Z3 Not Showing Infinity on Unbounded Optimization in Python
Question:
I am new to Z3 and trying the examples found here, implementing the examples in python. When I try the examples in the "Unbounded Objectives" section I get seemingly random integer values (not ‘oo’). For the following code:
x, y = Ints('x y')
opt = Optimize()
opt.add(x < 2)
opt.add((y - x) > 1)
opt.maximize(x + y)
print(opt.check())
print(opt.model())
I get the output:
sat
[y = 5, x = 1]
But the problem is unbounded, I expect it to give me y equal to infinity. A more simple example:
x, y, profit = Ints('x y profit')
opt = Optimize()
opt.add(profit == 2*x + y)
opt.maximize(profit)
print(opt.check())
print(opt.model())
This example gives me:
sat
[x = 0, y = 0, profit = 0]
My question is: Why am I not getting infinity here? Am I doing something wrong or is this the output I should expect from Z3 with python when I give it an unbounded optimization problem?
I am using python 3.9 on Pycharm 2021.2.1, Z3 version 4.8.15.
Answers:
You’re not quite using the API correctly. You should use the value function on the optimization goal instead. For instance, your second query is coded as:
from z3 import *
x, y, profit = Ints('x y profit')
opt = Optimize()
opt.add(profit == 2*x + y)
maxProfit = opt.maximize(profit)
print(opt.check())
print("maxProfit =", maxProfit.value())
This prints:
sat
maxProfit = oo
Note that when the optimization result is oo, then the model values for x/y/profit etc., are irrelevant. (They are no longer integers.) If the optimization result is a finite value, then you can look at opt.model() to figure out what assignment to your variables achieved the optimal goal. So, the values of x/y and profit you get in your example, while printed as 0, are meaningless; since the goal is not a proper integer value.
I am new to Z3 and trying the examples found here, implementing the examples in python. When I try the examples in the "Unbounded Objectives" section I get seemingly random integer values (not ‘oo’). For the following code:
x, y = Ints('x y')
opt = Optimize()
opt.add(x < 2)
opt.add((y - x) > 1)
opt.maximize(x + y)
print(opt.check())
print(opt.model())
I get the output:
sat
[y = 5, x = 1]
But the problem is unbounded, I expect it to give me y equal to infinity. A more simple example:
x, y, profit = Ints('x y profit')
opt = Optimize()
opt.add(profit == 2*x + y)
opt.maximize(profit)
print(opt.check())
print(opt.model())
This example gives me:
sat
[x = 0, y = 0, profit = 0]
My question is: Why am I not getting infinity here? Am I doing something wrong or is this the output I should expect from Z3 with python when I give it an unbounded optimization problem?
I am using python 3.9 on Pycharm 2021.2.1, Z3 version 4.8.15.
You’re not quite using the API correctly. You should use the value function on the optimization goal instead. For instance, your second query is coded as:
from z3 import *
x, y, profit = Ints('x y profit')
opt = Optimize()
opt.add(profit == 2*x + y)
maxProfit = opt.maximize(profit)
print(opt.check())
print("maxProfit =", maxProfit.value())
This prints:
sat
maxProfit = oo
Note that when the optimization result is oo, then the model values for x/y/profit etc., are irrelevant. (They are no longer integers.) If the optimization result is a finite value, then you can look at opt.model() to figure out what assignment to your variables achieved the optimal goal. So, the values of x/y and profit you get in your example, while printed as 0, are meaningless; since the goal is not a proper integer value.