Knapsack: Exercise 1.2 - Improved Solution Display

The knapsack.py example shown in the tutorial uses model.pprint() to see the value of the solution variables. Note that the Pyomo value function should be used to get the floating point value of Pyomo modeling components (e.g., print(value(model.x[i]))). We can also print the value of the items selected (the objective), and the total weight.

Learning Objectives:

• Learn to extract and display solution values using value() function

• Understand how to interpret optimization results

• Practice accessing decision variable values

• See better formatting for solution output

import pyomo.environ as pyo

A = ['hammer', 'wrench', 'screwdriver', 'towel']
b = {'hammer':8, 'wrench':3, 'screwdriver':6, 'towel':11}
w = {'hammer':5, 'wrench':7, 'screwdriver':4, 'towel':3}
W_max = 14

model = pyo.ConcreteModel()
model.x = pyo.Var( A, within=pyo.Binary )

model.obj = pyo.Objective(
    expr = sum( b[i]*model.x[i] for i in A ), 
    sense = pyo.maximize )

model.weight_con = pyo.Constraint(
    expr = sum( w[i]*model.x[i] for i in A ) <= W_max )

opt = pyo.SolverFactory('cbc')
opt_success = opt.solve(model)

total_weight = sum( w[i]*pyo.value(model.x[i]) for i in A )
print('Total Weight:', total_weight)
print('Total Benefit:', pyo.value(model.obj))

print('%12s %12s' % ('Item', 'Selected'))
print('=========================')
for i in A:
    acquired = 'No'
    if pyo.value(model.x[i]) >= 0.5:
        acquired = 'Yes'
    print('%12s %12s' % (i, acquired))
print('-------------------------')

Total Weight: 12.0
Total Benefit: 25.0
        Item     Selected
=========================
      hammer          Yes
      wrench           No
 screwdriver          Yes
       towel          Yes
-------------------------