def build_infeasible_cont_model(num_constraints: int = 10,
num_infeasible_sets: int = 20) -> mip.Model:
# build an infeasible model, based on many redundant constraints
mdl = mip.Model(name="infeasible_model_continuous")
var = mdl.add_var(name="x", var_type=mip.CONTINUOUS, lb=-1000, ub=1000)
for idx, rand_constraint in enumerate(np.linspace(1, 1000,
num_constraints)):
crt = mdl.add_constr(
var >= rand_constraint,
name="lower_bound_{0}_l{1}".format(idx, random.randint(1, 6)),
)
logger.debug("added {} to the model".format(crt))
num_constraint_inf = int(num_infeasible_sets / num_constraints)
for idx, rand_constraint in enumerate(
np.linspace(-1000, -1, num_constraint_inf)):
crt = mdl.add_constr(
var <= rand_constraint,
name="upper_bound_{0}_l{1}".format(idx, random.randint(1, 7)),
)
logger.debug("added {} to the model".format(crt))
mdl.emphasis = 1 # feasibility
mdl.preprocess = 1 # -1 automatic, 0 off, 1 on.
# mdl.pump_passes TODO configure to feasibility emphasis
return mdl
def upperbounding_hyperplane(A, b):
A = np.array(A)
b = np.array(b)
N = A.shape[1]
M = A.shape[0]
assert (b.shape[0] == M)
# print(N)
# print(M)
model = mip.Model(solver_name=mip.CBC)
model.verbose = 0
e = [model.add_var(name='e({})'.format(i + 1)) for i in range(M)]
x = [model.add_var(name='x({})'.format(i + 1)) for i in range(N)]
# e = A*x - b
for i in range(M):
e[i] = -1 * b[i]
for j in range(N):
e[i] = e[i] + A[i, j] * x[j]
model += e[i] >= 0
total_error = mip.xsum(e[i] for i in range(M))
model.objective = total_error
model.optimize()
# x_found = np.zeros(N)
x_found = np.array([x[i].x for i in range(N)])
# print(x_found)
return x_found, model.objective_value
def find_optimal_pairs(N, weights) -> list[tuple[int, int]]:
"""
find_optimal_pairs finds an optimal set of pairs of integers between 0 and
N-1 (incl) that minimize the sum of the weights specified for each pair.
"""
pairs = [(i, j) for i in range(N - 1) for j in range(i + 1, N)]
def pairs_containing(k):
return chain(((i, k) for i in range(k)),
((k, i) for i in range(k + 1, N)))
m = mip.Model()
p = {(i, j): m.add_var(var_type=mip.BINARY) for i, j in pairs}
# Constraint: a person can only be in one pair, so sum of all pairs with person k must be 1
for k in range(N):
m += mip.xsum(p[i, j] for i, j in pairs_containing(k)) == 1
m.objective = mip.minimize(
mip.xsum(weights(i, j) * p[i, j] for i, j in pairs))
m.verbose = False
status = m.optimize()
if status != mip.OptimizationStatus.OPTIMAL:
raise Exception("not optimal" + status)
print("Objective value =", m.objective_value)
return [(i, j) for i, j in pairs if p[i, j].x > 0.5]
def het_qp(t, B):
t = np.array(t)
B = np.array(B)
n = t.shape[0]
m = B.shape[0]
assert (B.shape[1] == n)
model = mip.Model(solver_name=mip.CBC)
model.verbose = 0
e = [[
model.add_var(name='e({},{})'.format(i + 1, j + 1)) for j in range(n)
] for i in range(m)]
h_1 = model.add_var(name='h_1')
h_2 = [model.add_var(name='h_2({})'.format(i + 1)) for i in range(m)]
# total_error = model.add_var(name='e_sum')
total_error = 0
for i in range(m):
for j in range(n):
if B[i][j] <= t[-1]:
e[i][j] = t[j] * h_1 + h_2[i] - B[i][j]
model += e[i][j] >= 0
total_error = total_error + e[i][j]
model.objective = total_error
model.optimize()
h1_found = h_1.x
h2_found = np.array([h_2[i].x for i in range(m)])
return h1_found, h2_found
def generate_model():
model = mip.Model(solver_name=solver_id)
# `in_committee` is a binary variable indicating whether `cand` is in the committee
in_committee = [
model.add_var(var_type=mip.BINARY, name=f"cand{cand}_in_committee")
for cand in profile.candidates
]
# find a new committee that has not been found yet by excluding previously found committees
for committee in committees:
model += mip.xsum(in_committee[cand]
for cand in committee) <= committeesize - 1
# note: verbose = 1 causes issues with unittests, seems as if output is printed too late
# and anyway the output does not seem to be very helpful
model.verbose = 0
set_opt_model_func(
model,
profile,
in_committee,
committeesize,
)
# emphasis is optimality:
# activates procedures that produce improved lower bounds, focusing in pruning the search
# tree even if the production of the first feasible solutions is delayed.
model.emphasis = 2
model.opt_tol = ACCURACY
model.max_mip_gap = ACCURACY
model.integer_tol = ACCURACY
return model, in_committee
def estimate_cp(bal_res, de_ads):
df_normal = bal_res.loc[lambda row: row.dp_phased == False]
df_abnormal = bal_res.loc[lambda row: row.dp_phased == True]
ads_abnormal = de_ads[df_abnormal.index]
M_, m_ = np.full(len(bal_res), np.nan), np.full(len(bal_res), np.nan)
hap_dp = df_normal.avg_depths.mean() / 2
for row in df_abnormal.itertuples():
ads = de_ads[row.Index]
mod = mip.Model()
M, m = mod.add_var(var_type=mip.INTEGER,
lb=1), mod.add_var(var_type=mip.INTEGER, lb=1)
eM = [mod.add_var() for i in range(len(ads))]
em = [mod.add_var() for i in range(len(ads))]
for i in range(len(ads)):
mod += ads[i].max() - M * hap_dp >= -eM[i]
mod += ads[i].max() - M * hap_dp <= eM[i]
mod += ads[i].min() - m * hap_dp >= -em[i]
mod += ads[i].min() - m * hap_dp <= em[i]
mod += M >= m
mod.objective = mip.xsum(eM[i] for i in range(len(ads))) + mip.xsum(
em[i] for i in range(len(ads)))
mod.optimize()
M_[row.Index] = M.x
m_[row.Index] = m.x
res = pd.concat(
[bal_res, pd.DataFrame({
'cp': M_ + m_,
'M': M_,
'm': m_
})], axis=1)
return res
def find_optimal_pairs(N, weights) -> (float, list[tuple[int, int]]):
"""
find_optimal_pairs finds an optimal set of pairs of integers between 0 and
N-1 (incl) that minimize the sum of the weights specified for each pair.
