Gurobi objective with python dictionary values

Question

I am using Gurobi 6.0 with Python 2.7. I am curious to know if Gurobi allows the objective function to have values coming from a dictionary with indices of the decision variables. Attaching the code:

from gurobipy import *

d = {
     (0, 0): 0,
     (0, 1): -5,
     (1, 0): 4,
     (1, 1): 2,
     (2, 0): 0,
     (0, 2): 10
     }

m = Model()
x = m.addVar(vtype=GRB.INTEGER)
y = m.addVar(vtype=GRB.INTEGER)

m.update()
m.addConstr(x + y <= 2)
m.setObjective(d[(x, y)], GRB.MAXIMIZE)
m.optimize()
print m.objVal
print x.x
print y.x

The answer to the model was

-5.0

-0.0

-0.0

which clearly makes no sense because max(d[(x,y)]) = 10 happens at x=0 and y=2 as per the given data. What is the issue here? Does Gurobi even allow such dictionary references ? Is it even allowed?

Answer 1

For a somewhat complex causal chain d[(x,y)] in your code is equivalent to d[(0,1)], so the constant -5 winds up being your objective function. The reasons are

• gurobi.Var has __hash__ defined
• gurobi.Var has __cmp__ defined. It returns a truthy object
• In your case, x and y have hash values of 0 and 1
• The python dictionary lookup algorithm resolves d[(x,y)] to d[(0,1)]

What you are trying to do doesn't fit into the integer programming framework. The best way to put this into gurobi is the indicator variables that x and y take on specific values.