def setup(self, solver):
variables = self.variables
coefficients = self.coefficients
sign = self.sign
rhs = self.rhs
name = self.name
if coefficients:
lhs = xsum([
variable.get_var(solver) * coefficient
for variable, coefficient in zip(variables, coefficients)
])
else:
lhs = xsum([var.get_var(solver) for var in variables])
if isinstance(rhs, MIPVariable):
rhs = rhs.get_var(solver)
if sign == SolverSign.EQ:
solver += (lhs == rhs, name) if name else lhs == rhs
elif sign == SolverSign.NOT_EQ:
solver += (lhs != rhs, name) if name else lhs != rhs
elif sign == SolverSign.GTE:
solver += (lhs >= rhs, name) if name else lhs >= rhs
elif sign == SolverSign.LTE:
solver += (lhs <= rhs, name) if name else lhs <= rhs
else:
raise SolverException('Incorrect constraint sign')
def test_cutting_stock(solver: str):
n = 10 # maximum number of bars
L = 250 # bar length
m = 4 # number of requests
w = [187, 119, 74, 90] # size of each item
b = [1, 2, 2, 1] # demand for each item
# creating the model
model = Model(solver_name=solver)
x = {(i, j): model.add_var(obj=0,
var_type=INTEGER,
name="x[%d,%d]" % (i, j))
for i in range(m) for j in range(n)}
y = {
j: model.add_var(obj=1, var_type=BINARY, name="y[%d]" % j)
for j in range(n)
}
# constraints
for i in range(m):
model.add_constr(xsum(x[i, j] for j in range(n)) >= b[i])
for j in range(n):
model.add_constr(xsum(w[i] * x[i, j] for i in range(m)) <= L * y[j])
# additional constraints to reduce symmetry
for j in range(1, n):
model.add_constr(y[j - 1] >= y[j])
# optimizing the model
model.optimize()
# sanity tests
assert model.status == OptimizationStatus.OPTIMAL
assert abs(model.objective_value - 3) <= 1e-4
assert sum(x.x for x in model.vars) >= 5
def set_linear_coefficients(self, coefficients):
if self.problem is None:
raise Exception(
'Can\'t change coefficients if objective is not associated with a model.'
)
self.problem.update()
model = self.problem.problem
expr = model.objective.expr
names = set(var.name for var in coefficients)
obj = mip.xsum(model.var_by_name('v_' + var.name) * coef
for var, coef in coefficients.items()) \
+ mip.xsum(var * coef for var, coef in expr.items()
if var.name[2:] not in names) \
+ model.objective.const
# TODO: why does this not work? It would likely be faster
# obj_update = mip.xsum(model.var_by_name('v_' + var.name) * coef
# for var, coef in coefficients.items()) \
# - mip.xsum(-var * coef for var, coef in expr.items()
# if var.name[2:] in names)
# model.objective.add_expr(obj_update)
self._changed_expression.update(coefficients)
model.objective = obj
def basic_cuts_plus_epsilon(self, S, a, k):
# right side
rs = 0
for j in S:
rs += self.instance.times[j][a] * self.x[j][a][1]
# left side
ls = 0
soma1 = 0
for j in range(len(S)):
for i in range(j + 1, len(S)):
soma1 += self.instance.times[S[i]][a] * self.instance.times[
S[j]][a]
soma1 += self.instance.e[k][a] * self.p(S, a)
ls += soma1
soma2 = 0
for j in S:
if (isinstance(self.y[j][k][a][0], int) == False):
soma2 += self.y[j][k][a][1] * max(
self.instance.e[k][a] - self.instance.e[j][a], 0)
else:
return 0
ls -= soma2 * self.p(S, a)
cuts = 0
if (ls - rs) > 0.00001: # if rs < ls:
return xsum(self.instance.times[j][a] * self.x[j][a][0]
for j in S) + xsum(self.y[j][k][a][0] * max(
self.instance.e[k][a] - self.instance.e[j][a], 0)
for j in S) * self.p(S, a) >= soma1
return 0
def set_opt_model_func(model, profile, in_committee, committeesize):
load = {}
for cand in profile.candidates:
for i, voter in enumerate(profile):
load[(voter, cand)] = model.add_var(lb=0.0,
ub=1.0,
var_type=mip.CONTINUOUS,
name=f"load{i}-{cand}")
# constraint: the committee has the required size
model += mip.xsum(in_committee[cand]
for cand in profile.candidates) == committeesize
for cand in profile.candidates:
for voter in profile:
