def __init__(self, prob_input: Input, solver_id: str, solver_output: bool):
self.prob_input = prob_input
self.solver_id = solver_id
self.solver = Solver.CreateSolver(solver_id)
self.production_vars = None
self.configuration_vars = None
self.stock_vars = None
self.transition_vars = None
self.pred_configuration_vars = None
self.succ_configuration_vars = None
if solver_output:
self.solver.EnableOutput()
else:
self.solver.SuppressOutput()
def cap_mip(customers, facilities, max_time=60):
n_fac = len(facilities)
n_cust = len(customers)
solver = Solver.CreateSolver("FacilityLocation", "SCIP")
x = []
y = []
for f in range(n_fac):
y.append([solver.BoolVar(f"y_{f}_{c}") for c in range(n_cust)])
x.append(solver.BoolVar(f"x_{f}"))
caps = [f.capacity for f in facilities]
setup = [f.setup_cost for f in facilities]
dist = distance_matrix(customers, facilities).astype(int)
demands = [c.demand for c in customers]
for f in range(n_fac):
for c in range(n_cust):
solver.Add(y[f][c] <= x[f])
for c in range(n_cust):
solver.Add(sum([y[f][c] for f in range(n_fac)]) == 1)
for f in range(n_fac):
solver.Add(sum([y[f][c] * demands[c] for c in range(n_cust)]) <= caps[f])
obj = 0
for f in range(n_fac):
obj += setup[f] * x[f]
obj += sum([dist[f][c] * y[f][c] for c in range(n_cust)])
solver.Minimize(obj)
STATUS = {
Solver.FEASIBLE: "FEASIBLE",
Solver.UNBOUNDED: "UNBOUNDED",
Solver.BASIC: "BASIC",
Solver.INFEASIBLE: "INFEASIBLE",
Solver.NOT_SOLVED: "NOT_SOLVED",
Solver.OPTIMAL: "OPTIMAL",
}
solver.SetTimeLimit(max_time * 1000)
status = solver.Solve()
STATUS[status]
a = []
for f in range(n_fac):
a.append([y[f][c].solution_value() for c in range(n_cust)])
sol = np.array(a).argmax(axis=0)
return sol, STATUS[status]
def cap_mip2(customers,
facilities,
max_time=60,
min_fac=None,
max_fac=None,
k_neigh=None):
n_fac = len(facilities)
n_cust = len(customers)
solver = Solver.CreateSolver("FacilityLocation", "SCIP")
if min_fac is None:
min_fac = min_facilities(customers, facilities)
print(f'Minimum Facilities: {min_fac}')
est_fac = est_facilities(customers, facilities)
est_fac = max(5, min_fac)
print('Estimated Facilities:', est_fac)
if k_neigh is None:
k_neigh = n_fac // est_fac * 2
k_neigh = min(k_neigh, n_fac // 2)
print(f'Only using {k_neigh} nearest facilities')
# Estimate Customers per Facilitiy
cpf = n_cust // min_fac
cpf = np.clip(cpf, 2, n_cust // 2)
# Define Variables
x = []
y = []
for f in range(n_fac):
y.append([solver.BoolVar(f"y_{f}_{c}") for c in range(n_cust)])
x.append(solver.BoolVar(f"x_{f}"))
caps = np.array([f.capacity for f in facilities])
setup = np.array([f.setup_cost * 100 for f in facilities])
dist = distance_matrix(customers, facilities) * 100
dist = dist.astype(int)
demands = np.array([c.demand for c in customers])
# Problem Analysis
free_setup = np.where(caps == 0)[0]
is_fixed_setup = True if np.std(caps[caps > 0]) == 0 else False
# Add Constraints
print('\t Adding Constaints')
# If facility is closed then it is not connected to any customer
for f in range(n_fac):
for c in range(n_cust):
solver.Add(y[f][c] <= x[f])
# Each customer is connected to only one facility
for c in range(n_cust):
solver.Add(sum([y[f][c] for f in range(n_fac)]) == 1)
# The demand is not more than the capacity of the facility
for f in range(n_fac):
solver.Add(
sum([y[f][c] * demands[c]
for c in range(n_cust)]) <= caps[f] * x[f])
solver.Add(
sum([y[f][c] * demands[c] for c in range(n_cust)]) <= caps[f])
# Customers per facility
for f in range(n_fac):
solver.Add(sum([y[f][c] for c in range(n_cust)]) <= n_cust * x[f])
# The free facilities must be open
for f in free_setup:
solver.Add(x[f] == 1)
# Customer can ONLY connect to nearby facilities
for c in range(n_cust):
idx = np.argsort(dist[:, c])
for f in idx[k_neigh:]:
solver.Add(y[f][c] == 0)
print('\t Adding Covercut Constaints')
