I am trying migrating the ampl car problem that comes in the Ipopt source code tarball as example. I am having got problems with the end condition (reach a place with zero speed at final iteration) and with the cost function (minimize final time).
Can someone help me revise the following model?
# min tf
# dx/dt = 0
# dv/dt = a - R*v^2
# x(0) = 0; x(tf) = 100
# v(0) = 0; v(tf) = 0
# -3 <= a <= 1 (a is the control variable)
#!Python3.5
from pyomo.environ import *
from pyomo.dae import *
N = 20;
T = 10;
L = 100;
m = ConcreteModel()
# Parameters
m.R = Param(initialize=0.001)
# Variables
def x_init(m, i):
return i*L/N
m.t = ContinuousSet(bounds=(0,1000))
m.x = Var(m.t, bounds=(0,None), initialize=x_init)
m.v = Var(m.t, bounds=(0,None), initialize=L/T)
m.a = Var(m.t, bounds=(-3.0,1.0), initialize=0)
# Derivatives
m.dxdt = DerivativeVar(m.x, wrt=m.t)
m.dvdt = DerivativeVar(m.v, wrt=m.t)
# Objetives
m.obj = Objective(expr=m.t[N])
# DAE
def _ode1(m, i):
if i==0:
return Constraint.Skip
return m.dxdt[i] == m.v[i]
m.ode1 = Constraint(m.t, rule=_ode1)
def _ode2(m, i):
if i==0:
return Constraint.Skip
return m.dvdt[i] == m.a[i] - m.R*m.v[i]**2
m.ode2 = Constraint(m.t, rule=_ode2)
# Constraints
def _init(m):
yield m.x[0] == 0
yield m.v[0] == 0
yield ConstraintList.End
m.init = ConstraintList(rule=_init)
'''
def _end(m, i):
if i==N:
return m.x[i] == L amd m.v[i] == 0
return Constraint.Skip
m.end = ConstraintList(rule=_end)
'''
# Discretize
discretizer = TransformationFactory('dae.finite_difference')
discretizer.apply_to(m, nfe=N, wrt=m.t, scheme='BACKWARD')
# Solve
solver = SolverFactory('ipopt', executable='C:\\EXTERNOS\\COIN-OR\\win32-msvc12\\bin\\ipopt')
results = solver.solve(m, tee=True)
Currently, a ContinuousSet in Pyomo has to be bounded. This means that in order to solve a minimum time optimal control problem using this tool, the problem must be reformulated to remove the time scaling from the ContinuousSet. In addition, you have to introduce an extra variable to represent the final time. I've added an example to the Pyomo github repository showing how this can be done for your problem.
After having seen the nice implementation of the "ampl car example" in Pyomo repository, I would like to keep extending the problem with new features and constraints, but I have found the next problems during development. Is someone able of fix them?
1) Added new constraint "electric car": Now the acceleration is limited by adherence until a determined speed and then constant power model is used. I am not able of implement this constraint as i would think. It is commented in the, but Pyomo complains about that a constraint is related to a variable. (now Umax depends of the car speed).
2) Added new comfort acceleration and jerk constraints. It seems they are working right, but should be nice if a Pyomo guru supervise them and tell me if they are really implemented in the correct way.
3) About last one, in order of reducing verbosity. Is there any way of combine accelerationL and accelerationU in a unique constraint? Same for jerkL and jerkU.
4) The last feature is a speed limit constraint divided in two steps. Again, I am not able of getting it works, so it is commented in code. Does anybody dare to fix it?