Returns the objective value and list of pairs.
"""
pairs = [(i, j) for i in range(N) for j in range(i, N)]
# note: people are excluded from the round by pairing with themselves
def pairs_containing(k):
return chain(((i, k) for i in range(k)), ((k, i) for i in range(k, N)))
m = mip.Model()
p = {(i, j): m.add_var(var_type=mip.BINARY) for i, j in pairs}
# Constraint: a person can only be in one pair, so sum of all pairs with person k must be 1
for k in range(N):
m += mip.xsum(p[i, j] for i, j in pairs_containing(k)) == 1
m.objective = mip.minimize(
mip.xsum(weights[i, j] * p[i, j] for i, j in pairs))
m.verbose = False
status = m.optimize()
if status != mip.OptimizationStatus.OPTIMAL:
raise Exception("not optimal")
return m.objective_value, [(i, j) for i, j in pairs if p[i, j].x > 0.5]
def _compute_integer_image_sizes(image_sizes: List[Size],
layout: Layout) -> List[Size]:
import mip
constraints = layout.get_constraints(image_sizes)
aspect_ratios = [h / w for w, h in image_sizes]
# set up a mixed-integer program, and solve it
n_images = len(image_sizes)
m = mip.Model()
var_widths = [m.add_var(var_type=mip.INTEGER) for _ in range(n_images)]
var_heights = [m.add_var(var_type=mip.INTEGER) for _ in range(n_images)]
for c in constraints:
if c.is_height:
vars = ([var_heights[i] for i in c.positive_ids] +
[-var_heights[i] for i in c.negative_ids])
else:
vars = ([var_widths[i] for i in c.positive_ids] +
[-var_widths[i] for i in c.negative_ids])
m.add_constr(mip.xsum(vars) == c.result)
# the errors come from a deviation in aspect ratio
var_errs = [m.add_var(var_type=mip.CONTINUOUS) for _ in range(n_images)]
for err, w, h, ar in zip(var_errs, var_widths, var_heights, aspect_ratios):
m.add_constr(err == h - w * ar)
# To minimise error, we need to create a convex cost function. Common
# options are either abs(err) or err ** 2. However, both these functions are
# non-linear, so cannot be directly computed in MIP. We can represent abs
# exactly with a type-1 SOS, and approximate ** 2 with a type-2 SOS. Here we
# use abs.
var_errs_pos = [
m.add_var(var_type=mip.CONTINUOUS) for _ in range(n_images)
]
var_errs_neg = [
m.add_var(var_type=mip.CONTINUOUS) for _ in range(n_images)
]
var_abs_errs = [
m.add_var(var_type=mip.CONTINUOUS) for _ in range(n_images)
]
for abs_err, err, err_pos, err_neg in zip(var_abs_errs, var_errs,
var_errs_pos, var_errs_neg):
# err_pos and err_neg are both positive representing each side of the
# abs function. Only one will be non-zero (SOS Type-1).
m.add_constr(err == err_pos - err_neg)
m.add_constr(abs_err == err_pos + err_neg)
m.add_sos([(err_pos, 1), (err_neg, -1)], sos_type=1)
m.objective = mip.minimize(mip.xsum(var_abs_errs))
m.optimize(max_seconds=30)
new_sizes = [
Size(int(w.x), int(h.x)) for w, h in zip(var_widths, var_heights)
]
return new_sizes
def test_conflict_finder_feasible():
mdl = mip.Model(name="feasible_model")
var = mdl.add_var(name="x",
var_type=mip.CONTINUOUS,
lb=-mip.INF,
ub=mip.INF)
mdl.add_constr(var >= 1, "lower_bound")
with pytest.raises(AssertionError, match="model is not linear infeasible"):
cf = ConflictFinder(model=mdl)
def create_model(sudoku: SudokuMatrix,
verbose: int) -> (mip.Model, SudokuVariableTensor):
model = mip.Model()
model.verbose = verbose
variable_tensor = init_model_variables(model)
add_general_sudoku_constraints(model, variable_tensor)
add_predefined_digits_constraints(model, variable_tensor, sudoku)
return model, variable_tensor
def init_model(self, **kwargs):
nb_facilities = self.facility_problem.facility_count
nb_customers = self.facility_problem.customer_count
use_matrix_indicator_heuristic = kwargs.get("use_matrix_indicator_heuristic", True)
if use_matrix_indicator_heuristic:
n_shortest = kwargs.get("n_shortest", 10)
n_cheapest = kwargs.get("n_cheapest", 10)
matrix_fc_indicator, matrix_length = prune_search_space(self.facility_problem,
n_cheapest=n_cheapest,
n_shortest=n_shortest)
else:
matrix_fc_indicator, matrix_length = prune_search_space(self.facility_problem,
n_cheapest=nb_facilities,
n_shortest=nb_facilities)
s = mip.Model(name="facilities", sense=mip.MINIMIZE,
solver_name=self.solver_name)
x = {}
for f in range(nb_facilities):
for c in range(nb_customers):
if matrix_fc_indicator[f, c] == 0:
x[f, c] = 0
elif matrix_fc_indicator[f, c] == 1:
x[f, c] = 1
elif matrix_fc_indicator[f, c] == 2:
x[f, c] = s.add_var(var_type=mip.BINARY,
obj=0,
name="x_" + str((f, c)))
facilities = self.facility_problem.facilities
customers = self.facility_problem.customers
used = s.add_var_tensor((nb_facilities, 1), var_type=GRB.BINARY, name="y")
constraints_customer = {}
for c in range(nb_customers):
constraints_customer[c] = s.add_constr(mip.xsum([x[f, c] for f in range(nb_facilities)]) == 1)
# one facility
constraint_capacity = {}
for f in range(nb_facilities):
for c in range(nb_customers):
s.add_constr(used[f, 0] >= x[f, c])
constraint_capacity[f] = s.add_constr(mip.xsum([x[f, c] * customers[c].demand
for c in range(nb_customers)]) <= facilities[f].capacity)
new_obj_f = mip.LinExpr(const=0.)
