def find_transform(x, y, limit, threshold=1e-7):
"""
find a integer solution to ax + b - cxy - dy = 0
this will give us the mobius transform: T(x) = y
:param x: numeric constant to check
:param y: numeric manipulation of constant
:param limit: range to look at
:param threshold: optimal solution threshold.
:return MobiusTransform in case of success or None.
"""
x1 = x
x2 = dec(1.0)
x3 = -x * y
x4 = -y
solver = Solver('mobius', Solver.CBC_MIXED_INTEGER_PROGRAMMING)
a = solver.IntVar(-limit, limit, 'a')
b = solver.IntVar(-limit, limit, 'b')
c = solver.IntVar(-limit, limit, 'c')
d = solver.IntVar(-limit, limit, 'd')
f = solver.NumVar(0, 1, 'f')
solver.Add(f == (a * x1 + b * x2 + c * x3 + d * x4))
solver.Add(a * x1 + b >=
1) # don't except trivial solutions and remove some redundancy
solver.Minimize(f)
status = solver.Solve()
if status == Solver.OPTIMAL:
if abs(solver.Objective().Value()) <= threshold:
res_a, res_b, res_c, res_d = int(a.solution_value()), int(b.solution_value()),\
int(c.solution_value()), int(d.solution_value())
ret = MobiusTransform(
np.array([[res_a, res_b], [res_c, res_d]], dtype=object))
ret.normalize()
return ret
else:
return None
def _solve_optimization(self, solver: pywraplp.Solver) -> None:
# The MIP solver is usually fast (milliseconds). If we hit a weird problem,
# accept a suboptimal solution after 10 seconds.
solver.SetTimeLimit(10000)
status = solver.Solve()
if status == pywraplp.Solver.INFEASIBLE:
raise Exception("Infeasible problem")
elif status == pywraplp.Solver.NOT_SOLVED:
raise Exception("Problem unsolved")
def _attempt_to_improve_var_bounds_one_hs(solver: pywraplp.Solver,
coefficient_part: str, is_leq: bool,
right_hand_side: str):
coefficient_part = coefficient_part.strip()
if re.match(_REGEXP_SINGLE_VAR_NAME_ALL, coefficient_part):
if is_leq:
solver.LookupVariable(coefficient_part).SetUb(
float(right_hand_side))
else:
solver.LookupVariable(coefficient_part).SetLb(
float(right_hand_side))
def main():
# Create the linear solver with the GLOP backend.
solver = Solver('simple_lp_program', Solver.GLOP_LINEAR_PROGRAMMING)
# Create the variables x and y.
x = solver.NumVar(0, 1, 'x')
y = solver.NumVar(0, 2, 'y')
print('Number of variables =', solver.NumVariables())
# Create a linear constraint, 0 <= x + y <= 2.
ct = solver.Constraint(0, 2, 'ct')
ct.SetCoefficient(x, 1)
ct.SetCoefficient(y, 1)
print('Number of constraints =', solver.NumConstraints())
# Create the objective function, 3 * x + y.
objective = solver.Objective()
objective.SetCoefficient(x, 3)
objective.SetCoefficient(y, 1)
objective.SetMaximization()
solver.Solve()
print('Solution:')
print('Objective value =', objective.Value())
print('x =', x.solution_value())
print('y =', y.solution_value())
def _solve_optimization(self, solver: pywraplp.Solver) -> bool:
# The MIP solver is usually fast (milliseconds). If we hit a weird problem,
# accept a suboptimal solution after 10 seconds.
solver.SetTimeLimit(10000)
status = solver.Solve()
if status == pywraplp.Solver.INFEASIBLE:
logger.warning("Optimization problem is infeasible")
return False
elif status == pywraplp.Solver.NOT_SOLVED:
logger.warning("Optimization problem could not be solved in time")
return False
return True
def solve_problem() -> None:
solver: Solver = Solver("simple_mip_program",
Solver.CBC_MIXED_INTEGER_PROGRAMMING)
x: Any = solver.IntVar(0, 100, "x")
y: Any = solver.IntVar(0, 100, "y")
solver.Add(1 * x + 2 * y <= 40)
solver.Add(4 * x + 4 * y <= 80)
solver.Add(3 * x + 1 * y <= 50)
solver.Maximize(x * 5.0 + y * 4.0)
status: Any = solver.Solve()
if status == Solver.OPTIMAL or status == Solver.FEASIBLE:
print("Solution: OK")
print("Objective value =", solver.Objective().Value())
if x.solution_value() > 0.5:
print("x =", x.solution_value())
print("y =", y.solution_value())
print("Time = ", solver.WallTime(), " milliseconds")
else:
print("The problem does not have an optimal solution.")
def _parse_objective_function(solver: pywraplp.Solver, core_line: str,
line_nr: int, var_names: set):
spl_colon = core_line.split(":", maxsplit=1)
objective = solver.Objective()
# Set maximization / minimization if specified
if len(spl_colon) == 1:
raise ValueError(
"Objective function on line %d must start with \"max:\" or \"min:\"."
