfun_optimize_twist) opt_prob_fc.addVar('omega', 'c', value=omega, lower=omega_lower, upper=omega_upper) opt_prob_fc.addVar('twist0', 'c', value=twist0, lower=twist0_lower, upper=twist0_upper) opt_prob_fc.addVarGroup('dtwist', n_elements - 1, 'c', value=dtwist, lower=dtwist_lower, upper=dtwist_upper) opt_prob_fc.addObj('f') opt_prob_fc.addCon('thrust', 'i') n_blades = k['n_blades'] root_cutout = k['root_cutout'] radius = k['radius'] dy = k['dy'] dr = k['dr'] y = k['y'] r = k['r'] pitch = k['pitch'] airfoils = k['airfoils'] thrust = k['thrust'] chord = k['chord'] allowable_Re = k['allowable_Re'] Cl_tables = k['Cl_tables'] Cd_tables = k['Cd_tables'] Cl_funs = k['Cl_funs'] Cd_funs = k['Cd_funs'] tip_loss = k['tip_loss'] mach_corr = k['mach_corr'] alt = k['alt'] # Routine for optimizing twist with a constant chord slsqp2 = SLSQP() slsqp2.setOption('IPRINT', 1) slsqp2.setOption('MAXIT', 200) slsqp2.setOption('ACC', 1e-7) fstr, xstr, inform = slsqp2(opt_prob_fc, sens_type='FD', n_blades=n_blades, n_elements=n_elements, root_cutout=root_cutout, radius=radius, dy=dy, dr=dr, y=y, r=r, pitch=pitch, airfoils=airfoils, thrust=thrust, tip_loss=tip_loss, mach_corr=mach_corr, omega=omega, chord=chord, allowable_Re=allowable_Re, Cl_tables=Cl_tables, Cd_tables=Cd_tables, Cl_funs=Cl_funs, Cd_funs=Cd_funs, alt=alt) return fstr, xstr
class SLSQP_pyOpt(Algorithm): """ Utilization of the SLSQP algorithm of pyOpt package.""" def __init__(self): """Initialize the SLSQP algorithm for a specific building. """ print("Initializing the SLSQP Optimizer...") self.opt_prob = [] self.opt = [] self.building = Building() def configure(self, building): # Get building and optimization setup properties self.building = deepcopy(building) self.T, self.states, self.actions, self.disturbances, self.controlLim, self.actionLim, self.comfort, self.occ, self.nvars, self.ncons = self.building.getConfiguration( ) # Define Box Constraints (min/max values) for the control parameters boxConstraints = [] for ii in range(self.nvars): boxConstraints.append(self.controlLim) # Link to the python function calculating the cost and the constraints self.opt_prob = Optimization('SLSQP Constrained Problem', self.wrapSimulation) # Setupt Box Constrains in pyOpt for ii in range(self.nvars): self.opt_prob.addVar('x' + str(ii + 1), 'c', lower=boxConstraints[ii][0], upper=boxConstraints[ii][1], value=self.building.policy[0, ii]) # Setupt Cost Function in pyOpt self.opt_prob.addObj('f') # Setupt Inequality Constraints in pyOpt for ii in range(self.ncons): self.opt_prob.addCon('g' + str(ii + 1), 'i') # Print the Optimization setup print("----------------------------------------") print("----------------------------------------") print("SLSQP Optimization setup:") print(self.opt_prob) def optimize(self, options=[]): # Set SLSQP as the optimizer self.opt = SLSQP() # Set optimization options if (len(options) > 0): for ii in range(len(options)): self.opt.setOption(options.keys()[ii], options.values()[ii]) # Print the Optimizer Options print("----------------------------------------") print("----------------------------------------") print("SLSQP Optimizer options:") print(self.opt.options) # Get optimized controller self.opt(self.opt_prob, sens_step=1e-6) print(self.opt_prob.solution(0)) a = self.opt_prob.solution(0) for ii in range(self.building.policy.shape[1]): self.building.policy[0, ii] = a.getVar(ii).value return self.building.policy def wrapSimulation(self, policy): """A function that runs a building simulation and wraps the results in the format required by PyOpt library. Args: policy (numpy array): the controller to be used for the simulation Returns: f (float): the cost function value g (list): the vales of all constraints fail (0/1): indicates if the function finished successfully """ # Cost and Constraints f = 0 g = [] fail = 0 # Run building simulation x, cost, constraints = self.building.simulate(policy) f = np.sum(cost) g.append(np.sum(constraints)) # print(f) # print(g[0]) return f, g, fail