new_obj_f.add_expr(mip.xsum([facilities[f].setup_cost * used[f, 0] for f in range(nb_facilities)]))
new_obj_f.add_expr(mip.xsum([matrix_length[f, c] * x[f, c]
for f in range(nb_facilities)
for c in range(nb_customers)]))
s.objective = new_obj_f
self.model = s
self.variable_decision = {"x": x}
self.constraints_dict = {"constraint_customer": constraints_customer,
"constraint_capacity": constraint_capacity}
self.description_variable_description = {"x": {"shape": (nb_facilities, nb_customers),
"type": bool,
"descr": "for each facility/customer indicate"
" if the pair is active, meaning "
"that the customer c is dealt with facility f"}}
self.description_constraint = {"Im lazy."}
print("Initialized")
def mip_model(self, representation, labeled_idx, budget, delta, outlier_count, greedy_indices=None):
model = mip.Model("Core Set Selection")
# set up the variables:
points = {}
outliers = {}
feasible_start = []
for i in range(representation.shape[0]):
if i in labeled_idx:
points[i] = model.add_var(ub=1.0, lb=1.0, var_type=BINARY, name="points_{}".format(i))
else:
points[i] = model.add_var(var_type=BINARY, name="points_{}".format(i))
for i in range(representation.shape[0]):
name = "outliers_{}".format(i)
outliers[i] = model.add_var(var_type=BINARY, name=name)
# outliers[i].start = 0
feasible_start.append((outliers[i], 0.0))
# initialize the solution to be the greedy solution:
if greedy_indices is not None:
for i in greedy_indices:
# points[i].start = 1.0 # gurobi
feasible_start.append((points[i], 1))
model.start = feasible_start
# set the outlier budget:
model.add_constr(xsum(outliers[i] for i in outliers) <= outlier_count, "budget")
# build the graph and set the constraints:
model.add_constr(xsum(points[i] for i in range(representation.shape[0])) == budget, "budget")
neighbors = {}
graph = {}
print("Updating Neighborhoods In MIP Model...")
for i in range(0, representation.shape[0], 1000):
print("At Point " + str(i))
if i + 1000 > representation.shape[0]:
distances = self.get_distance_matrix(representation[i:], representation)
amount = representation.shape[0] - i
else:
distances = self.get_distance_matrix(representation[i:i + 1000], representation)
amount = 1000
distances = np.reshape(distances, (amount, -1))
for j in range(i, i + amount):
graph[j] = [(idx, distances[j - i, idx]) for idx in
np.reshape(np.where(distances[j - i, :] <= delta), (-1))]
neighbors[j] = [points[idx] for idx in np.reshape(np.where(distances[j - i, :] <= delta), (-1))]
neighbors[j].append(outliers[j])
model.add_constr(xsum(neighbors[j]) >= 1, "coverage+outliers")
model.__data = points, outliers
model.emphasis = 1
model.threads = -1
# model.max_seconds = self.max_seconds
return model, graph
def test_conflict_finder():
mdl = mip.Model(name="infeasible_model_continuous")
var = mdl.add_var(name="x", var_type=mip.CONTINUOUS, lb=-mip.INF, ub=mip.INF)
mdl.add_constr(var >= 1, "lower_bound")
mdl.add_constr(var <= 0, "upper_bound")
cf = ConflictFinder(model=mdl)
iis = cf.find_iis()
iis_names = set([crt.name for crt in iis])
assert set(["lower_bound", "upper_bound"]) == iis_names
def test_conflict_finder_iis_additive_method_two_options():
mdl = mip.Model(name="infeasible_model_continuous")
var_x = mdl.add_var(name="x", var_type=mip.CONTINUOUS, lb=-mip.INF, ub=mip.INF)
mdl.add_constr(var_x >= 1, "lower_bound")
mdl.add_constr(var_x <= 0, "upper_bound")
mdl.add_constr(var_x <= -3, "upper_bound_2")
cf = ConflictFinder(model=mdl)
iis = cf.find_iis(method = IISFinderAlgorithm.ADDITIVE_ALGORITHM)
iis_names = set([crt.name for crt in iis])
assert set(["lower_bound", "upper_bound"]) == iis_names or set(["lower_bound", "upper_bound_2"]) == iis_names
def additive_algorithm(self) -> mip.ConstrList:
"""Additive algorithm to find an IIS
Returns:
mip.ConstrList: IIS
"""
# Create some aux models to test feasibility of the set of constraints
aux_model_testing = mip.Model()
for var in self.model.vars:
aux_model_testing.add_var(
name=var.name,
lb=var.lb,
ub=var.ub,
var_type=var.var_type,
# obj= var.obj,
# column=var.column #!! libc++abi.dylib: terminating with uncaught exception of type CoinError
)
aux_model_testing.objective = 1
aux_model_testing.emphasis = 1 # feasibility
aux_model_testing.preprocess = 1 # -1 automatic, 0 off, 1 on.