% line_nr)
else:
if spl_colon[0] != "max" and spl_colon[0] != "min":
raise ValueError(
"Objective function on line %d must start with \"max:\" or \"min:\"."
% line_nr)
elif spl_colon[0] == "max":
objective.SetMaximization()
else:
objective.SetMinimization()
# Set the remainder
coefficient_part = spl_colon[1].strip()
# Finally set the coefficients of the objective
constant = _set_coefficients(solver, objective, coefficient_part,
line_nr, var_names)
objective.SetOffset(constant)
def _declare_constraint(
solver: pywraplp.Solver,
group: "Group",
variables: typing.Tuple[typing.Tuple[pywraplp.Variable]],
) -> None:
higher_groups = group.get_simultaneous_groups_of_higher_cycle()
if higher_groups:
# fixed duration of group
summed_active_transitions_of_group = Group._sum_active_transitions_of_group(
group, higher_groups)
# fixed duration of higher groups
summed_transitions_of_higher_groups = sum(
Group._calculate_duration_of_n_phases(higher_group,
higher_group.attack)
for higher_group in higher_groups)
summed_transitions_of_higher_groups += Group._calculate_duration_of_n_phases(
higher_groups[-1], higher_groups[-1].release)
difference_of_duration = (summed_active_transitions_of_group -
summed_transitions_of_higher_groups)
constraint = sum(
Group._calculate_duration_of_n_phases(higher_group, var)
for var, higher_group in zip(variables[1], higher_groups))
constraint = constraint - (Group._calculate_duration_of_n_phases(
group, variables[0][0]))
solver.Add(constraint == difference_of_duration)
def _declare_variable(self, solver: pywraplp.Solver, nth_cycle: int,
nth_index: int) -> None:
return solver.NumVar(
MIN_N_PHASES_FOR_SUSTAIN,
MIN_N_PHASES_FOR_SUSTAIN * MAX_N_MIN_PHASES_FOR_SUSTAIN,
self._get_variable_name(nth_cycle, nth_index),
)
def solve_problem() -> None:
solver: Solver = Solver("simple_mip_program",
Solver.CBC_MIXED_INTEGER_PROGRAMMING)
backet: Dict = {j: solver.BoolVar(f"x{j}") for j in range(5)}
solver.Add(
solver.Sum(list(VOLUMES[j] * backet[j]
for j in range(len(VOLUMES)))) <= CAPASITY)
solver.Maximize(
solver.Sum(list(VALUES[j] * backet[j] for j in range(len(VOLUMES)))))
status: Any = solver.Solve()
if status == Solver.OPTIMAL or status == Solver.FEASIBLE:
print("Solution: OK")
print("Objective value =", solver.Objective().Value())
print("culculate Time = ", solver.WallTime(), " milliseconds")
print("select item")
for j in range(len(VOLUMES)):
print(j, backet[j].solution_value())
print("total value")
print(
sum(VALUES[j] * backet[j].solution_value()
for j in range(len(VOLUMES))))
else:
print("The problem does not have an optimal solution.")
def _add_stock_variables(num_types: int, num_time_periods: int, solver: Solver) \
-> Dict[V, Variable]:
"""Create stock variables.
A stock variable $s^t_p$ is a non-negative real variable which represents the number of
items of type $t$ on stock in time period $p$.
