Solving an Optimization Problem with Python – Step by Step

In this example, we are going to solve a typical Constraint Optimization problem. In the previous tutorial, we tool a simple example of just one constraint.

Example 1: Maximize the function 2x + 2y + 3z with respect to the following constraints:

Note: Since we are performing integer optimization, we must make sure the coefficients of the first constraint are all integer. We can achieve this by multiplying through by 2.

So let’s now take the steps

Step 1: Declare the model

 # Declare the Model
from ortools.sat.python import cp_model
model = cp_model.CpModel()

Step 2: Define the variables

# Define the variables
num_vars = 3
x = model.NewIntVar(0, 50, 'x')
y = model.NewIntVar(0, 50, 'y')
z = model.NewIntVar(0, 50, 'z')

Step 3: Create the constraints

# Set up the constraints
model.Add(2*x + 7*y + 3*z <= 50)
model.Add(3*x - 5*y + 7*z <= 45)
model.Add(5*x + 2*y - 6*z <= 37)

Step 4: Define the cost function

# Define the objective function 2x + 2y + 3z
model.Maximize(2*x + 2*y + 3*z)

Step 5: Invoke the solver

# Invoke the solver
solver = cp_model.CpSolver()
status = solver.Solve(model)

Step 6: Display the results

# Display the results
if status == cp_model.OPTIMAL:
    print('Value of objective function: %i' % solver.ObjectiveValue())
    print('x = %i' %solver.Value(x))
    print('y = %i' %solver.Value(y))
    print('z = %i' %solver.Value(z))

The output would be as shown below:

Value of objective function: 35
x = 7
y = 3
z = 5

Complete program is given below: