examples/notebook/contrib/covering_opl.ipynb
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First, you must install ortools package in this colab.
%pip install ortools
Set covering problem in Google CP Solver.
This example is from the OPL example covering.mod ''' Consider selecting workers to build a house. The construction of a house can be divided into a number of tasks, each requiring a number of skills (e.g., plumbing or masonry). A worker may or may not perform a task, depending on skills. In addition, each worker can be hired for a cost that also depends on his qualifications. The problem consists of selecting a set of workers to perform all the tasks, while minimizing the cost. This is known as a set-covering problem. The key idea in modeling a set-covering problem as an integer program is to associate a 0/1 variable with each worker to represent whether the worker is hired. To make sure that all the tasks are performed, it is sufficient to choose at least one worker by task. This constraint can be expressed by a simple linear inequality. '''
Solution from the OPL model (1-based) ''' Optimal solution found with objective: 14 crew= {23 25 26} '''
Solution from this model (0-based): ''' Total cost 14 We should hire these workers: 22 24 25 '''
Compare with the following models:
This model was created by Hakan Kjellerstrand ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/
import sys
from ortools.constraint_solver import pywrapcp
def main():
# Create the solver.
solver = pywrapcp.Solver("Set covering")
#
# data
#
nb_workers = 32
Workers = list(range(nb_workers))
num_tasks = 15
Tasks = list(range(num_tasks))
# Which worker is qualified for each task.
# Note: This is 1-based and will be made 0-base below.
Qualified = [[1, 9, 19, 22, 25, 28, 31],
[2, 12, 15, 19, 21, 23, 27, 29, 30, 31, 32],
[3, 10, 19, 24, 26, 30, 32], [4, 21, 25, 28, 32],
[5, 11, 16, 22, 23, 27, 31], [6, 20, 24, 26, 30, 32],
[7, 12, 17, 25, 30, 31], [8, 17, 20, 22, 23],
[9, 13, 14, 26, 29, 30, 31], [10, 21, 25, 31, 32],
[14, 15, 18, 23, 24, 27, 30, 32], [18, 19, 22, 24, 26, 29, 31],
[11, 20, 25, 28, 30, 32], [16, 19, 23, 31],
[9, 18, 26, 28, 31, 32]]
Cost = [
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5,
5, 6, 6, 6, 7, 8, 9
]
#
# variables
#
Hire = [solver.IntVar(0, 1, "Hire[%i]" % w) for w in Workers]
total_cost = solver.IntVar(0, nb_workers * sum(Cost), "total_cost")
#
# constraints
#
solver.Add(total_cost == solver.ScalProd(Hire, Cost))
for j in Tasks:
# Sum the cost for hiring the qualified workers
# (also, make 0-base)
b = solver.Sum([Hire[c - 1] for c in Qualified[j]])
solver.Add(b >= 1)
# objective: Minimize total cost
objective = solver.Minimize(total_cost, 1)
#
# search and result
#
db = solver.Phase(Hire, solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE)
solver.NewSearch(db, [objective])
num_solutions = 0
while solver.NextSolution():
num_solutions += 1
print("Total cost", total_cost.Value())
print("We should hire these workers: ", end=" ")
for w in Workers:
if Hire[w].Value() == 1:
print(w, end=" ")
print()
print()
solver.EndSearch()
print()
print("num_solutions:", num_solutions)
print("failures:", solver.Failures())
print("branches:", solver.Branches())
print("WallTime:", solver.WallTime())
main()