:param num_types: the number of considered types
:param num_time_periods: the number of considered time periods
:param solver: the underlying solver for which to built the variables
:return: A dictionary mapping each stock variable to its solver variable
"""
stock_vars = dict()
for (item_type, time_period) in product(range(num_types),
range(-1, num_time_periods)):
stock_vars[V(type=item_type, period=time_period)] = \
solver.NumVar(lb=0., ub=solver.infinity(), name=f's_{item_type}_{time_period}')
module_logger.info(f'Created {len(stock_vars)} stock variables.')
return stock_vars
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 _parse_declaration(solver: pywraplp.Solver, core_line: str, line_nr: int,
var_names: set):
spl_whitespace = core_line.split(maxsplit=1)
if spl_whitespace[0] != "int":
raise ValueError("Declaration on line %d should start with \"int \"." %
line_nr)
if len(spl_whitespace) != 2:
raise ValueError("Declaration on line %d has no variables." % line_nr)
spl_variables = spl_whitespace[1].split(",")
for raw_var in spl_variables:
clean_var = raw_var.strip()
if not re.match(_REGEXP_SINGLE_VAR_NAME_ALL, clean_var):
raise ValueError(
"Non-permitted variable name (\"%s\") on line %d." %
(clean_var, line_nr))
if clean_var in var_names:
raise ValueError("Variable \"%s\" declared again on line %d." %
(clean_var, line_nr))
var_names.add(clean_var)
solver.IntVar(-solver.infinity(), solver.infinity(), clean_var)
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 _add_production_variables(num_types: int, num_time_periods: int,
solver: Solver) -> Dict[V, Variable]:
"""Create production variables.
A production variable $x^t_p$ is a binary variable which is one if and only if an item of
type $t$ is produced in time period $p$.
:param num_types: the number of considered types
:param num_time_periods: the number of considered time periods
:param solver: the underlying solver for which to built the variables
:return: A dictionary mapping each production variable to its solver variable
"""
production_vars = dict()
for (item_type, time_period) in product(range(num_types),
range(num_time_periods)):
production_vars[V(type=item_type,
period=time_period)] = solver.BoolVar(
name=f'x_{item_type}_{time_period}')
module_logger.info(
f'Created {len(production_vars)} production variables.')
return production_vars
def _add_configuration_variables(num_types: int, num_time_periods: int, solver: Solver) \
-> Dict[V, Variable]:
"""Create configuration variables.
A configuration variable $y^t_p$ is a binary variable which is one if and only if the
machine is configured for type $t$ in time period $p$.
:param num_types: the number of considered types
:param num_time_periods: the number of considered time periods
:param solver: the underlying solver for which to built the variables
:return: A dictionary mapping each configuration tuple to its solver variable
"""
configuration_vars = dict()
for (item_type, time_period) in product(range(num_types),
range(num_time_periods)):
configuration_vars[V(type=item_type,
period=time_period)] = solver.BoolVar(
name=f'y_{item_type}_{time_period}')
module_logger.info(
f'Created {len(configuration_vars)} configuration variables.')
return configuration_vars
def solve_problem() -> None:
solver: Solver = Solver("simple_mip_program",
Solver.CBC_MIXED_INTEGER_PROGRAMMING)
amount: Dict = {}
for i in range(3):
for j in range(4):
amount[i, j] = solver.IntVar(0, 50, f"val{i}_{j}")
amount_w1, amount_w2, amount_w3 = get_quantity_carried_out(amount)
solver.Add(amount_w1 <= 35)
solver.Add(amount_w2 <= 41)
solver.Add(amount_w3 <= 42)
amount_f1, amount_f2, amount_f3, amount_f4 = get_quantity_carried_in(
amount)
solver.Add(amount_f1 >= 28)
solver.Add(amount_f2 >= 29)
solver.Add(amount_f3 >= 31)
solver.Add(amount_f4 >= 25)
solver.Minimize(
solver.Sum(
[amount[i, j] * COST[i][j] for i in range(3) for j in range(4)]))
status: Any = solver.Solve()
if status == Solver.OPTIMAL or status == Solver.FEASIBLE:
print("Solution: OK")
print("Objective value =", solver.Objective().Value())
print("=============================================")
for i in range(3):
for j in range(4):
if amount[i, j].SolutionValue() > 0:
print(i, j, amount[i, j].SolutionValue())
print("Time = ", solver.WallTime(), " milliseconds")
else:
print("The problem does not have an optimal solution.")
def _add_transition_variables(num_types: int, num_time_periods: int, solver: Solver) \
-> Dict[W, Variable]:
"""Create transition variables.
A transition variable $u^ij_p$ is a binary variable which is one if and only if the
machine's configuration changes from type $i$ to type $j$ in time period $p$.