# Cover cut for customers which can be connected to a facility
# round1 = []
# round2 = []
# for f in range(n_fac):
# argsort = np.argsort(dist[f, :])
# idx = argsort[:cpf]
# if sum(demands[idx]) > caps[f]:
# round1.append(f)
# solver.Add(sum([y[f][c] for c in idx]) <= (cpf - 1))
# if cpf > 4:
# k = int(cpf * .9)
# idx = argsort[:k]
# if sum(demands[idx]) > caps[f]:
# round2.append(f)
# solver.Add(sum([y[f][c] for c in idx]) <= (k - 1))
# print(round1)
# print(round2, flush=True)
# Maximum Facility open
solver.Add(sum(x) >= min_fac)
if max_fac is not None:
solver.Add(sum(x) <= max_fac)
# solver.Add(sum(x)>=2)
# Define objective
obj = 0
for f in range(n_fac):
# Setup cost
if not is_fixed_setup:
obj += setup[f] * x[f]
# Service cost
obj += sum([dist[f][c] * y[f][c] for c in range(n_cust)])
solver.Minimize(obj)
STATUS = {
Solver.FEASIBLE: "FEASIBLE",
Solver.UNBOUNDED: "UNBOUNDED",
Solver.BASIC: "BASIC",
Solver.INFEASIBLE: "INFEASIBLE",
Solver.NOT_SOLVED: "NOT_SOLVED",
Solver.OPTIMAL: "OPTIMAL",
}
solver.SetTimeLimit(max_time * 1000)
# Solve
print('\t Starting the Solver')
status = solver.Solve()
STATUS[status]
# Retreive values
a = []
for f in range(n_fac):
a.append([y[f][c].solution_value() for c in range(n_cust)])
# Convert solution matrix to facility index
sol = np.array(a).argmax(axis=0)
return sol, STATUS[status]
#!/bin/python
from ortools.linear_solver import pywraplp
from ortools.linear_solver.pywraplp import Solver
# A person needs three nutrients. Let's assume they are vitamins A, B and C.
Nutrition = [2000, 300, 430]
# They can be supplied by four foods. The first number if the calories supplied
# by a food type. The remaining three numbers are the nutrients.
Foods = [['Trout', 600, 203, 92, 100], ['CB Sandwich', 350, 90, 84, 230],
['Burrito', 250, 270, 80, 512], ['Hamburger', 500, 500, 90, 210]]
# A person needs a certain minimum calories.
MinCalories = 2500
solver = Solver.CreateSolver('diet', 'CBC')
# The decision variables. How much quantity of each food typu should a person
# consume?
consumption = [None] * len(Foods)
for i in range(0, len(Foods)):
consumption[i] = solver.IntVar(1, solver.infinity(), Foods[i][0])
# The objective function is to minimize the number of calories.
objf = solver.Objective()
for i in range(0, len(Foods)):
objf.SetCoefficient(consumption[i], Foods[i][1])
objf.SetMinimization()
# Add constraints. Unlike the previous examples where we had our constraints
# given to us as inequalities, here we will have to build them from the given
# data.
# certain number of items.
#
# Suppose that we are given items of a certain weight. They should be
# transported through wagons of a certain capacity. What is the least number
# of wagons that we should hire to carry all goods?
itemWts = [48, 30, 19, 36, 36, 27, 42, 42, 36, 24, 30]
maxwt = 100
# We ensure that every item can be fitted in a wagon. That is, none of them
# has a weight more than the wagon's capacity.
from ortools.linear_solver import pywraplp
from ortools.linear_solver.pywraplp import Solver
solver = Solver.CreateSolver('bin-packing', 'CBC')
# The decision variables are of the form x_{ij}. They take a value 1 if
# item i is put in wagon j, 0 otherwise.
nItems = len(itemWts)
nWagons = nItems
x = {}
for i in range(0, nItems):
for j in range(0, nWagons):
vname = f'x[{i}, {j}]'
x[(i, j)] = solver.IntVar(0, 1, vname)
# Recall that we need at most as many wagons as we have items. w[i] is 1
# is wagon i is used.
w = [None] * nWagons
# The data.
nResources = 7
nItems = 12
resourceAvailability = [18209, 7692, 1333, 924, 26638, 61188, 13360]
itemValue = [96, 76, 56, 11, 86, 10, 66, 86, 83, 12, 9, 81]
resourceUse = [
[19, 1, 10, 1, 1, 14, 152, 11, 1, 1, 1, 1],
[ 0, 4, 53, 0, 0, 80, 0, 4, 5, 0, 0, 0],
[ 4, 660, 3, 0, 30, 0, 3, 0, 4, 90, 0, 0],
[ 7, 0, 18, 6, 770, 330, 7, 0, 0, 6, 0, 0],
[ 0, 20, 0, 4, 52, 3, 0, 0, 0, 5, 4, 0],
[ 0, 0, 40, 70, 4, 63, 0, 0, 60, 0, 4, 0],
[ 0, 32, 0, 0, 0, 5, 0, 3, 0, 660, 0, 9]]
solver = Solver.CreateSolver('multi-knapsack', 'CBC')
