Gurobi says the model is infeasible, yet I can come up with a solution by hand (Python)

Answered

yechan pyeong

July 06, 2023 01:34

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I optimized the model below, but guroby says the model is infeasible.

from gurobipy import *

m = Model('test')
a = m.addVar(name="a", vtype=GRB.INTEGER)
b = m.addVar(name="b", vtype=GRB.INTEGER)
c = m.addVar(name="c", vtype=GRB.INTEGER)

m.addConstr(a >= 0)
m.addConstr(a <= 0)
m.addConstr(a <= 3)
m.addConstr(a-b <= 1)
m.addConstr(a+b <= 5)
m.addConstr(b >= -1)
m.addConstr(b <= 1)
m.addConstr(a-c <= 0)
m.addConstr(a+c <= 0)
m.addConstr(c >= -1)
m.addConstr(c <= 1)
m.addConstr(b+c == -1)

objective = LinExpr(-b)
m.setObjective(objective, GRB.MINIMIZE)
m.setParam(GRB.Param.PoolSearchMode, 2)
m.setParam(GRB.Param.PoolSolutions, 10000)
m.setParam(GRB.Param.PoolGap, 1e-4)
m.optimize()

if m.status != GRB.Status.OPTIMAL:
    print('No Solution')
    m.write("file.lp")
else:
    m.setParam(GRB.Param.SolutionNumber, 0)
    print(m.getVarByName("a").Xn)
    print(m.getVarByName("b").Xn)
    print(m.getVarByName("c").Xn)

I think that the model is feasible if a=0, b=-1, c=0. Why is the model infeasible? Any help is appreciated.

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  Chung-Kyun Han

  • Gurobi Staff

  July 06, 2023 02:35

  Thank you for reaching us.

  The default lower bound of a variable is zero (please refer to our manual about Model.addVar()).
  If you add variables like as follows, you will get the optimal solution you want.

  a = m.addVar(lb=-GRB.INFINITY, name="a", vtype=GRB.INTEGER)
  b = m.addVar(lb=-GRB.INFINITY, name="b", vtype=GRB.INTEGER)
  c = m.addVar(lb=-GRB.INFINITY, name="c", vtype=GRB.INTEGER)

  Whenever you have any questions, feel free to contact us.

   

  Best regards,
  Chung-Kyun Han

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  yechan pyeong

  July 06, 2023 02:58

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  Thank you very much!

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  Riley Clement

  • Gurobi Staff

  July 06, 2023 02:59

  Hi Yechan,

  You should also take a look at our article How do I determine why my model is infeasible?
  
  With this knowledge, you will run

  m.computeIIS()
  m.write("model.ilp")

  and inspect the file that is written.
  
  - Riley

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