Two Phase method
AnsweredI want to solve the following model using Two-Phase method.
minz = -x1 + 2x2 - 3x3
x1 + x2 + x3 = 6
-x1 + x2 +2x3 = 4
2x2 + 3x3 = 10
x3 <= 2
i have written the following code, but it gives me infeasibility
import gurobipy as gp
import itertools
import os
from gurobipy import Model, GRB
# Solving the main linear model directly, without implementing Two-Phase and CG
# Create the initial master problem
model = gp.Model("Model Problem")
model.setParam('OutputFlag', 1)
for i in range(3):
x[i] = model.addVar(vtype=GRB.CONTINUOUS, name=f'x_{i}')
R = {}
for j in range(4):
R[j] = model.addVar(lb=0, vtype=GRB.CONTINUOUS, name=f'R_{j}')
model.setObjective(gp.quicksum(R[j] for j in range(4)))
model.addConstr(x[0] + x[1] + x[2] + R[0] == 6, "First_Constraint")
model.addConstr(-1 * x[0] + x[1] + 2 * x[2] + R[1] == 4, "Second_Constraint")
model.addConstr(2 * x[1] + 3 * x[2] + R[2] == 10, "Third_Constraint")
model.addConstr(x[2] + R[3] == 2, "Fourth_Constraint")
if model.status == GRB.OPTIMAL:
# Get the objective value
objective_value = model.objVal
# Check if the objective value is approximately zero
if abs(objective_value) < 1e-6:
model.remove(model.getConstrByName("First_Constraint"))
model.remove(model.getConstrByName("Second_Constraint"))
model.remove(model.getConstrByName("Third_Constraint"))
model.remove(model.getConstrByName("Fourth_Constraint"))
model.setObjective(0, GRB.MINIMIZE)
obj = -1 * x[0] + 2 * x[1] -3 * x[2]
model.setObjective(obj, GRB.MINIMIZE)
model.addConstr(x[0] + x[1] + x[2] == 6, "First_Constraint")
model.addConstr(-1 * x[0] + x[1] + 2 * x[2] == 4, "Second_Constraint")
model.addConstr(2 * x[1] + 3 * x[2] == 10, "Third_Constraint")
model.addConstr(x[2] == 2, "Fourth_Constraint")
model.optimize()
for i in range(3):
variable_value = x[i].X # Get the value of the variable
if variable_value > 1e-6:
non_zero_primal += 1
print(f"x[{i}] = {x[i].x}")
else:
print("infeasible")
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Official comment
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Gurobi Staff
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Hi Shahrzad,
It seems like you forgot to call model.optimize() to solve the model before checking if model.status is GRB.OPTIMAL.
Best regards,
Simran0 -
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Dear Simranjit, thank you for your response. You're right, it was a mistake.
Overall, is this approach correct for writing the Two-Phase method?
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Overall it looks correct. Just two points:
1. The call model.setObjective(0, GRB.MINIMIZE) in the Phase 2 is not required. The following two lines are enough to set the original objective of the model
obj = -1 * x[0] + 2 * x[1] -3 * x[2]
model.setObjective(obj, GRB.MINIMIZE)2. In Phase two, instead of removing the constraints and re-adding them again, you can simply change the coefficients of the artificial variables to zero using model.chgCoeff method, for example, if you have
c1 = model.addConstr(x[0] + x[1] + x[2] + R[0] == 6, "First_Constraint")
then to change the coefficient of R[0] to zero in Phase 2, you can call
model.chgCoeff(c1, R[0], 0)
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Thank you so much for your guidance.
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Thank you for your valuable responses.
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