#!/usr/bin/env python # -*- coding: utf-8 -*- """ *********************************************************************************** opt_tutorial4.py DAE Tools: pyDAE module, www.daetools.com Copyright (C) Dragan Nikolic *********************************************************************************** DAE Tools is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License version 3 as published by the Free Software Foundation. DAE Tools is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with the DAE Tools software; if not, see <http://www.gnu.org/licenses/>. ************************************************************************************ """ __doc__=""" This tutorial shows the interoperability between DAE Tools and 3rd party optimization software (scipy.optimize) used to minimize the Rosenbrock function. DAE Tools simulation is used to calculate the objective function and its gradients, while scipy.optimize.fmin function (Nelder-Mead Simplex algorithm) to find the minimum of the Rosenbrock function. """ import sys from time import localtime, strftime from scipy.optimize import fmin, fmin_bfgs, fmin_l_bfgs_b from daetools.pyDAE import*classmodTutorial(daeModel):def__init__(self, Name, Parent=None, Description=""): daeModel.__init__(self, Name, Parent, Description) self.x1=daeVariable("x1", no_t, self) self.x2=daeVariable("x2", no_t, self) self.x3=daeVariable("x3", no_t, self) self.x4=daeVariable("x4", no_t, self) self.x5=daeVariable("x5", no_t, self) self.dummy=daeVariable("dummy", no_t, self, "A dummy variable to satisfy the condition that there should be at least one-state variable and one equation in a model")defDeclareEquations(self): daeModel.DeclareEquations(self) eq=self.CreateEquation("Dummy") eq.Residual=self.dummy()classsimTutorial(daeSimulation):def__init__(self): daeSimulation.__init__(self) self.m=modTutorial("opt_tutorial4") self.m.Description=__doc__defSetUpParametersAndDomains(self):passdefSetUpVariables(self): self.m.x1.AssignValue(1) self.m.x2.AssignValue(1) self.m.x3.AssignValue(1) self.m.x4.AssignValue(1) self.m.x5.AssignValue(1)defSetUpSensitivityAnalysis(self): self.SetNumberOfObjectiveFunctions(1) self.ObjectiveFunction.Residual=100*(self.m.x2()-self.m.x1()**2)**2+(1-self.m.x1())**2+\100*(self.m.x3()-self.m.x2()**2)**2+(1-self.m.x2())**2+\100*(self.m.x3()-self.m.x3()**2)**2+(1-self.m.x3())**2+\100*(self.m.x5()-self.m.x4()**2)**2+(1-self.m.x4())**2 self.ov1=self.SetContinuousOptimizationVariable(self.m.x1,-10, 10, 1.3) self.ov2=self.SetContinuousOptimizationVariable(self.m.x2,-10, 10, 0.7) self.ov3=self.SetContinuousOptimizationVariable(self.m.x3,-10, 10, 0.8) self.ov4=self.SetContinuousOptimizationVariable(self.m.x4,-10, 10, 1.9) self.ov5=self.SetContinuousOptimizationVariable(self.m.x5,-10, 10, 1.2)defObjectiveFunction(x,*args): simulation=args[0] # This function will be called repeatedly to obtain the values of the objective function. # In order to call DAE Tools repedeatly the following sequence of calls is necessary: # 1. Set initial conditions, initial guesses, initially active states etc (function simulation.SetUpVariables) # In general, variables values, active states, initial conditions etc can be saved in some arrays and # later re-used. However, keeping the initialization data in SetUpVariables looks much better. simulation.SetUpVariables() # 2. Change values of optimization variables (this will call function daeVariable.ReAssignValue) by setting # the optimization variable's Value property. Optimization variables can be obtained in two ways: # 2a) Use OptimizationVariables attribute to get a list of optimization variables and then set their values: opt_vars=simulation.OptimizationVariables opt_vars[0].Value=x[0] opt_vars[1].Value=x[1] opt_vars[2].Value=x[2] opt_vars[3].Value=x[3] opt_vars[4].Value=x[4] # 2b) Use stored optimization variable objects in simulation object (ov1, ..., ov5): #simulation.ov1.Value = x[0] #simulation.ov2.Value = x[1] #simulation.ov3.Value = x[2] #simulation.ov4.Value = x[3] #simulation.ov5.Value = x[4] # 3. Call simulations's Reset (to reset simulation and DAE solver objects), SolveInitial (to re-initialize the system), # and Run (to simulate the model and to calculate sensitivities) functions. simulation.Reset() simulation.SolveInitial() simulation.Run() # 4. Once finished with simulation, use ObjectiveFunction and Constraints properties of simulation object. # Objective function and constraints have Value (float) and Gradients (numpy array) properties where # their values and gradients in respect to optimization variables are stored. Here, as the example, # the value and gradients of the objective function are printed (since no constraints are involved). print('Objective function inputs: ') print(' Inputs: {0}'.format(x)) print(' Value = {0}'.format(simulation.ObjectiveFunction.Value)) print(' Gradients = {0}'.format(simulation.ObjectiveFunction.Gradients)) print('')returnsimulation.ObjectiveFunction.Valuedefrun(): log=daePythonStdOutLog() daesolver=daeIDAS() datareporter=daeTCPIPDataReporter() simulation=simTutorial() # Do no print progress log.PrintProgress=False # Enable reporting of all variables simulation.m.SetReportingOn(True) simulation.ReportingInterval=1 simulation.TimeHorizon=5 simName=simulation.m.Name+strftime(" [%d.%m.%Y %H:%M:%S]", localtime())if(datareporter.Connect("", simName)==False): sys.exit() # ACHTUNG, ACHTUNG!! # To request simulation to calculate sensitivities use the keyword argument CalculateSensitivities: simulation.Initialize(daesolver, datareporter, log, calculateSensitivities=True) simulation.m.SaveModelReport(simulation.m.Name+".xml") simulation.m.SaveRuntimeModelReport(simulation.m.Name+"-rt.xml") # Get the starting point from optimization variables x0=[simulation.ov1.StartingPoint, simulation.ov2.StartingPoint, simulation.ov3.StartingPoint, simulation.ov4.StartingPoint, simulation.ov5.StartingPoint] print(fmin(ObjectiveFunction, x0, args=(simulation,), xtol=1e-8))if__name__=="__main__": run()