aux_model_iis = (
aux_model_testing.copy()
) # a second aux model to test feasibility of the incumbent iis
# algorithm start
all_constraints = self.model.constrs
testing_crt_set = mip.ConstrList(model=aux_model_testing) # T
iis = mip.ConstrList(model=aux_model_iis) # I
while True:
for crt in all_constraints:
testing_crt_set.add(crt.expr, name=crt.name)
aux_model_testing.constrs = testing_crt_set
aux_model_testing.optimize()
if aux_model_testing.status == mip.OptimizationStatus.INFEASIBLE:
iis.add(crt.expr, name=crt.name)
aux_model_iis.constrs = iis
aux_model_iis.optimize()
if aux_model_iis.status == mip.OptimizationStatus.INFEASIBLE:
return iis
elif aux_model_iis.status in [
mip.OptimizationStatus.FEASIBLE,
mip.OptimizationStatus.OPTIMAL,
]:
testing_crt_set = mip.ConstrList(
model=aux_model_testing)
for (crt) in (
iis
): # basically this loop is for set T=I // aux_model_iis = iis.copy()
testing_crt_set.add(crt.expr, name=crt.name)
break
def equivalent_tol(self):
"""Return list of components which in series/parallel are within tolerance
of the target value, minimising the number of components in use.
Args:
components: float values of the resistors/capacitors to choose from. A component
value can be used as many times as it occurs in this list.
target: The target value.
series: True for series, false for parallel.
tol: Solved resistance will be in range [(1-tol)*target, (1+tol)*target, %
resistor: True for resistors and inductors, False for capacitors
Returns:
Optimal component values, or empty list if no solution.
"""
tol = self.tolerance/100
# This is what sets the different parallel and series combination
# depending on the component type. Reasoning = Boolean algebra.
condition = (not self.resistor and not self.series) or (self.series and self.resistor)
_target = self.target if condition else 1/self.target
_components = self.components if condition else [1/x for x in self.components]
lower = (1-tol) * self.target if condition else 1/((1+tol) * self.target)
upper = (1+tol) * self.target if condition else 1/((1-tol) * self.target)
m = mip.Model() # Create new mixed integer/linear model.
r_in_use = [m.add_var(var_type=mip.BINARY) for _ in _components]
opt_r = sum([b * r for b, r in zip(r_in_use, _components)])
m += opt_r >= lower
m += opt_r <= upper
m.objective = mip.minimize(mip.xsum(r_in_use))
m.verbose = False
sol_status = m.optimize()
if sol_status != mip.OptimizationStatus.OPTIMAL:
print('No solution found')
return []
r_in_use_sol = [float(v) for v in r_in_use]
r_to_use = [r for r, i in zip(self.components, r_in_use_sol) if i > 0]
solved_values = sum(x for x in r_to_use) if condition else 1/sum(1/x for x in r_to_use)
solved_error = 100 * (solved_values - self.target) / self.target
print(f'{"Resistors/Inductors" if self.resistor else "Capacitors"}; {r_to_use} in {"series" if self.series else "parallel"} '
f'will produce {"resistance/inductance" if self.resistor else "capacitance"} = {solved_values:.3f}'\
f' {"R/I" if self.resistor else "C"}. Aiming for {"R/I" if self.resistor else "C"} = {self.target:.3f}, '
f'error of {solved_error:.2f}%')
return r_to_use
def __init__(self, obj):
self.obj = obj
self.model = mip.Model()
self.getIndex = make_getIndex(obj)
self.objlen = obj['size']
self.constraints = np.zeros(self.objlen)
self.constraints[self.getIndex('Transform', 'T')] = 1
self.direction = ['==']
self.rhs = [1]
self.instructions = []
self.state_order = [['Transform', 'Normal']]
self.boost_on = None
self.boost_num = 0
self.rules = {}
def optimize_player_strategy(player_cards: List[int],
opponent_cards: List[int],
payoff_matrix: Matrix) -> Strategy:
"""
Get the optimal strategy for the player, by solving
a simple linear program based on payoff matrix.
"""
lp = mip.Model("player_strategy", solver_name=mip.CBC)
lp.verbose = False # the problems are simple and we don't need to see the output
x = [
lp.add_var(f"x_{card}", var_type=mip.CONTINUOUS)
for card in player_cards
]
v = lp.add_var("v", var_type=mip.CONTINUOUS, lb=-mip.INF)
for opponent_card in opponent_cards:
transposed_row = [
payoff_matrix[(player_card, opponent_card)]
for player_card in player_cards
]
constraint = (mip.xsum(transposed_row[i] * x_i
for i, x_i in enumerate(x)) - v >= 0)
lp += constraint, f"strategy_against_{opponent_card}"
logging.debug(f"constraint={constraint}")
lp += mip.xsum(x) == 1, "probability_distribution"
lp.objective = mip.maximize(v)
# all variables are continuous so we only need to solve relaxed problem
lp.optimize(max_seconds=30, relax=True)
if lp.status is not mip.OptimizationStatus.OPTIMAL:
logging.error(f"lp.status={lp.status}")
raise RuntimeError(
f"Solver couldn't optimize the problem and returned status {lp.status}"
)
strategy = Strategy(
card_probabilities={
card: lp.var_by_name(f"x_{card}").x
for card in player_cards
},
expected_value=lp.var_by_name("v").x,
)
logging.debug(f"strategy.expected_value={strategy.expected_value}")
logging.debug("\n")
return strategy
def mip_model_subsample(self, data, subsample_num, budget, dist, delta, outlier_count, greedy_indices=None):
model = mip.Model("Core Set Selection")
# calculate neighborhoods:
data_1, data_2 = np.where(dist <= delta)
feasible_start = {}
# set up the variables:
points = {}
outliers = {}
for i in range(data.shape[0]):
if i >= subsample_num:
points[i] = model.add_var(ub=1.0, lb=1.0, var_type=BINARY, name="points_{}".format(i))
else:
points[i] = model.add_var(var_type=BINARY, name="points_{}".format(i))
for i in range(data.shape[0]):
name = "outliers_{}".format(i)
outliers[i] = model.add_var(var_type=BINARY, name=name)