# Ampl Car Example (Extended)
#
# Shows how to convert a minimize final time optimal control problem
# to a format pyomo.dae can handle by removing the time scaling from
# the ContinuousSet.
#
# min tf
# dx/dt = v
# dv/dt = u - R*v^2
# x(0)=0; x(tf)=L
# v(0)=0; v(tf)=0
# -3 <= u <= 1 (engine constraint)
#
# {v <= 7m/s ===> u < 1
# u <= { (electric car constraint)
# {v > 7m/s ===> u < 1*7/v
#
# -1.5 <= dv/dt <= 0.8 (comfort constraint -> smooth driving)
# -0.5 <= d2v/dt2 <= 0.5 (comfort constraint -> jerk)
# v <= Vmax (40 kmh[0-500m] + 25 kmh(500-1000m])
from pyomo.environ import *
from pyomo.dae import *
m = ConcreteModel()
m.R = Param(initialize=0.001) # Friction factor
m.L = Param(initialize=1000.0) # Final position
m.T = Param(initialize=50.0) # Estimated time
m.aU = Param(initialize=0.8) # Acceleration upper bound
m.aL = Param(initialize=-1.5) # Acceleration lower bound
m.jU = Param(initialize=0.5) # Jerk upper bound
m.jL = Param(initialize=-0.5) # Jerk lower bound
m.NFE = Param(initialize=100) # Number of finite elements
'''
def _initX(m, i):
return m.x[i] == i*m.L/m.NFE
def _initV(m):
return m.v[i] == m.L/50
'''
m.tf = Var()
m.tau = ContinuousSet(bounds=(0,1)) # Unscaled time
m.t = Var(m.tau) # Scaled time
m.x = Var(m.tau, bounds=(0,m.L))
m.v = Var(m.tau, bounds=(0,None))
m.u = Var(m.tau, bounds=(-3,1), initialize=0)
m.dt = DerivativeVar(m.t)
m.dx = DerivativeVar(m.x)
m.dv = DerivativeVar(m.v)
m.da = DerivativeVar(m.v, wrt=(m.tau, m.tau))
m.obj = Objective(expr=m.tf)
def _ode1(m, i):
if i==0:
return Constraint.Skip
return m.dt[i] == m.tf
m.ode1 = Constraint(m.tau, rule=_ode1)
def _ode2(m, i):
if i==0:
return Constraint.Skip
return m.dx[i] == m.tf * m.v[i]
m.ode2 = Constraint(m.tau, rule=_ode2)
def _ode3(m, i):
if i==0:
return Constraint.Skip
return m.dv[i] == m.tf*(m.u[i] - m.R*m.v[i]**2)
m.ode3 = Constraint(m.tau, rule=_ode3)
def _accelerationL(m, i):
if i==0:
return Constraint.Skip
return m.dv[i] >= m.aL*m.tf
m.accelerationL = Constraint(m.tau, rule=_accelerationL)
def _accelerationU(m, i):
if i==0:
return Constraint.Skip
return m.dv[i] <= m.aU*m.tf
m.accelerationU = Constraint(m.tau, rule=_accelerationU)
def _jerkL(m, i):
if i==0:
return Constraint.Skip
return m.da[i] >= m.jL*m.tf**2
m.jerkL = Constraint(m.tau, rule=_jerkL)
def _jerkU(m, i):
if i==0:
return Constraint.Skip
return m.da[i] <= m.jU*m.tf**2
m.jerkU = Constraint(m.tau, rule=_jerkU)
'''
def _electric(m, i):
if i==0:
return Constraint.Skip
elif value(m.v[i])<=7:
return m.a[i] <= 1
else:
return m.v[i] <= 1*7/m.v[i]
m.electric = Constraint(m.tau, rule=_electric)
'''
'''
def _speed(m, i):
if i==0:
return Constraint.Skip
elif value(m.x[i])<=500:
return m.v[i] <= 40/3.6
else:
return m.v[i] <= 25/3.6
m.speed = Constraint(m.tau, rule=_speed)
'''
def _initial(m):
yield m.x[0] == 0
yield m.x[1] == m.L
yield m.v[0] == 0
yield m.v[1] == 0
yield m.t[0] == 0
m.initial = ConstraintList(rule=_initial)
discretizer = TransformationFactory('dae.finite_difference')
discretizer.apply_to(m, nfe=value(m.NFE), wrt=m.tau, scheme='BACKWARD')
#discretizer = TransformationFactory('dae.collocation')
#discretizer.apply_to(m, nfe=value(m.NFE), ncp=4, wrt=m.tau, scheme='LAGRANGE-RADAU')
solver = SolverFactory('ipopt')
solver.solve(m,tee=True)
print("final time = %6.2f" %(value(m.tf)))
t = []
x = []
v = []
a = []
u = []
for i in m.tau:
t.append(value(m.t[i]))
x.append(value(m.x[i]))
v.append(3.6*value(m.v[i]))
a.append(10*value(m.u[i] - m.R*m.v[i]**2))
u.append(10*value(m.u[i]))
import matplotlib.pyplot as plt
plt.plot(x, v, label='v (km/h)')
plt.plot(x, a, label='a (dm/s2)')
plt.plot(x, u, label='u (dm/s2)')
plt.xlabel('distance')
plt.grid('on')
plt.legend()
plt.show()
Thanks a lot in advance,
Pablo
(1) You should not think of Pyomo constraint rules as callbacks that are used by the solver. You should think of them more as a function to generate a container of constraint objects that gets called once for each index when the model is constructed. Meaning it is invalid to use a variable in an if statement unless you are really only using its initial value to define the constraint expression. There are ways to express what I think you are trying to do, but they involve introducing binary variables into the problem, in which case you can no longer use Ipopt.