class GP_SS(Algorithm): """ Implementation of Building Identification and Control using Gaussian Process State-Space models. A GP regression model per state is created and then the constrained optimization problem is solved using PyOpt's SLSQP solver.""" def __init__(self): """Initialize the GP_SS algorithm for a specific building. """ print("Initializing the GP_SS...") self.building = Building() self.X = [] self.Y = [] self.dynModels = [] # Number of Initial Exploration Simulation self.initExploration = 36 # Number of Samples for witching to Sparse Gaussian Processes self.num_inducing = 2000 # Safety constraint for exploration self.explorationConstraint = 0.03 # Needed to determine the best controller out of all iterations self.costs = [] self.constraints = [] self.policies = [] self.baseline = [] def configure(self, building): # Get building and optimization setup properties self.building = deepcopy(building) self.T, self.states, self.actions, self.disturbances, self.controlLim, self.actionLim, self.comfort, self.occ, self.nvars, self.ncons = self.building.getConfiguration( ) # Run initial random simulations and contstruct initial dataset for ii in range(0, self.initExploration): self.building.rand = 1 xa, cf, cc = self.building.simulate(self.building.policy) xx = xa[0:-1, ] yy = xa[1:, self.states] if (ii == 0): self.X = xx self.Y = yy else: self.X = np.concatenate((self.X, xx), axis=0) self.Y = np.concatenate((self.Y, yy), axis=0) # Last simulation is the baseline controller self.building.rand = 0 xa, cf, cc = self.building.simulate(self.building.policy) self.baseline.append(self.building.policy) self.baseline.append(np.sum(cf)) self.baseline.append(np.sum(cc)) xx = xa[0:-1, ] yy = xa[1:, self.states] self.X = np.concatenate((self.X, xx), axis=0) self.Y = np.concatenate((self.Y, yy), axis=0) def optimize(self, options): # Set max number of optimization iterations maxIter = 1 if (len(options) > 0): maxIter = options["MAXIT"] # Log costs and constraints for all internal iterations self.costs = np.zeros((maxIter + 1, 1)) self.constraints = np.zeros((maxIter + 1, self.ncons)) self.policies = np.zeros((maxIter + 1, self.nvars)) # GP_SS process initPolicy = self.building.policy.copy() for ii in range(maxIter): # Train GP state-space models kernel = GPy.kern.Matern52(self.X.shape[1], ARD=False) for jj in range(0, len(self.states)): if (self.X.shape[0] > self.num_inducing): print("Using Sparse GP Model...") dynModel = GPy.models.SparseGPRegression( self.X, self.Y[:, jj].reshape(self.Y.shape[0], 1), kernel, num_inducing=self.num_inducing) self.dynModels.append(dynModel.copy()) else: print("Using Full GP Model...") dynModel = GPy.models.GPRegression( self.X, self.Y[:, jj].reshape(self.Y.shape[0], 1), kernel) dynModel.optimize_restarts(num_restarts=2) dynModel.optimize('bfgs', messages=True, max_iters=5000) self.dynModels.append(dynModel.copy()) print(self.dynModels[jj]) self.checkModelAccuracy(dynModel, self.X, self.Y[:, jj]) # Define Box Constraints (min/max values) for the control parameters boxConstraints = [] for jj in range(self.nvars): boxConstraints.append(self.controlLim) # Link to the python function calculating the cost and the constraints. Note that # this is not the actual simulation, but the propagate function self.opt_prob = Optimization('GPSS_SLSQP Constrained Problem', self.propagate) # Setupt Box Constrains in pyOpt for jj in range(self.nvars): self.opt_prob.addVar('x' + str(jj + 1), 'c', lower=boxConstraints[jj][0], upper=boxConstraints[jj][1], value=self.building.policy[0, jj]) # Setupt Cost Function in pyOpt self.opt_prob.addObj('f') # Setupt Inequality Constraints in pyOpt for jj in range(self.ncons + 1): self.opt_prob.addCon('g' + str(jj + 1), 'i') # Print the Optimization setup print("----------------------------------------") print("----------------------------------------") print("GPSS_SLSQP Optimization setup:") print(self.opt_prob) optionsSLSQP = {'ACC': 1.0e-20, 'MAXIT': 10000, 'IPRINT': 1} # Set SLSQP as the optimizer self.opt = SLSQP() # Set optimization options for jj in range(len(optionsSLSQP)): self.opt.setOption(optionsSLSQP.keys()[jj], optionsSLSQP.values()[jj]) # Print the Optimizer Options print("----------------------------------------") print("----------------------------------------") print("SLSQP Optimizer options:") print(self.opt.options) # Get optimized controller self.opt(self.opt_prob, sens_step=1e-6) print(self.opt_prob.solution(0)) a = self.opt_prob.solution(0) for jj in range(self.building.policy.shape[1]): self.building.policy[0, jj] = a.getVar(jj).value # Evaluate the optimized controller in the simulation model xa, cf, cc = self.building.simulate(self.building.policy) print("COST: = =========== " + str(np.sum(cf))) print("CONSTRAINT: = =========== " + str(np.sum(cc))) xx = xa[0:-1, ] yy = xa[1:, self.states] if (ii == 0): self.X = xx self.Y = yy else: self.X = np.concatenate((self.X, xx), axis=0) self.Y = np.concatenate((self.Y, yy), axis=0) self.costs[ii, 0] = np.sum(cf) for jj in range(self.ncons): self.constraints[ii, jj] = np.sum(cc[:, jj]) self.policies[ii, :] = self.building.policy.copy() self.building.policy = initPolicy.copy() self.policies[ii + 