# outliers[i].start = 0
# feasible_start[name] = 0
# initialize the solution to be the greedy solution:
if greedy_indices is not None:
for i in greedy_indices:
# points[i].start = 1.0
feasible_start[points[i].name] = 1
# set up the constraints:
model.add_constr(xsum(points[i] for i in range(data.shape[0])) == budget, "budget")
neighbors = {}
for i in range(data.shape[0]):
neighbors[i] = []
neighbors[i].append(outliers[i])
for i in range(len(data_1)):
neighbors[data_1[i]].append(points[data_2[i]])
for i in range(data.shape[0]):
model.add_constr(xsum(neighbors[i]) >= 1, "coverage+outliers")
model.add_constr(xsum(outliers[i] for i in outliers) <= outlier_count, "budget")
model.objective = xsum(outliers[i] for i in outliers)
model.__data = points, outliers
model.emphasis = 1
# model.max_seconds = self.max_seconds
return model
def get_mip_model_silent():
"""Create a mip model but filter out the Gurobi prints"""
try:
f = io.BytesIO()
with stdout_redirector(f):
m = mip.Model()
m.verbose = 0
return m
except:
logger = get_cli_logger()
logger.error(
'*** ERROR: Failed to start Gurobi. Check if GUROBI_HOME and GRB_LICENSE_FILE are correctly set'
)
logger.error('GUROBI_HOME is currently set to %s',
os.environ.get('GUROBI_HOME', ''))
logger.error('GRB_LICENSE_FILE is currently set to %s',
os.environ.get('GRB_LICENSE_FILE', ''))
exit(1)
def optimizepy():
import mip
from mip import OptimizationStatus
import sys
m = mip.Model()
m.read('ifrum.lp')
m.max_gap = 0.05
status = m.optimize(max_seconds=300)
if status == OptimizationStatus.OPTIMAL:
print('optimal solution cost {} found'.format(m.objective_value))
elif status == OptimizationStatus.FEASIBLE:
print('sol.cost {} found, best possible: {}'.format(m.objective_value, m.objective_bound))
elif status == OptimizationStatus.NO_SOLUTION_FOUND:
print('no feasible solution found, lower bound is: {}'.format(m.objective_bound))
if status == OptimizationStatus.OPTIMAL or status == OptimizationStatus.FEASIBLE:
print('solution:')
for v in m.vars:
if abs(v.x) > 1e-3: # only printing non-zeros
print('{} : {}'.format(v.name, v.x))
def mip_from_std_form(A, b, c):
# initialize
n = len(c)
m = len(b)
ilp = mip.Model()
# variables
x = [
ilp.add_var(name='x({})'.format(i), var_type=mip.INTEGER)
for i in range(n)
]
# constraints
for j in range(m):
a, bi = A[j, :], b[j]
cons = mip.xsum(a[i] * x[i] for i in range(n) if a[i] != 0) <= 0
cons.add_const(-bi)
ilp.add_constr(cons)
# objective
ilp.objective = mip.minimize(mip.xsum(c[i] * x[i] for i in range(n)))
return ilp
def pl_tft(n):
m = mip.Model()
m.verbose = 1
E = range(n)
colors = range(1, 2)
x = {s: m.add_var(var_type=mip.BINARY) for s in combinations(E, 4)}
c = {(k, s): m.add_var(var_type=mip.BINARY)
for k in colors for s in combinations(E, 4)}
# c[k, s] == True iff s has color k
for p in combinations(E, 2):
S_i = []
for s in combinations(E, 4):
if p[0] in s and p[1] in s:
S_i.append(x[s])
m += mip.xsum(S_i) == 2
for s in combinations(E, 4):
m += x[s] <= mip.xsum(c[(k, s)] for k in colors) <= 1
for k in colors:
for s1 in combinations(E, 4):
for s2 in combinations(E, 4):
set_s1, set_s2 = set(s1), set(s2)
if len(set_s1 & set_s2) != 0 and set_s1 != set_s2:
m += c[k, s1] + c[k, s2] <= 1
# m.objective = mip.minimize(mip.xsum(c))
print(f"{m.num_cols} variables")
print(f"{m.num_rows} constraints")
m.optimize()
for k, s in c:
if c[k, s] == 1:
print(k, s)
def optimal_comb(api: GBD, query, runtimes, timeout, k):
result = api.query_search(query, [], runtimes)
result = [[
int(float(val))
if is_number(val) and float(val) < float(timeout) else int(2 * timeout)
for val in row[1:]
] for row in result]
dataset = pd.DataFrame(result, columns=runtimes)
dataset = dataset[(dataset != 2 * timeout).any(axis='columns')]
model = mip.Model()
instance_solver_vars = [[
model.add_var(f'x_{i}_{j}', var_type=mip.BINARY)
for j in range(dataset.shape[1])
] for i in range(dataset.shape[0])]
solver_vars = [
model.add_var(f's_{j}', var_type=mip.BINARY)
for j in range(dataset.shape[1])
]
for var_list in instance_solver_vars: # per-instance constraints
model.add_constr(mip.xsum(var_list) == 1)
for j in range(dataset.shape[1]): # per-solver-constraints
model.add_constr(
mip.xsum(instance_solver_vars[i][j]
for i in range(dataset.shape[0])) <=
dataset.shape[0] * solver_vars[j]) # "Implies" in Z3
model.add_constr(mip.xsum(solver_vars) <= k)
model.objective = mip.minimize(
mip.xsum(instance_solver_vars[i][j] * int(dataset.iloc[i, j])
for i in range(dataset.shape[0])
for j in range(dataset.shape[1])))
print(dataset.sum().min())
print(model.optimize())
print(model.objective_value)
for index, item in enumerate([var.x for var in solver_vars]):
if item > 0:
print(runtimes[index])
def _build_model(self, structure: Atoms, solver_name: str,
verbose: bool) -> mip.Model:
"""
Build a Python-MIP model based on the provided structure
Parameters
----------
structure
atomic configuration
solver_name
'gurobi', alternatively 'grb', or 'cbc', searches for
available solvers if not informed
verbose
whether to display solver messages on the screen
"""
# Create cluster maps
self._create_cluster_maps(structure)
# Initiate MIP model
model = mip.Model('CE', solver_name=solver_name)
model.solver.set_mip_gap(0) # avoid stopping prematurely
model.solver.set_emphasis(2) # focus on finding optimal solution
model.preprocess = 2 # maximum preprocessing
# Set verbosity
model.verbose = int(verbose)
# Spin variables (remapped) for all atoms in the structure
xs = {
i: model.add_var(name='atom_{}'.format(i), var_type=BINARY)
for subl in self._active_sublattices for i in subl.indices
}
ys = [
model.add_var(name='cluster_{}'.format(i), var_type=BINARY)