(2) Can't really provide any help. Syntax looks fine.
(3) Pyomo allows you to return double-sided inequality expressions (e.g., L <= f(x) <= U) from constraint rules, but they can not involve variable expressions in the L and U locations. It doesn't look like the constraints you are referring to can be combined into this form.
(4) See (1)
This is my code and when i try to run it and use it by entering numbers into the entry fields, an attribute error occurs when i try to call on the entry variable. This is the message that appears:
Exception in Tkinter callback
Traceback (most recent call last):
File "C:\Python27\lib\lib-tk\Tkinter.py", line 1486, in call
return self.func(*args)
File "F:\HomeWork\Yr13\Extended Project\Notepad++\Python27\Programs\GUI{c} menu+check+gen+Nth.py", line 224, in OnGenButtonClick
n= str(Prime_Generation(Prime_Gen.entryVariable5.get(),Prime_Gen.entryVariable6.get()))
File "C:\Python27\lib\lib-tk\Tkinter.py", line 1845, in getattr
return getattr(self.tk, attr)
AttributeError: entryVariable5
any help would be greatly appreciated.
i have stuck on this problem for three days and have tried getting around the problem by using different functions and names and the error still occurs
import Tkinter
from Tkinter import *
import math
def SoS(limit):
numbers = range(3, limit+1, 2)
half = (limit)//2
initial = 4
for step in xrange(3, limit+1, 2):
for i in xrange(initial, half, step):
numbers[i-1] = 0
initial += 2*(step+1)
if initial > half:
plist = [2] + filter(None, numbers)
return plist
break
def S(m):
sieve = [True] * m
for i in xrange(3,(int(m**0.5)+1),2):
if sieve[i]:
sieve[i*i::2*i]=[False]*((m-i*i-1)/(2*i)+1)
plist = [2] + [i for i in xrange(3,m,2) if sieve[i]]
return plist
def OTS(n):
n, correction = n-n%6+6, 2-(n%6>1)
sieve = [True] * (n/3)
for i in xrange(1,(int(n**0.5)/3)+1):
if sieve[i]:
k=3*i+1|1
sieve[ k*k/3 ::2*k] = [False] * ((n/6-k*k/6-1)/k+1)
sieve[k*(k-2*(i&1)+4)/3::2*k] = [False] * ((n/6-k*(k-2*(i&1)+4)/6-1)/k+1)
plist = [2,3] + [3*i+1|1 for i in xrange(1,n/3-correction) if sieve[i]]
return plist
def is_prime(num):
if num <= 3:
if num <= 1:
return False
return True
if not num % 2 or not num % 3:
return False
for i in xrange(5, int(num ** 0.5) + 1, 6):
if not num % i or not num % (i + 2):
return False
return True
def is_prime_multiple(Lower,Upper):
NumberList = dict()