1, :] = self.baseline[0].copy() self.costs[ii + 1, 0] = self.baseline[1] self.constraints[ii + 1, 0] = self.baseline[2] policyIndex = self.selectBestController(self.costs, self.constraints) self.building.policy = self.policies[policyIndex, :].copy() return self.building.policy def selectBestController(self, costs, constraints): """A function that selects the best controller out of a set of controllers, based on their performance on the cost function and the constraints. Args: costs (numpy array): The resulting cost of each controller, as evaluated on the simulation model constraints (numpy array): The resulting constraints of each controller, as evaluated on the simulation model Returns: policyIndex (float): the index of the best controller """ wCost = 1 wConstraints = 10000000 p = np.zeros((costs.shape[0], 1)) for ii in range(costs.shape[0]): p[ii, 0] = p[ii, 0] + wCost * costs[ii, 0] for jj in range(constraints.shape[1]): p[ii, 0] = p[ii, 0] + wConstraints * constraints[ii, jj] policyIndex = np.argmin(p) return policyIndex def propagate(self, policy): """A function that uses the GP state-space models identified from the data to perform rollouts based on a given controller. Args: policy (numpy array): the controller to be used for the rollout Returns: f (float): the cost function value g (list): the vales of all constraints fail (0/1): indicates if the function finished successfully """ # Initial state xx = np.zeros((self.building.T + 1, len(self.building.states) + self.building.w.shape[1])) uu = np.zeros((self.building.T + 1, len(self.building.actions))) cc = np.zeros((self.building.T + 1, 1)) cf = np.zeros((self.building.T + 1, 1)) var = np.zeros((self.building.T, len(self.building.states))) xx[0, ] = self.X[0, 0:2] # [17, w[0,]] uu[0, ] = self.building.controller(policy, xx[0, ], 0) cc[0, ] = self.building.comfortConstraints(xx[0, self.building.states], 0) cf[0, ] = self.building.costFunction(uu[0, ], 0) # state propagation using the provided controller for ii in range(1, self.building.T + 1): newX = np.hstack([xx[ii - 1, ], uu[ii - 1]]).reshape(1, xx.shape[1] + uu.shape[1]) for jj in range(0, len(self.building.states)): results = self.dynModels[jj].predict(newX) xx[ii, jj] = results[0] var[ii - 1, jj] = results[1] xx[ii, 1] = self.building.w[ii, ] uu[ii, ] = self.building.controller(policy, xx[ii, ], ii) cc[ii, ] = self.building.comfortConstraints( xx[ii, self.building.states], ii) cf[ii, ] = self.building.costFunction(uu[ii, ], ii) f = np.sum(cf) g = [] g.append(np.mean(var) - self.explorationConstraint) # Exploration constraint g.append(np.sum(cc)) fail = 0 return f, g, fail def checkModelAccuracy(self, dynModel, xtest, ytest): """A function that evaluates the accuracy of the GP state-space model. Args: dynModel (GPy object): The GP model xtest (numpy array): The features of the regression ytest (numpy array): The targets of the regression """ results = dynModel.predict(xtest) ypred = results[0] # sGP = results[1] rsqTrain, maeTrain, rsqAdjTrain = self.evaluateGoodnessOfFit( xtest, ytest, ypred) print("Rsq train Gaussian Processes Regression = " + str(rsqTrain)) print("Rsq Adjusted train Gaussian Processes Regression = " + str(rsqAdjTrain)) print("MAE train Gaussian Processes Regression = " + str(maeTrain)) def evaluateGoodnessOfFit(self, x, y, ypred): """A function that evaluates the goodness of fit, under different measures. Args: x (numpy array): The features of the regression y (numpy array): The targets of the regression ypred (numpy array): The predictions of the regression model Returns: Rsquared (float): R-squared mae (float): Mean Absolute Error rsqAdj (float): The Adjusted R-square """ print(y.shape[0]) print(x.shape[1]) y_hat = np.mean(y) SStot = np.sum(np.power(y - y_hat, 2)) SSres = np.sum(np.power(y - ypred.flatten(), 2)) if (SStot == 0): rsq = 1 else: rsq = 1 - SSres / SStot mae = np.sum(np.abs(y - ypred.flatten())) / ypred.shape[0] rsqAdj = 1 - (1 - rsq) * (y.shape[0] - 1) / (y.shape[0] - x.shape[1] - 1) return rsq, mae, rsqAdj def wrapSimulation(self, policy): """A function that runs a building simulation and wraps the results in the format required by PyOpt library. Args: policy (numpy array): the controller to be used for the simulation Returns: f (float): the cost function value g (list): the vales of all constraints fail (0/1): indicates if the function finished successfully """ # Cost and Constraints f = 0 g = [] fail = 0 # Run building simulation x, cost, constraints = self.building.simulate(policy) f = np.sum(cost) g.append(np.sum(constraints)) # print(f) # print(g[0]) return f, g, fail