if cand not in voter.approved:
load[(voter, cand)] = 0
# a candidate's load is distributed among his approvers
for cand in profile.candidates:
model += (mip.xsum(
voter.weight * load[(voter, cand)] for voter in profile
if cand in profile.candidates) >= in_committee[cand])
loadbound = model.add_var(lb=0,
ub=committeesize,
var_type=mip.CONTINUOUS,
name="loadbound")
for voter in profile:
model += mip.xsum(load[(voter, cand)]
for cand in voter.approved) <= loadbound
# maximizing the negative distance makes code more similar to the other methods here
model.objective = mip.maximize(-loadbound)
def solve(active: list, centers: list, sets: list, M: int) -> list:
N, K = len(active), len(sets)
### model and variables
m = Model(sense=MAXIMIZE, solver_name=CBC)
# whether the ith set is picked
x = [m.add_var(name=f"x{i}", var_type=BINARY) for i in range(K)]
# whether the ith point is covered
y = [m.add_var(name=f"y{i}", var_type=BINARY) for i in range(N)]
### constraints
m += xsum(x) == M, "number_circles"
for i in range(N):
# if yi is covered, at least one set needs to have it
included = [x[k] for k in range(K) if active[i] in sets[k]]
m += xsum(included) >= y[i], f"inclusion{i}"
### objective: maximize number of circles covered
m.objective = xsum(y[i] for i in range(N))
m.emphasis = 2 # emphasize optimality
m.verbose = 1
status = m.optimize()
circles = [centers[i] for i in range(K) if x[i].x >= 0.99]
covered = {active[i] for i in range(N) if y[i].x >= 0.99}
return circles, covered
def set_opt_model_func(model, profile, in_committee, committeesize,
previously_found_committees, scorefct):
max_hamming_distance = model.add_var(
var_type=mip.INTEGER,
lb=0,
ub=profile.num_cand,
name="max_hamming_distance",
)
model += mip.xsum(in_committee[cand]
for cand in profile.candidates) == committeesize
for voter in profile:
not_approved = [
cand for cand in profile.candidates
if cand not in voter.approved
]
# maximum Hamming distance is greater of equal than the Hamming distances
# between individual voters and the committee
model += max_hamming_distance >= mip.xsum(
1 - in_committee[cand] for cand in voter.approved) + mip.xsum(
in_committee[cand] for cand in not_approved)
# find a new committee that has not been found before
for committee in previously_found_committees:
model += mip.xsum(in_committee[cand]
for cand in committee) <= committeesize - 1
# maximizing the negative distance makes code more similar to the other methods here
model.objective = mip.maximize(-max_hamming_distance)
def mip_optimization(cal_df, y, constrain=3, daily_weights=None):
"""Mixed integer linear programming optimization with constraints.
Args:
y (numpy.ndarray): sum of daily features (dim=#ofdays)
constrain (int): minimum days in office
daily_weights (array): weighting of days, e.g. if you prefer to come on mondays
Return:
"""
# daily weighting
u = np.ones(len(y)) if daily_weights == None else daily_weights
I = range(len(y)) # idx for days for summation
m = Model("knapsack") # MIP model
w = [m.add_var(var_type=BINARY) for i in I] # weights to optimize
m.objective = maximize(xsum(y[i] * w[i]
for i in I)) # optimization function
m += xsum(w[i] * u[i] for i in I) <= constrain # constraint
m.optimize()
#selected = [i for i in I if w[i].x >= 0.99]
selected = [w[i].x for i in I]
df = pd.DataFrame(columns=["home_office"],
index=cal_df.index,
data={'home_office': selected})
return df
def do_matching(graph, visualize=True):
print("Starting model")
weights = dict()
graph = {int(key): graph[key] for key in graph}
E = set()
V = graph.keys()
for v in V:
original = v
for u, weight in graph[original]:
s, t = (u, v) if u < v else (v, u)
edge = (s, t)
E.add(edge)
weights[original, u] = weight
if visualize:
graph = nx.Graph()
graph.add_nodes_from(V)
graph.add_edges_from(E)
