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Model optimized to 0 & all constraints removed by presolve

Answered
Rosa Muijderman
  • Gurobi-versary
  • First Comment
  • First Question

I am very new to Gurobi/Python and I've run into a problem. I have written the following code, but for some reason the model optimizes to 0, because apparently all constraints are removed by presolve because they are redundant. I can't seem to figure out why my constraints are redundant. Can somebody help me out?

import gurobipy as gp
from gurobipy import GRB


model = gp.Model("ObjectiveFunction")

# Parameters    
num_regions = 2
num_age_groups = 2
num_time_periods = 3 
num_control_measures = 2

days_per_period = 28

eff = 0.78

death_rate = {
    0: 0.005,
    1: 0.01
}

infection_rate = {
    0: 0.1,
    1: 0.05
}

susceptibility_rate = {
    0: 0.01,
    1: 0.02
}

population = {
    0: {0:3, 1:4},
    1: {0:5, 1:2}
}

total_population = {
    0 : 8,
    1 : 6
}

social_contact = {
    0 : {0:18, 1:5},
    1 : {0:10, 1:2}
}

a = {
    1: 2,
    2: 6
}

Q = {
    0: {1: 2, 2:1},
    1: {1: 0, 2:6}
}

y = [[0, 0],
     [0, 1],
     [0, 1]]

# Variables  
        
V = {}
for r in range(num_regions):
    for i in range(num_age_groups):
            for t in range(1, num_time_periods):
                    V[i, r, t] = model.addVar(vtype=GRB.CONTINUOUS, lb=0, name=f"V_{i}_{r}_{t}")

C = {}

for i in range(num_age_groups):
    for r in range(num_regions):
        for t in range(num_time_periods):
            C[i, r, 'u', t] = model.addVar(vtype=GRB.CONTINUOUS, lb=0, name=f"C_{i}_{r}_u_{t}")
            C[i, r, 'v1', t] = model.addVar(vtype=GRB.CONTINUOUS, lb=0,name=f"C_{i}_{r}_v1_{t}")
         
# Objective function
objective = gp.LinExpr()
for r in range(num_regions):
    for i in range(num_age_groups):
        for t in range(num_time_periods):
                 objective += (
                     infection_rate[i] * susceptibility_rate[i] * death_rate[i] / total_population[r] *
                     gp.quicksum(
                          social_contact[i][c] * days_per_period * (C[i, r, 'u', t]*y[t][c] + (1 - eff)*C[i, r, 'v1', t]*y[t][c]) for c in range(num_control_measures))
                     )

model.setObjective(objective, GRB.MINIMIZE)

# Constraint 1 - total vaccines distributed at time t not more than availability at time t
for t in range(1, num_time_periods):
    model.addConstr(gp.quicksum(V[i, r, t] for i in range(num_age_groups) for r in range(num_regions)) <= a[t], name=f"c1_t{t}")

# Constraint 2 - total vaccines distributed in region r at time t not more than capable in region r
for r in range(num_regions):
    for t in range(1, num_time_periods):
        model.addConstr(gp.quicksum(V[i, r, t] for i in range(num_age_groups)) <= Q[r][t], name=f"c2_r{r}_t{t}")

# Constraint 3 - unvaccinated and vaccinated people in region r not more than population in region r at every time t
for r in range(num_regions):
    for t in range(num_time_periods):
        for i in range(num_age_groups):
            model.addConstr(gp.quicksum(C[i, r, 'u', t] + C[i, r, 'v1', t]) <= population[i][r], name=f"c3_r{r}_t{t}_i{i}")
        
# Constraint 4 - total vaccines distributed in region r not more than population in region r over all t
for r in range(num_regions):
    model.addConstr(gp.quicksum(V[i, r, t] for i in range(num_age_groups) for t in range(1, num_time_periods)) <= gp.quicksum(population[i][r] for i in range(num_age_groups)), name=f"c4_r{r}")