for i in range(len(self._cluster_to_orbit_map))
]
# The objective function is added to 'model' first
model.objective = mip.minimize(mip.xsum(self._get_total_energy(ys)))
# Connect cluster variables to spin variables with cluster constraints
# TODO: don't create cluster constraints for singlets
constraint_count = 0
for i, cluster in enumerate(self._cluster_to_sites_map):
orbit = self._cluster_to_orbit_map[i]
parameter = self._transformed_parameters[orbit + 1]
assert parameter != 0
if len(cluster) < 2 or parameter < 0: # no "downwards" pressure
for atom in cluster:
model.add_constr(
ys[i] <= xs[atom],
'Decoration -> cluster {}'.format(constraint_count))
constraint_count = constraint_count + 1
if len(cluster) < 2 or parameter > 0: # no "upwards" pressure
model.add_constr(
ys[i] >= 1 - len(cluster) + mip.xsum(xs[atom]
for atom in cluster),
'Decoration -> cluster {}'.format(constraint_count))
constraint_count = constraint_count + 1
for sym, subl in zip(self._count_symbols, self._active_sublattices):
# Create slack variable
slack = model.add_var(name='slackvar_{}'.format(sym),
var_type=INTEGER,
lb=0,
ub=len(subl.indices))
# Add slack constraint
model.add_constr(slack <= -1, name='{} slack'.format(sym))
# Set species constraint
model.add_constr(mip.xsum([xs[i]
for i in subl.indices]) + slack == -1,
name='{} count'.format(sym))
# Update the model so that variables and constraints can be queried
if model.solver_name.upper() in ['GRB', 'GUROBI']:
model.solver.update()
return model
def get_mip_model_silent():
f = io.BytesIO()
with stdout_redirector(f):
m = mip.Model()
m.verbose = 0
return m
for p in conf.participants:
for s in sessions.keys():
for talk in s:
if talk in p.preferences:
W[p, s] += 1/3
for s, times in sessions.items():
for t in times:
if t<0 or t>=conf.num_hours:
continue
all_times.add(t)
A[s, t] = 1
print(f'Finished setting up input matrices. {int(time.time()-start_time)}s')
print(f' A has {len(A)} entries.')
print(f' W has {len(W)} entries.')
# create the model
model = mip.Model()
# Add decision variables
S = {}
V = {}
for (s, t) in A.keys():
S[s, t] = model.add_var(var_type=mip.BINARY)
for p in conf.participants:
if (p, s) in W:
V[p, s, t] = model.add_var(var_type=mip.BINARY)
print(f"Finished setting up decision variables. {int(time.time()-start_time)}s")
print(f" S: {len(S)}, V: {len(V)}, total {len(S)+len(V)}")
# Add constraints
for s in sessions.keys():
model += mip.xsum(S[s, t] for t in all_times if (s, t) in S)==1 # only assign talk to 1 time
for t in all_times:
model += mip.xsum(S[s, t] for s in sessions.keys() if (s, t) in S)<=max_track_vector[t] # only use at most max tracks
def init_model(self, **kwargs):
greedy_start = kwargs.get("greedy_start", True)
verbose = kwargs.get("verbose", False)
use_cliques = kwargs.get("use_cliques", False)
if greedy_start:
if verbose:
print("Computing greedy solution")
greedy_solver = GreedyColoring(self.coloring_problem,
params_objective_function=self.params_objective_function)
result_store = greedy_solver.solve(strategy=NXGreedyColoringMethod.best, verbose=verbose)
self.start_solution = result_store.get_best_solution_fit()[0]
else:
if verbose:
print("Get dummy solution")
solution = self.coloring_problem.get_dummy_solution()
self.start_solution = solution
nb_colors = self.start_solution.nb_color
color_model = mip.Model("color",
sense=mip.MINIMIZE,
solver_name=self.solver_name)
colors_var = {}
range_node = range(self.number_of_nodes)
range_color = range(nb_colors)
for node in self.nodes_name:
for color in range_color:
colors_var[node, color] = color_model.add_var(var_type=BINARY,
obj=0,
name="x_" + str((node, color)))
one_color_constraints = {}
for n in range_node:
one_color_constraints[n] = color_model.add_constr(xsum([colors_var[n, c] for c in range_color]) == 1)
cliques = []
g = self.graph.to_networkx()
if use_cliques:
for c in nx.algorithms.clique.find_cliques(g):
cliques += [c]
cliques = sorted(cliques, key=lambda x: len(x), reverse=True)
else:
cliques = [[e[0], e[1]] for e in g.edges()]
cliques_constraint = {}
index_c = 0
opt = color_model.add_var(var_type=INTEGER, lb=0, ub=nb_colors, obj=1)
if use_cliques:
for c in cliques[:100]:
cliques_constraint[index_c] = color_model.add_constr(xsum([(color_i + 1) * colors_var[node, color_i]
for node in c
for color_i in range_color])
>= sum([i + 1 for i in range(len(c))]))
cliques_constraint[(index_c, 1)] = color_model.add_constr(xsum([colors_var[node, color_i]
for node in c
for color_i in range_color])
<= opt)
index_c += 1
edges = g.edges()
constraints_neighbors = {}
for e in edges:
for c in range_color:
constraints_neighbors[(e[0], e[1], c)] = \
color_model.add_constr(colors_var[e[0], c] + colors_var[e[1], c] <= 1)
for n in range_node:
color_model.add_constr(xsum([(color_i + 1) * colors_var[n, color_i] for color_i in range_color]) <= opt)
self.model = color_model
self.variable_decision = {"colors_var": colors_var}
self.constraints_dict = {"one_color_constraints": one_color_constraints,
"constraints_neighbors": constraints_neighbors}
self.description_variable_description = {"colors_var": {"shape": (self.number_of_nodes, nb_colors),
"type": bool,
"descr": "for each node and each color,"
" a binary indicator"}}
self.description_constraint["one_color_constraints"] = {"descr": "one and only one color "
"should be assignated to a node"}
self.description_constraint["constraints_neighbors"] = {"descr": "no neighbors can have same color"}
def multiple_pairs(dist_matrices, voi_ind_to_S_sets, threshold=None, api='py-mip', solver='pulp', variable_num_tol=0.001, max_seconds=np.inf):
"""
Doc string to be written.