if Lower%2 == 1:
for i in xrange(Lower, Upper,2):
NumberList[i] = is_prime(i)
else:
for i in xrange(Lower-1,Upper,2):
NumberList[i] = is_prime(i)
NumberList[1] = False
return [i for i in NumberList if NumberList[i] == True]
def Prime_Generation(L,U):
Lower = int(L)
Upper = int(U)
if Lower == 1:
if Upper < 92:
print SoS(Upper)
if Upper >= 92 and Upper < 2250:
print S(Upper)
if Upper >= 2250 :
print OTS(Upper)
else:
print sorted(is_prime_multiple(Lower,Upper))
def factors(n):
f = 3
fs = []
while n % 2 == 0:
fs.append(2)
n /= 2
while f*f <= n:
while n % f == 0:
fs.append(f)
n /= f
f += 2
if n > 1:
fs.append(n)
return fs
def Prime_Checker(N):
NStr = str(N)
N = int(N)
Nfs = factors(N)
for i in Nfs:
if i != N:
NfsStr = str(Nfs).strip('[]')
resultb = [NStr,' is not a prime. The prime factors of ',NStr,' are ',NfsStr]
return resultb.join()
else:
return N,' is a prime. The prime factors of ',N ,' are ',N
def PrimeFinderLamda(n,limit):
nums = range(3,limit,2)
for i in range(2, int(limit**0.5)):
nums = filter(lambda x: x == i or x % i, nums)
return [2]+nums
def NthPrime(N):
N = int(N)
Lower = 1
limit = N*N
if N == 1:
return 2
else:
return PrimeFinderLamda(N,limit)[N-1]
class Prime_app_tk(Tkinter.Tk):
def __init__(self,parent):
Tk.__init__(self,parent)
self.parent = parent
self.initialize()
def Prime_Gen_Win(self):
Prime_Gen = Toplevel()
Prime_Gen.grid()
Prime_Gen.labelVariable3 = StringVar()
Title_label2 = Label(Prime_Gen,textvariable=Prime_Gen.labelVariable3,
relief = RAISED,fg="black",bg="white"
,font = "Arial")
Title_label2.grid(column=0,row=0,columnspan=4)
Prime_Gen.labelVariable3.set(u"Please enter the upper and lower limits of the prime number generation")
Prime_Gen.labelVariable4 = StringVar()
SubTitle_label1 = Label(Prime_Gen,textvariable=Prime_Gen.labelVariable4,fg="black",bg="white")
SubTitle_label1.grid(column=0,row=1,columnspan=4)
Prime_Gen.labelVariable4.set(u"(Please enter values no greater than 10 million)")
Prime_Gen.entryVariable5 = StringVar()
Prime_Gen.entry = Entry(Prime_Gen,textvariable=Prime_Gen.entryVariable5)
Prime_Gen.entry.grid(column=0,row=4)
Prime_Gen.entryVariable5.set(u"Lower.")
Prime_Gen.entryVariable6 = StringVar()
Prime_Gen.entry = Entry(Prime_Gen,textvariable=Prime_Gen.entryVariable6)
Prime_Gen.entry.grid(column=0,row=5)
Prime_Gen.entryVariable6.set(u"Upper.")