# Constraint 5 - cumulative unvaccinated at time t equal to unvaccinated at time t-1 minus the newly vaccinated at time t
for t in range(1, num_time_periods):
    for i in range(num_age_groups): 
        for r in range(num_regions): 
            model.addConstr(
                C[i, r, 'u', t] == C[i, r, 'u', t-1] - V[i, r, t], name=f"c5_r{r}_t{t}_i{i}")

# Constraint 6 - cumulative vaccinated at time t equal to vaccinated at time t-1 plus the newly vaccinated at time t
for t in range(1, num_time_periods):
    for i in range(num_age_groups): 
        for r in range(num_regions): 
                model.addConstr(
                    C[i, r, 'v1', t] == C[i, r, 'v1', t-1] + V[i, r, t], name=f"c6_r{r}_t{t}_i{i}")               

# Set starting values   
for i in range(num_age_groups):
    for r in range(num_regions):
            C[i, r, 'u', 0].start = population[i][r]  # Set the starting value for C_{i}_{r}_u_{t}
            C[i, r, 'v1', 0].start = 0 

                   
# Usage
model.optimize()

if model.status == GRB.OPTIMAL:
    print("Objective value:", model.objVal)

    for t in range(1, num_time_periods):
        for i in range(num_age_groups): 
            for r in range(num_regions): 
                print(f"V_{i}_{r}_{t} = {V[i, r, t].X}")
                print(f"C_{i}_{r}_u_{t} = {C[i, r, 'u', t].X}")
                print(f"C_{i}_{r}_v1_{t} = {C[i, r, 'v1', t].X}")

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Comments

5 comments

Date Votes
  • Official comment
    Simranjit Kaur
    • Gurobi Staff
    This post is more than two years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum, or try Gurobot, our chatbot interface offering instant, expert-level support.
  • Jaromił Najman
    • Gurobi Staff

    Executing your code results in

    Traceback (most recent call last):
      File "test.py", line 103, in <module>
        model.addConstr(gp.quicksum(C[i, r, 'u', t] + C[i, r, 'v1', t]) <= population[i][r], name=f"c3_r{r}_t{t}_i{i}")
      File "src/gurobipy/gurobi.pxi", line 3706, in gurobipy.quicksum
    TypeError: 'gurobipy.LinExpr' object is not iterable

    which points to the constraint

    # Constraint 3 - unvaccinated and vaccinated people in region r not more than population in region r at every time t
    for r in range(num_regions):
        for t in range(num_time_periods):
            for i in range(num_age_groups):
                model.addConstr(gp.quicksum(C[i, r, 'u', t] + C[i, r, 'v1', t]) <= population[i][r], name=f"c3_r{r}_t{t}_i{i}")

    There is a \(\texttt{for}\) statement missing inside of the \(\texttt{gp.quicksum}\) call.

    0
  • Rosa Muijderman
    • Gurobi-versary
    • First Comment
    • First Question

    Hi Jaromil,

    Thanks for looking at my code! You’re right, I forgot to remove the quicksum. Unfortunately I still run into the same problem after I fix this error. The constraints are not considered, which makes the code return 0 as the optimal value. Do you have any idea how I could fix this? Or some tips as to how I can figure it out?

    0
  • Jaromił Najman
    • Gurobi Staff
    Edited

    Hi Rosa,

    I think the best way to find out what is wrong is to write the model to an LP file and inspect it.

    # Usage
    model.write("myLP.lp")
    model.optimize()

    You can open the \(\texttt{myLP.lp}\) file in any standard text editor and analyze your model. From what I can see is that the current version of your model is a small purely continuous model with a couple of equality constraints which all can be used for substitution. Setting all variables to \(0\) is a feasible point and it's simultaneously the optimal solution because all objective coefficients are non-negative. There is no constraint which would force any of the variable to be \(>0\).

    Best regards, 
    Jaromił

    0
  • Rosa Muijderman
    • Gurobi-versary
    • First Comment
    • First Question

    Hi Jaromil,

    Thanks for the tip! I figured out what the problem was. The initial value for C_i_r_u_0 was not set correctly, which ended in an optimal value of 0. I now added a constraint to ensure the correct initial value.

    Kind regards,
    Rosa

    0

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