# How many numbers of each items should be packed? Each one of these is a
# decision variable.
take = [None] * nItems
for i in range(0, nItems):
take[i] = solver.IntVar(0, solver.infinity(), f'take[{i}]')
# Build the objective function.
objf = solver.Objective()
for i in range(0, nItems):
objf.SetCoefficient(take[i], itemValue[i])
objf.SetMaximization()
for i in range(0, nResources):
[5, 7, 9, 2, 1],
[18, 4, -9, 10, 12],
[4, 7, 3, 8, 5],
[5, 13, 16, 3, -7],
]
data['bounds'] = [250, 285, 211, 315]
data['obj_coeffs'] = [7, 8, 2, 9, 6]
data['num_vars'] = 5
data['num_constraints'] = 4
return data
data = create_data_model()
solver = Solver.CreateSolver('mip', 'CBC')
# Quite like in the case of the 'Diet problem' the decision variables are
# created as elements of a list.
x = [None] * data['num_vars']
for i in range(0, len(x)):
x[i] = solver.IntVar(0, solver.infinity(), f'x[{i}]')
print(f'Number of variables = {solver.NumVariables()}')
# Build the constraints.
for i in range(0, data['num_constraints']):
cn = solver.Constraint(0, data['bounds'][i], f'cn[{i}]')
for j in range(0, data['num_vars']):
cn.SetCoefficient(x[j], data['constraint_coeffs'][i][j])
print(f'Number of constraints = {solver.NumConstraints()}')
def _compute_compact_linearisation_sets(self, *, z_weight: float, f_weight: float) \
-> Tuple[Dict[int, List[V]], List[Tuple[V, V]]]:
"""Computes sets F and B_k used in Liberti's compact formulation."""
_solver = Solver.CreateSolver(self.solver_id)
f_vars = dict()
z_vars = dict()
N = bidict()
for time_period in range(self.prob_input.num_time_periods):
for item_type in range(self.prob_input.num_types):
N[V(type=item_type, period=time_period)] = 1 + len(N)
M = lambda i: (j for j in N.values() if i <= j)
K = list(range(self.prob_input.num_time_periods))
# create f_ij \in [0,1] for all 1 <= i <= j <= n
for i in N.values():
for j in M(i):
f_vars[(i, j)] = _solver.NumVar(lb=0.,
ub=1.,
name=f'f_{str(i)}{str(j)}')
# create z_ik \in {0,1} for all k \in K, 1 <= i <= n
for k in K:
for i in N.values():
z_vars[(i, k)] = _solver.BoolVar(name=f'z_{str(i)}{str(k)}')
# add constraints: f_ij = 1 \forall (i,j) \in E
for var in self.transition_vars.keys():
i = N[V(type=var.from_type, period=var.from_period)]
j = N[V(type=var.to_type, period=var.to_period)]
_solver.Add(f_vars[(i, j)] == 1, name='cons_10')
# add constraints: f_ij >= z_jk \forall k \in K, i \in A_k, j \in N, i <= j
for k in K:
A_k = [
N[V(type=item_type, period=k)]
for item_type in range(self.prob_input.num_types)
]
for i in A_k:
for j in M(i):
lhs = f_vars[(i, j)]
rhs = z_vars[(j, k)]
_solver.Add(lhs >= rhs, name='cons_11')
# add constraints: f_ji >= z_jk \forall k \in K, i \in A_k, j \ín N, j < i
for k in K:
A_k = [
N[V(type=item_type, period=k)]
for item_type in range(self.prob_input.num_types)
]
for i in A_k:
for j in (j for j in N.values() if j < i):
lhs = f_vars[(j, i)]
rhs = z_vars[(j, k)]
_solver.Add(lhs >= rhs, name='cons_12')
# add constraints: \sum_{k: i \in A_k} z_jk >= f_ij \forall 1 <= i <= j <= n
for i in N.values():
for j in M(i):
k = N.inverse[i].period
lhs = z_vars[(j, k)]
rhs = f_vars[(i, j)]
_solver.Add(lhs >= rhs, name='cons_13')
# add constraints: \sum_{k: j \in A_k} z_ik >= f_ij \forall 1 <= i <= j <= n
for i in N.values():
for j in M(i):
k = N.inverse[j].period
lhs = z_vars[(i, k)]
rhs = f_vars[(i, j)]
_solver.Add(lhs >= rhs, name='cons_14')
# add objective
z_obj = _solver.Sum(z_weight * var for var in z_vars.values())
f_obj = _solver.Sum(f_weight * var for var in f_vars.values())
_solver.Minimize(z_obj + f_obj)
# solve
status = _solver.Solve()
if status == Solver.OPTIMAL:
B = defaultdict(list)
for i, k in (key for key, var in z_vars.items()
if var.solution_value() > 0.99):
B[k].append(N.inverse[i])
F = [(N.inverse[i], N.inverse[j])
for (i, j), var in f_vars.items()
if var.solution_value() > 0.99]
return B, F
else:
raise RuntimeError('No optimal solution found.')