"""
voi_indices = list(voi_ind_to_S_sets.keys())
n_voi = len(voi_indices)
S_sets = list(voi_ind_to_S_sets.values())
M = np.max(np.max(abs(dist_matrices), axis=0))
a, b, c = dist_matrices.shape
if b == c:
J = a
n = b
dist_matrices = dist_matrices.transpose((1, 2, 0))[voi_indices]
else:
n = b
J = c
voi_to_Q_indices = {voi: np.array([int(i) for i in np.concatenate((range(0, voi), range(voi+1, n))) if i not in voi_ind_to_S_sets[voi]]) for voi in voi_indices}
if variable_num_tol is not None:
up_bound = int(np.math.ceil(1 / variable_num_tol))
variable_num_tol = 1 / up_bound
cat='Integer'
else:
up_bound=1
cat='Continuous'
if threshold is not None:
if b == c:
raise ValueError('dist_matrices not shaped correctly')
temp_dist_matrices = np.zeros((n_voi, n, J))
for i, voi in enumerate(voi_indices):
temp_ranks = evaluate_best_vertices(dist_matrices[i], np.arange(J), S_sets[i])
temp_dist_matrices[i] = edit_dist_matrices(dist_matrices[i], S_sets[i], temp_ranks, threshold)
if api == 'pulp':
model=pulp.LpProblem(sense=pulp.LpMinimize)
inds = pulp.LpVariable.dicts("indicators for elements not in S",
('voi' + str(voi) + str(q) for voi in voi_indices for q in voi_to_Q_indices[voi]),
cat='Integer',
upBound=1,
lowBound=0
)
weights = pulp.LpVariable.dicts("weights for representations",
(j for j in range(J)),
cat=cat,
upBound=up_bound,
lowBound=0
)
model += (
pulp.lpSum(
[inds[('voi' + str(voi) + str(q))] for voi in voi_indices for q in voi_to_Q_indices[voi]]
)
)
model += (
pulp.lpSum(
[weights[(j)] for j in range(J)]
) == up_bound
)
for i, voi in enumerate(voi_indices):
dist_matrix = dist_matrices[i, :, :]
for s in voi_ind_to_S_sets[voi]:
for q in voi_to_Q_indices[voi]:
model += (
pulp.lpSum(
[weights[(j)] * dist_matrix[s, j] for j in range(J)]
)
<=
pulp.lpSum(
[weights[(j)] * dist_matrix[q, j] for j in range(J)]
)
+
pulp.lpSum(inds[('voi' + str(voi) + str(q))] * M * up_bound)
)
try:
if solver == 'pulp':
model.solve()
elif solver == 'coin_cmd':
model.solve(solver=pulp.COIN_CMD())
alpha_hat = np.array([w.varValue for w in weights.values()])
except Exception as e:
print(e)
return None
elif api=='py-mip':
model = mip.Model(sense=mip.MINIMIZE)
# Need to fix inds
inds = [[model.add_var(name='inds', var_type=mip.BINARY) for q in voi_to_Q_indices[voi]] for voi in voi_indices]
# if variable_num_tol is None:
weights = [model.add_var(name='weights', lb=0.0, ub=up_bound, var_type=cat) for j in range(J)]
model += mip.xsum(w for w in weights) == up_bound
# else:
# weights = [model.add_var(name='weights', lb=0, ub=up_bound, var_type='I') for j in range(J)]
# model += mip.xsum(w for w in weights) == up_bound
for i, voi in enumerate(voi_indices):
dist_matrix = dist_matrices[i, :, :]
for s in voi_ind_to_S_sets[voi]:
for k, q in enumerate(voi_to_Q_indices[voi]):
model += mip.xsum(weights[j] * dist_matrix[s, j] for j in range(J)) <= mip.xsum(weights[j] * dist_matrix[q, j] for j in range(J)) + inds[i][k]*M*up_bound
model.objective = mip.xsum(mip.xsum(i for i in ind) for ind in inds)
model.optimize(max_seconds=max_seconds)
alpha_hat = np.array([w.x for w in weights])
if alpha_hat[0] is None:
return None
else:
return alpha_hat / np.sum(alpha_hat)
def combine_representations(dist_matrix, voi_index, S_indices, return_new_dists=True, threshold=None, solver='coin_cmd', api='py-mip', variable_num_tol=0.001, max_seconds=np.inf):
"""
A function to find the weights of optimal linear combination of representations.
Input
dist_matrix - np.array (shape=(n, J))
Array containing the distances between the vertex of interest and the other n - 1
vertices.
voi_index - int
Index of vertex of interest.
S_indices - array-like
Indices of the vertices that should be at the top of the
nomination list for the vertex of interest.
return_new_dists - bool
If true, returns both the weights and the corresponding distance matrix.
threshold - maximum value of the rank of an element of S_indices.
solver - solver to use. in {'coin_cmd'}
api - api to use. in {'gurobi', 'py-mip', 'pulp'}
variable_num_tol - float in (0, 1]. resolution of the approximation of the continuous weights.
If None, continuous weights are found.
max_seconds - float in (0, inf)
Return
weights - np.array (length=J)
Array containing the coefficients for the optimal distance function.