:param num_types: the number of considered types
:param num_time_periods: the number of considered time periods
:param solver: the underlying solver for which to built the variables
:return: A dictionary mapping each transition variable to its solver variable
"""
transition_vars = dict()
for type_i, type_j, time_period in product(range(num_types),
range(num_types),
range(1, num_time_periods)):
transition_vars[W(from_type=type_i,
to_type=type_j,
from_period=time_period - 1,
to_period=time_period)] = solver.BoolVar(
name=f'u_{type_i}_{type_j}_{time_period}')
module_logger.info(
f'Created {len(transition_vars)} transition variables.')
return transition_vars
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.
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.')
# 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 _parse_constraint(solver: pywraplp.Solver, core_line: str, line_nr: int,
var_names: set):
# We don't care about the coefficient name before the colon
constraint_part = core_line
spl_colon = core_line.split(":", maxsplit=1)
if len(spl_colon) > 1:
constraint_part = spl_colon[1].strip()
# Equality constraint
if constraint_part.find("=") >= 0 and constraint_part.find(
"<=") == -1 and constraint_part.find(">=") == -1:
equality_spl = constraint_part.split("=")
if len(equality_spl) > 2:
raise ValueError(
"Equality constraint on line %d has multiple equal signs." %
line_nr)
if not _is_valid_constant_float(equality_spl[1]):
raise ValueError(
"Right hand side (\"%s\") of equality constraint on line %d is not a float "
"(e.g., variables are not allowed there!)." %
(equality_spl[1], line_nr))
equal_value = float(equality_spl[1])
constraint = solver.Constraint(equal_value, equal_value)
constant = _set_coefficients(solver, constraint, equality_spl[0],
line_nr, var_names)
constraint.SetLb(constraint.Lb() - constant)
constraint.SetUb(constraint.Ub() - constant)
_attempt_to_improve_var_bounds_two_hs(solver, equality_spl[0], True,
equality_spl[1], equality_spl[1])
# Inequality constraints
else:
# Replace all of these inequality signs, because they are equivalent
constraint_part = constraint_part.replace("<=", "<").replace(">=", ">")
# lower bound < ... < upper bound
if constraint_part.count("<") == 2:
spl = constraint_part.split("<")
if not _is_valid_constant_float(spl[0]):
raise ValueError(
"Left hand side (\"%s\") of inequality constraint on line %d is not a float "
"(e.g., variables are not allowed there!)." %
(spl[0], line_nr))
if not _is_valid_constant_float(spl[2]):
raise ValueError(
"Right hand side (\"%s\") of inequality constraint on line %d is not a float "
"(e.g., variables are not allowed there!)." %
(spl[2], line_nr))
constraint = solver.Constraint(float(spl[0]), float(spl[2]))
constant = _set_coefficients(solver, constraint, spl[1], line_nr,
var_names)
constraint.SetLb(constraint.Lb() - constant)
constraint.SetUb(constraint.Ub() - constant)
_attempt_to_improve_var_bounds_two_hs(solver, spl[1], True, spl[0],
spl[2])
# upper bound > ... > lower bound
elif constraint_part.count(">") == 2:
spl = constraint_part.split(">")
if not _is_valid_constant_float(spl[0]):
raise ValueError(
"Left hand side (\"%s\") of inequality constraint on line %d is not a float "
"(e.g., variables are not allowed there!)." %
(spl[0], line_nr))
if not _is_valid_constant_float(spl[2]):
raise ValueError(
"Right hand side (\"%s\") of inequality constraint on line %d is not a float "
"(e.g., variables are not allowed there!)." %
(spl[2], line_nr))
constraint = solver.Constraint(float(spl[2]), float(spl[0]))
constant = _set_coefficients(solver, constraint, spl[1], line_nr,
var_names)
constraint.SetLb(constraint.Lb() - constant)
constraint.SetUb(constraint.Ub() - constant)
_attempt_to_improve_var_bounds_two_hs(solver, spl[1], False,
spl[0], spl[2])
# ... < upper bound
elif constraint_part.count("<") == 1:
spl = constraint_part.split("<")
if not _is_valid_constant_float(spl[1]):
raise ValueError(
"Right hand side (\"%s\") of inequality constraint on line %d is not a float "
"(e.g., variables are not allowed there!)." %
(spl[1], line_nr))
constraint = solver.Constraint(-solver.infinity(), float(spl[1]))
constant = _set_coefficients(solver, constraint, spl[0], line_nr,
var_names)
constraint.SetUb(constraint.Ub() - constant)
_attempt_to_improve_var_bounds_one_hs(solver, spl[0], True, spl[1])
# ... > lower bound
elif constraint_part.count(">") == 1:
spl = constraint_part.split(">")
if not _is_valid_constant_float(spl[1]):
raise ValueError(
"Right hand side (\"%s\") of inequality constraint on line %d is not a float "
"(e.g., variables are not allowed there!)." %
(spl[1], line_nr))
constraint = solver.Constraint(float(spl[1]), solver.infinity())
constant = _set_coefficients(solver, constraint, spl[0], line_nr,
var_names)
constraint.SetLb(constraint.Lb() - constant)
_attempt_to_improve_var_bounds_one_hs(solver, spl[0], False,
spl[1])
