How to obtain a feasible solution within constraints?

Answered

Linne Li

• April 01, 2022 12:59
• Edited

Here's my model, and the output x has no assigned value, how could I obtain a feasible solution?

 

def Optimisation(distance, P, log_file=None):

    setParam("LogToConsole", 0)

    R = [i for i in range(distance.shape[0])]
    J = [i for i in range(distance.shape[1])]
    A = [[i, j] for i in range(distance.shape[0]) for j in range(distance.shape[1])]

    d = {(i, j): 
        distance[i,j].
        tolist()
        for i in range(distance.shape[0]) 
        for j in range(distance.shape[1])}

    combinations, ms = multidict(d)

    # Create a new model: resource assignment problem
    m = gp.Model()

    # Create variables
    x = m.addVars(combinations, name="assign")    
    
    # Add constraint: x + 2 y + 3 z <= 4
    jobs = m.addConstrs((x.sum('*', j) <= 1 for j in J), "job")
    
    # Add constraint: x + y >= 1
    resources = m.addConstrs((x.sum(r, '*')<=1 for r in R), "resource")
    
    # add constraints: 不可行区域sum为零
    m.addConstrs((x[j, r]<=ms[j, r] for j in J for r in R))
    
#     m.addConstr(x.sum("*", "*")>=P)
    m.addConstr(quicksum([x[j,r] for j,r in A])>=P, 'total num')#(x[j,r]) for j in J for r in R)
#     m.addConstr(sum(x.prod(ms))>P)
    
    # Set objective 
    m.setObjective(x[0,1], GRB.MAXIMIZE)
    
    # SAVE MODEL FOR INSPECTION                        
    m.write('RAP.lp')
    
    # Optimize model
    m.optimize()

    m.terminate()
    
    return x

0

• 

  Jaromił Najman

  Gurobi Staff

  • April 01, 2022 09:29

  Could you please elaborate a bit more on what exactly is your issue? Gurobi can solve models with constant objective functions. After a call to optimize() and a successful optimization run, you can access the feasible solution point via the X attribute.

  0
• 

  Linne Li

  • April 01, 2022 13:17
  • Edited

  

  

  

  I upload some details. Actually, after optimization, the var in m.getVars() has no accessible X attribute. I tried several ways with different objective functions, but they weren't working at all.  Does this mean the optimization didn't run properly? but I got no error or warning. My test is 

  Optimisation(np.array([[1,1],[1,1]]), N)

  0
• 

  Linne Li

  • April 01, 2022 13:23

  

  

  

  OK, I got it. The problem is my bound N, I got no assigned value because I have no feasible solution at all. Very negligent. Thanks for your time!

  0
• 

  Jaromił Najman

  Gurobi Staff

  • April 01, 2022 13:33
  • Edited

  This is a scoping issue. The model you define lives only within the \(\texttt{Optimisation}\) function. There are two ways to deal with this. The first option is to gather all solution information you need at the end of the \(\texttt{Optimization}\) function and return this information

  def Optimisation(...)
    [...]
    m.optimize()
    result = []
    for x in m.getVars():
        result.append((x.VarName,x.X))
  
    return result
  
  # outside of the Optimisation function
  res = Optimisation(np.array([[1,1],[1,1]]), 1)
  print(res)

  An alternative would be to generate the model before the function call and pass it as an argument

  def Optimisation(m, distance, P, log_file=None):
    [...]
    m.optimize()
  
  # outside of the Optimisation function
  # Create a new model: resource assignment problem
  m = gp.Model()
  Optimisation(m, np.array([[1,1],[1,1]]), 1)
  for v in m.getVars():
    print("%s: %f"%(v.VarName,v.X))

  Any of the two works. Note that I removed the call to the terminate method, because it only interrupts a currently running optimization process and does nothing when called after optimization has already been performed. Moreover, you should always check for a model's Status attribute before accessing the solution point, because a solution point will not be available if the model is infeasible.

  Best regards, 
  Jaromił

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