Genbutton = Button(Prime_Gen,text=u"Generate !",command=self.OnGenButtonClick #placing and aesthetics of button
,bg="yellow",relief=RAISED,padx=10,pady=10
,activebackground="red",activeforeground="white")
Genbutton.grid(column=0,row=6)
scrollbar = Scrollbar(Prime_Gen)
scrollbar.grid(column=1,row=8,sticky="ns")
Prime_Gen.Result_label = Text(Prime_Gen, yscrollcommand=scrollbar.set
,fg="blue",bg="white",wrap=WORD
,width=100,relief = SUNKEN)
Prime_Gen.Result_label.grid(column=0,row=8,columnspan=2)
scrollbar.config(command=Prime_Gen.Result_label.yview)
Prime_Gen.labelVariable = StringVar()
SubTitle_label = Label(Prime_Gen,textvariable=Prime_Gen.labelVariable,fg="black",bg="white")
SubTitle_label.grid(column=0,row=9,columnspan=4)
Prime_Gen.labelVariable.set(u"To see full list please click on the results\n and use the up and down arrows to scroll through the list")
Prime_Gen.grid_columnconfigure(0,weight=1)
Prime_Gen.resizable(True,True)
Prime_Gen.update()
Prime_Gen.geometry(Prime_Gen.geometry())
Prime_Gen.entry.focus_set()
Prime_Gen.entry.selection_range(0, Tkinter.END)
def OnGenButtonClick(Prime_Gen):
n= str(Prime_Generation(Prime_Gen.entryVariable5.get(),Prime_Gen.entryVariable6.get()))
Prime_Gen.Result_label.insert(END,"\nPrimes Found\n")
Prime_Gen.Result_label.insert(END,n)
Prime_Gen.entry.focus_set()
Prime_Gen.entry.selection_range(0, Tkinter.END)
def Prime_Check_Win(self):
Prime_Check = Toplevel()
Prime_Check.grid()
Prime_Check.labelVariable8 = StringVar()
Title_label3 = Label(Prime_Check,textvariable=Prime_Check.labelVariable8,
relief = RAISED,fg="black",bg="white"
,font = "Arial")
Title_label3.grid(column=0,row=0,columnspan=4)
Prime_Check.labelVariable8.set(u"Please enter a Number to be checked for primality")
Prime_Check.labelVariable9 = StringVar()
SubTitle_label3 = Label(Prime_Check,textvariable=Prime_Check.labelVariable9,fg="black",bg="white")
SubTitle_label3.grid(column=0,row=1,columnspan=4)
Prime_Check.labelVariable9.set(u"(Please enter values no greater than 10 million)")
Prime_Check.entryVariable = StringVar()
Prime_Check.entry = Entry(Prime_Check,textvariable=Prime_Check.entryVariable)
Prime_Check.entry.grid(column=0,row=2)
Prime_Check.entryVariable.set(u"Enter Number here.")
Checkbutton = Button(Prime_Check,text=u"Check !",command=self.OnCheckButtonClick
,bg="blue",fg="white",relief=RAISED,padx=10,pady=10
,activebackground="red",activeforeground="white")
Checkbutton.grid(column=0,row=4)
Prime_Check.labelVariable10 = StringVar()
Result_label2 = Message(Prime_Check,textvariable=Prime_Check.labelVariable10
,anchor="w",fg="blue",bg="white"
,width=500,relief = SUNKEN,padx=3,pady=3)
Result_label2.grid(column=0,row=5,columnspan=2,rowspan=100)
Prime_Check.labelVariable10.set(u"Hello")
Prime_Check.grid_columnconfigure(0,weight=1)
Prime_Check.resizable(True,False)
Prime_Check.update()
Prime_Check.geometry(Prime_Check.geometry())
Prime_Check.entry.focus_set()
Prime_Check.entry.selection_range(0, Tkinter.END)
def OnCheckButtonClick(Prime_Check):
Prime_Check.labelVariable10.set(Prime_Checker(Prime_Check.entryVariable.get())) #Had to call on prime gen and display results
Prime_Check.entry.focus_set()
Prime_Check.entry.selection_range(0, Tkinter.END)
def Nth_Prime_Win(self):
Nth_Prime = Toplevel()
Nth_Prime.grid()
Nth_Prime.labelVariable12 = StringVar()
Title_label = Label(Nth_Prime,textvariable=Nth_Prime.labelVariable12,
relief = RAISED,fg="black",bg="white"
,font = "Arial")
Title_label.grid(column=0,row=0,columnspan=4)
Nth_Prime.labelVariable12.set(u"Please enter the Nth prime you would like to find")
Nth_Prime.labelVariable13 = StringVar()
SubTitle_label = Label(Nth_Prime,textvariable=Nth_Prime.labelVariable13,fg="black",bg="white")
SubTitle_label.grid(column=0,row=1,columnspan=4)
Nth_Prime.labelVariable13.set(u"(Please enter values no greater than 664579")
Nth_Prime.entryVariable = StringVar()
Nth_Prime.entry = Entry(Nth_Prime,textvariable=Nth_Prime.entryVariable)
Nth_Prime.entry.grid(column=0,row=4)
Nth_Prime.entryVariable.set(u"Enter Number here.")