# ...
elif constraint_part.count(">") == 0 and constraint_part.count(
"<") == 0:
raise ValueError(
"No (in)equality sign present for constraint on line %d." %
line_nr)
# Some strange combination
else:
raise ValueError(
"Too many (in)equality signs present for constraint on line %d."
% line_nr)
def init_model():
global _MODEL
_MODEL = Solver("No name", Solver.CBC_MIXED_INTEGER_PROGRAMMING)
def _set_coefficients(solver: pywraplp.Solver, objective_or_constraint,
coefficient_part: str, line_nr: int, var_names: set):
# Strip the coefficient whitespace
remainder = coefficient_part.strip()
if len(remainder) == 0:
raise ValueError("No variables present in equation on line %d." %
line_nr)
# All variables found
var_names_found = set()
running_constant_sum = 0.0
had_at_least_one_variable = False
while len(remainder) != 0:
# Combination sign
coefficient = 1.0
combination_sign_match = re.search(r"^[-+]", remainder)
if combination_sign_match is not None:
if combination_sign_match.group() == "-":
coefficient = -1.0
remainder = remainder[1:].strip()
# Real sign
sign_match = re.search(r"^[-+]", remainder)
if sign_match is not None:
if sign_match.group() == "-":
coefficient = coefficient * -1.0
remainder = remainder[
1:] # There is no strip() here, as it must be directly in front of the mantissa
# Mantissa and exponent
mantissa_exp_match = re.search(r"^(\d+(\.\d*)?|\.\d+)([eE][-+]?\d+)?",
remainder)
whitespace_after = False
if mantissa_exp_match is not None:
coefficient = coefficient * float(mantissa_exp_match.group())
remainder = remainder[mantissa_exp_match.span()[1]:]
stripped_remainder = remainder.strip()
if len(remainder) != len(stripped_remainder):
whitespace_after = True
remainder = stripped_remainder
# Variable name
var_name_match = re.search(_REGEXP_SINGLE_VAR_NAME_START, remainder)
if var_name_match is not None:
# It must have had at least one variable
had_at_least_one_variable = True
# Retrieve clean variable name
clean_var = var_name_match.group()
var_names.add(clean_var)
if clean_var in var_names_found:
raise ValueError(
"Variable \"%s\" found more than once on line %d." %
(clean_var, line_nr))
var_names_found.add(clean_var)
solver_var = solver.LookupVariable(clean_var)
if solver_var is None:
solver_var = solver.NumVar(-solver.infinity(),
solver.infinity(), clean_var)
# Set coefficient
objective_or_constraint.SetCoefficient(solver_var, coefficient)
# Strip what we matched
remainder = remainder[var_name_match.span()[1]:]
stripped_remainder = remainder.strip()
whitespace_after = False
if len(remainder) != len(stripped_remainder):
whitespace_after = True
remainder = stripped_remainder
elif mantissa_exp_match is None:
raise ValueError(
"Cannot process remainder coefficients of \"%s\" on line %d." %
(remainder, line_nr))
else:
running_constant_sum += coefficient
# At the end of each element there either:
# (a) Must be whitespace (e.g., x1 x2 <= 10)
# (b) The next combination sign (e.g., x1+x2 <= 10)
# (c) Or it was the last one, as such remainder is empty (e.g., x1 <= 10)
if len(remainder) != 0 and not whitespace_after and remainder[
0:1] != "-" and remainder[0:1] != "+":
raise ValueError(
"Unexpected next character \"%s\" on line %d (expected whitespace or "
"combination sign character)." % (remainder[0:1], line_nr))
# There must have been at least one variable
if not had_at_least_one_variable:
raise ValueError(
"Not a single variable present in the coefficients on line %d." %
line_nr)
return running_constant_sum