In this section we will construct a simple model and explain every step along the way.
The are more complex examples in the JuMP/examples/ folder. Here is the code we will walk through:
using JuMP
m = Model()
@variable(m, 0 <= x <= 2 )
@variable(m, 0 <= y <= 30 )
@objective(m, Max, 5x + 3*y )
@constraint(m, 1x + 5y <= 3.0 )
print(m)
status = solve(m)
println("Objective value: ", getobjectivevalue(m))
println("x = ", getvalue(x))
println("y = ", getvalue(y))
Once JuMP is :ref:`installed <jump-installation>`, to use JuMP in your programs, you just need to say:
using JuMP
Models are created with the Model() function:
m = Model()
Note
Your model doesn't have to be called m - it's just a name.
There are a few options for defining a variable, depending on whether you want
to have lower bounds, upper bounds, both bounds, or even no bounds. The following
commands will create two variables, x and y, with both lower and upper bounds.
Note the first argument is our model variable m. These variables are associated
with this model and cannot be used in another model.:
@variable(m, 0 <= x <= 2 ) @variable(m, 0 <= y <= 30 )
Next we'll set our objective. Note again the m, so we know which model's
objective we are setting! The objective sense, Max or Min, should
be provided as the second argument. Note also that we don't have a multiplication *
symbol between 5 and our variable x - Julia is smart enough to not need it!
Feel free to stick with * if it makes you feel more comfortable, as we have
done with 3*y:
@objective(m, Max, 5x + 3*y )
Adding constraints is a lot like setting the objective. Here we create a
less-than-or-equal-to constraint using <=, but we can also create equality
constraints using == and greater-than-or-equal-to constraints with >=:
@constraint(m, 1x + 5y <= 3.0 )
If you want to see what your model looks like in a human-readable format,
the print function is defined for models.
print(m)
Models are solved with the solve() function. This function will not raise
an error if your model is infeasible - instead it will return a flag. In this
case, the model is feasible so the value of status will be :Optimal,
where : again denotes a symbol. The possible values of status
are described :ref:`here <solvestatus>`.
status = solve(m)
Finally, we can access the results of our optimization. Getting the objective value is simple:
println("Objective value: ", getobjectivevalue(m))
To get the value from a variable, we call the getvalue() function. If x
is not a single variable, but instead a range of variables, getvalue() will
return a list. In this case, however, it will just return a single value.
println("x = ", getvalue(x))
println("y = ", getvalue(y))