Genbutton = Button(Nth_Prime,text=u"Generate !",command=self.OnButtonNthClick
,bg="green",relief=RAISED,padx=10,pady=10
,activebackground="red",activeforeground="white")
Genbutton.grid(column=0,row=5)
Nth_Prime.labelVariable14 = StringVar()
Result_label = Message(Nth_Prime,textvariable=Nth_Prime.labelVariable14
,anchor="w",fg="blue",bg="white"
,width=1000,relief = SUNKEN,justify=LEFT,padx=3,pady=3)
Result_label.grid(column=0,row=6,columnspan=2,rowspan=100)
Nth_Prime.labelVariable14.set(u"Hello")
Nth_Prime.grid_columnconfigure(0,weight=1)
Nth_Prime.resizable(False,False)
Nth_Prime.update()
Nth_Prime.geometry(Nth_Prime.geometry())
Nth_Prime.entry.focus_set()
Nth_Prime.entry.selection_range(0, Tkinter.END)
def OnButtonNthClick(Nth_Prime):
Nth_Prime.labelVariable14.set(NthPrime(Nth_Prime.entryVariable.get()))
Nth_Prime.entry.focus_set()
Nth_Prime.entry.selection_range(0, Tkinter.END)
def initialize(self):
self.grid()
self.labelVariable1 = StringVar()
Title_label1 = Label(self,textvariable=self.labelVariable1,
relief = RAISED,fg="black",bg="white"
,font = "Arial")
Title_label1.grid(column=0,row=0,columnspan=4)
self.labelVariable1.set(u"Welcome to the Prime Program")
self.labelVariable2 = StringVar()
SubTitle_label = Label(self,textvariable=self.labelVariable2,fg="black",bg="white")
SubTitle_label.grid(column=0,row=1,columnspan=4)
self.labelVariable2.set(u"(Please select the function you would like to use)")
PrimeGenbutton = Button(self,text=u"Find Primes between 2 limits !",command=self.Prime_Gen_Win
,bg="yellow",relief=RAISED,padx=10,pady=10
,activebackground="red",activeforeground="white")
PrimeGenbutton.grid(column=0,row=3)
PrimeCheckbutton = Button(self,text=u"Check if a number is prime !",command=self.Prime_Check_Win
,bg="blue",fg="white",relief=RAISED,padx=14,pady=10
,activebackground="red",activeforeground="white")
PrimeCheckbutton.grid(column=0,row=4)
NthPrimebutton = Button(self,text=u"Find the Nth prime !",command=self.Nth_Prime_Win
,bg="green",relief=RAISED,padx=35,pady=10
,activebackground="red",activeforeground="white")
NthPrimebutton.grid(column=0,row=5)
self.grid_columnconfigure(0,weight=1)
self.resizable(False,False)
self.update()
self.geometry(self.geometry())
if __name__ == "__main__":
app = Prime_app_tk(None)
app.title('Prime Program')
app.mainloop()
There's no quick fix for your code. It attempts to be object-oriented, but is doing so incorrectly. You need to properly define your methods, and should also adhere to PEP8 naming conventions -- specifically, methods and functions should start with a lowercase, and classes should start with an uppercase. Because you don't follow PEP8, and because of the odd way you use Prime_Gen to mean different things at different times, your code is incredibly hard to understand.
The crux of the problem is that inside OnGenButtonClick, Prime_Gen is not what you think it is. It is an instance of Prime_app_tk rather than the value that you set the local variable Prime_Gen to in Prime_Gen_Win. Thus, any attributes you assigned to the original Prime_Gen don't exist in this other Prime_Gen.
The reason is that the button is defined like this:
Genbutton = Button(..., command=self.OnGenButtonClick, ...)
In this context, self is the instance of Prime_app_tk, so that becomes the parameter passed to OnGenButtonClick. Inside that function you call the parameter Prime_Gen, in spite of the universal convention to name it self. This causes confusion in your code, because you also have a local variable named Prime_Gen in the code that creates the toplevel window.