I am trying to run a MINLP problem on Pyomo. I have formulated an objective function and one of my constraints is this:
model.c2 = Constraint(expr = sum(model.x[i] for i in blocks) <= 4560)
I want something like this:
x+y+z<=3 with x not equal to y not equal to z.
How do I write a constraint for this?
The answer depends a bit on the details (are the variables integers, are all values in the domain covered). Here is a reference that may be of interest:
Williams, H. Paul and Yan, Hong (2001), Representations of the 'all_different' predicate of constraint satisfaction in integer programming, Informs Journal on Computing, 13 (2). 96-103.
Let's define the problem more precisely. Say we have n integers, x[i], that take unique values between 1,...,n. We can implement this as:
We can introduce binary variables
y[i,k] = 1 if x[i]=k
0 otherwise
With this, we can write:
x[i] = sum(k, k*y[i,k]) (1)
sum(k, y[i,k]) = 1 ∀i (2)
sum(i, y[i,k]) = 1 ∀k (3)
y[i,k] ∈ {0,1}
where i ∈ {1,..,n} and k ∈ {1,..,n}.
If you have fewer variables than n, say i ∈ {1,..,m} with m < n, then we need to replace (3) by:
sum(i, y[i,k]) ≤ 1 ∀k (3a)