nx.draw_kamada_kawai(graph)
plt.show()
model = Model("Maximum matching")
edge_vars = {e: model.add_var(var_type=BINARY) for e in E}
for v in V:
model += xsum(edge_vars[s, t] for s, t in E if v in [s, t]) <= 1
model.objective = maximize(
xsum(
xsum(((weights[edge] + weights[edge[1], edge[0]]) / 2) *
edge_vars[edge] for edge in E) for edge in E))
model.optimize(max_seconds=300)
return sorted([e for e in E if edge_vars[e].x > .01])
def ilp(prods, n_prods, alpha):
S1, S2, S3, S4 = segregate(prods, n_prods, alpha)
x = np.array([0.0 for i in range(n_prods)])
d = 0
for prod in S1:
x[prod.index] = 1
d = d + (prod.q - alpha)
rev = [-1.0 for i in range(n_prods)]
qdiff = [-1.0 for i in range(n_prods)]
for prod in S2:
ind = prod.index
rev[ind] = prod.r
qdiff[ind] = prod.q - alpha
for prod in S3:
ind = prod.index
rev[ind] = prod.r
qdiff[ind] = prod.q - alpha
m = Model('ilp')
m.verbose = False
y = [m.add_var(var_type=BINARY) for i in range(n_prods)]
m.objective = maximize(xsum(rev[i] * y[i] for i in range(n_prods)))
m += xsum(qdiff[i] * y[i] for i in range(n_prods)) >= -1 * d
m.optimize()
selected = np.array([y[i].x for i in range(n_prods)])
import pdb
pdb.set_trace()
selected = np.floor(selected + 0.01)
import pdb
pdb.set_trace()
return x + selected, d
def test_knapsack(solver: str):
p = [10, 13, 18, 31, 7, 15]
w = [11, 15, 20, 35, 10, 33]
c, I = 47, range(len(w))
m = Model("knapsack", solver_name=solver)
x = [m.add_var(var_type=BINARY) for i in I]
m.objective = maximize(xsum(p[i] * x[i] for i in I))
m += xsum(w[i] * x[i] for i in I) <= c, "cap"
m.optimize()
assert m.status == OptimizationStatus.OPTIMAL
assert round(m.objective_value) == 41
m.constr_by_name("cap").rhs = 60
m.optimize()
assert m.status == OptimizationStatus.OPTIMAL
assert round(m.objective_value) == 51
# modifying objective function
m.objective = m.objective + 10 * x[0] + 15 * x[1]
assert abs(m.objective.expr[x[0]] - 20) <= 1e-10
assert abs(m.objective.expr[x[1]] - 28) <= 1e-10
def update_model(vrp_model: VrpProblem, model: MyModelMilp, x_var,
components_per_vehicle, edges_in_customers,
edges_out_customers):
for vehicle in components_per_vehicle:
comps = components_per_vehicle[vehicle]
print("Updating model : Nb component : ", len(comps))
if len(comps) > 1:
for si in comps:
s = (set([x[1] for x in si[0]]), si[1])
print(vehicle, ":", s)
edge_in_of_interest = [
e for n in s[0] for e in edges_in_customers[n]
if e[0][1] not in s[0]
]
edge_out_of_interest = [
e for n in s[0] for e in edges_out_customers[n]
if e[1][1] not in s[0]
]
print(edge_in_of_interest)
print("Len of interest : ", len(edge_out_of_interest),
len(edge_in_of_interest))
model.add_constr(
xsum([x_var[e] for e in edge_in_of_interest]) >= 1)
model.add_constr(
xsum([x_var[e] for e in edge_out_of_interest]) >= 1)
model.update()
def build(self, min_obj_value=None, max_n_solutions=None):
self.V = set(self.graph.nodes())
self.n = len(self.V)
seed(0)
self.Arcs = self.graph.edges()
self.add_variables()
self.add_constraints()
if min_obj_value is not None:
constr = xsum(self.graph[i][j]['weight'] * self.x[(i, j)]
for (i, j) in self.Arcs) > min_obj_value
self.model += constr
# objective function: minimize the distance
self.model.objective = minimize(
xsum(self.graph[i][j]['weight'] * self.x[(i, j)]
for (i, j) in self.Arcs))
self.F = self.get_farthest_point_list()
self.model.cuts_generator = SubTourCutGenerator(
self.F, self.x, self.V, self.graph)
return self
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 __init__(self, facilities: List[Facility], customers: List[Customer]):
self.m = Model('NaiveFacilityMIP', solver_name=CBC)
self.customer_facility_map = [[self.m.add_var(var_type=BINARY)
for facility in range(len(facilities))] for customer in range(len(customers))]