-- optional -- new_dists - np.array (length=n)
Array containing the distances after applying the learned weight vector.
"""
# Grab the shape of the data that was passed int
n, J = dist_matrix.shape
# Pre-process the data so that there are no elements of S_indices that are above threshold
if threshold is not None:
ranks = evaluate_best_vertices(dist_matrix, vertices=np.arange(J), s_star=S_indices)
dist_matrix = edit_dist_matrices(dist_matrix, S_indices, ranks, threshold)
# Grab the maximum value of dist_matrix (to be used as an upper bound later)
M = np.max(abs(dist_matrix))
# Grab the number of elements known to be similar to voi_index
S = len(S_indices)
# Define an array of integers corresponding to elements not in S_indices
Q_indices = np.array([int(i) for i in np.concatenate((range(0, voi_index), range(voi_index+1, n))) if i not in S_indices])
# Grab the number of elements not known to be similar to voi_index
Q = len(Q_indices)
# We can either use continuous weights for the representations or use discrete approximation
if variable_num_tol is not None:
# Here, we are using a discrete approximation
# variable_num_tol is in the interval (0, 1]. If variable_num_tol is close to 0 that means
# we want our approximation to be of a high resolution. To achieve this, we define 1 / variable_num_tol
# to be the maximum value that a particular weight can take on.
# i.e. with variable_num_tol = 0.1, the weights can take on values 0.0, 0.1, 0.2, 0.3, .., 1.
# We normalize later.
up_bound = int(np.math.ceil(1 / variable_num_tol))
variable_num_tol = 1 / up_bound
cat='Integer'
else:
# Here, we let the weights be continuous
up_bound=1
cat='Continuous'
# We've implemented the ILP in 3 different APIs: pulp, py-mip and gurobi.
# Gurobi seems to be the industry standard but licensing is a bit prohibitive.
# Each API is relatively similar. First, you define a set of variables.
# Then, using these variables, you define an objective function and a set of constraints that you assign to a model object.
if api == 'pulp':
# Define a model.
model=pulp.LpProblem(sense=pulp.LpMinimize)
# Define indicator variables (as defined in section 1.2 of https://arxiv.org/pdf/2005.10700.pdf) for every vertex
# That is not in S_indices.
# NB: i am more than happy to walk through the paper if that would be helpful!
inds = pulp.LpVariable.dicts("indicators for elements not in S",
(q for q in Q_indices),
cat='Integer',
upBound=1,
lowBound=0
)
# Define non-negative weight variables for each of the representations.
weights = pulp.LpVariable.dicts("weights for representations",
(j for j in range(J)),
cat=cat,
upBound=up_bound,
lowBound=0
)
# Set the objective function.
model += (
pulp.lpSum(
[inds[(q)] for q in Q_indices]
)
)
# Add constraint that the weights must sum to the upper bound defined by variable_num_tol.
model += (
pulp.lpSum(
[weights[(j)] for j in range(J)]
) == up_bound
)
# Add constraint that elements of S_indices should be closer than elements not in S_indices (or, the Q_indices)
for s in S_indices:
for q in Q_indices:
model += (
pulp.lpSum(
[weights[(j)] * dist_matrix[s, j] for j in range(J)]
)
<=
pulp.lpSum(
[weights[(j)] * dist_matrix[q, j] for j in range(J)]
)
+
pulp.lpSum(inds[(q)] * M * up_bound)
)
# Different solvers for api == 'pulp'
try:
if solver == 'pulp':
model.solve()
elif solver == 'coin_cmd':
model.solve(solver=pulp.COIN_CMD())
alpha_hat = np.array([w.varValue for w in weights.values()])
except Exception as e:
print(e)
return None
alpha_hat = np.array([w.varValue for w in weights.values()])
elif api=='gurobi':
model= gp.Model()
model.setParam('OutputFlag', 0)
model.setParam('TimeLimit', max_seconds)
ind = model.addVars(Q, vtype=GRB.BINARY, name='ind')
model.setObjective(gp.quicksum(ind), GRB.MINIMIZE)
w = model.addVars(J, lb=0, ub=1, vtype=GRB.CONTINUOUS, name='w')
model.addConstr(w.sum() == 1)
for s in S_indices:
temp_s = gp.tupledict([((i), dist_matrix[s, i]) for i in range(J)])
for i, q in enumerate(Q_indices):
temp_q = gp.tupledict([((i), dist_matrix[q, i]) for i in range(J)])
model.addConstr(w.prod(temp_s) <= w.prod(temp_q) + ind[i]*M)
model.optimize()
alpha_hat = np.array([i.X for i in list(w.values())])
elif api=='py-mip':
model = mip.Model(sense=mip.MINIMIZE)
inds = [model.add_var(name='inds', var_type=mip.BINARY) for q in range(Q)]
# if variable_num_tol is None:
weights = [model.add_var(name='weights', lb=0.0, ub=up_bound, var_type=cat) for j in range(J)]
model += mip.xsum(w for w in weights) == 1
# else:
# weights = [model.add_var(name='weights', lb=0, ub=up_bound, var_type='I') for j in range(J)]
# model += mip.xsum(w for w in weights) == up_bound
for s in S_indices:
for i, q in enumerate(Q_indices):
model += mip.xsum(weights[j] * dist_matrix[s, j] for j in range(J)) <= mip.xsum(weights[j] * dist_matrix[q, j] for j in range(J)) + inds[i]*M*up_bound
model.objective = mip.xsum(ind for ind in inds)
model.optimize(max_seconds=max_seconds)
alpha_hat = np.array([w.x for w in weights])
else:
raise ValueError("api %s not implemented"%(api))
# Return the new distances if told to do so.
if return_new_dists:
if np.sum(alpha_hat == 0) == J:
return alpha_hat, dist_matrix
else:
return alpha_hat, np.average(dist_matrix, axis=1, weights=alpha_hat)
if alpha_hat[0] is None:
return None
else:
# Normalize
return alpha_hat / np.sum(alpha_hat)