self.facility_customer_map = list(zip(*self.customer_facility_map))
for customer in range(len(customers)):
self.m.add_constr(xsum(self.customer_facility_map[customer]) == 1)
for facility in range(len(facilities)):
self.m.add_constr(xsum([customers[index].demand * variable
for index, variable in enumerate(self.facility_customer_map[facility])]) <=
facilities[facility].capacity)
facility_enabled = [self.m.add_var(var_type=BINARY) for facility in range(len(facilities))]
for facility in range(len(facilities)):
for customer in range(len(customers)):
self.m.add_constr(self.facility_customer_map[facility][customer] <= facility_enabled[facility])
self.m.objective = xsum([facilities[f].setup_cost * facility_enabled[f] for f in range(len(facilities))]) + \
xsum([euclideam_length(facilities[facility].location, customers[customer].location) *
self.facility_customer_map[facility][customer]
for facility in range(len(facilities)) for customer in range(len(customers))])
self.m.verbose = True
self.m.max_seconds = 60 * 20
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 build_model(self, solver):
"""MIP model n-queens"""
n = 50
queens = Model('queens', MAXIMIZE, solver_name=solver)
queens.verbose = 0
x = [[
queens.add_var('x({},{})'.format(i, j), var_type=BINARY)
for j in range(n)
] for i in range(n)]
# one per row
for i in range(n):
queens += xsum(x[i][j] for j in range(n)) == 1, 'row{}'.format(i)
# one per column
for j in range(n):
queens += xsum(x[i][j] for i in range(n)) == 1, 'col{}'.format(j)
# diagonal \
for p, k in enumerate(range(2 - n, n - 2 + 1)):
queens += xsum(x[i][j] for i in range(n) for j in range(n)
if i - j == k) <= 1, 'diag1({})'.format(p)
# diagonal /
for p, k in enumerate(range(3, n + n)):
queens += xsum(x[i][j] for i in range(n) for j in range(n)
if i + j == k) <= 1, 'diag2({})'.format(p)
return n, queens
def _add_area_constraints(
self,
m: Model,
v2var: Dict[str, Var],
direction: Dir,
max_usage_ratio: float,
) -> None:
for s, v_group in self.curr_s2v.items():
bottom_or_left, up_or_right = self.slot_manager.partitionSlotByHalf(
s, direction)
for r in RESOURCE_TYPES:
v_var_list = [v2var[v] for v in v_group]
area_list = [
v.getVertexAndInboundFIFOArea()[r] for v in v_group
]
I = range(len(v_group))
# for the up/right child slot (if mod_x is assigned 1)
m += xsum(
v_var_list[i] * area_list[i]
for i in I) <= up_or_right.getArea()[r] * max_usage_ratio
# for the down/left child slot (if mod_x is assigned 0)
m += xsum((1 - v_var_list[i]) * area_list[i] for i in
I) <= bottom_or_left.getArea()[r] * max_usage_ratio
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 _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 implement_less_than(r1: int, c1: int, r2: int, c2: int) -> None:
"""
Implements the constraint value[r1, c1] < value[r2, c2].
"""
nonlocal m
m += (xsum(x[r1][c1][d] * d
for d in range(n)) <= xsum(x[r2][c2][d] * d
for d in range(n)) - 1)
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 _create_constraints_to_balance_unit_nodes(self):
for unit in self.units:
for i in range(0, self.planning_horizon):
in_flow_vars = [var for var_name, var in self.unit_in_flow_variables[unit][i].items()]
out_flow_vars = [var for var_name, var in self.unit_out_flow_variables[unit][i].items()]
if unit in self.unit_commitment_vars:
min_loading_var = [self.unit_commitment_vars[unit]['state'][i] * self.unit_min_loading[unit] * -1]
self.model += xsum(in_flow_vars + [-1 * var for var in out_flow_vars] + min_loading_var) == 0.0
else:
self.model += xsum(in_flow_vars + [-1 * var for var in out_flow_vars]) == 0.0
def add_sbox(model, Q_t, xs, ys=None):
# non-zero input `xs` active the corresponding sbox
model += mip.xsum(xs) >= Q_t
for xs_i in xs:
model += Q_t >= xs_i
if ys is not None:
# Because impossible constraints of SBox is conditional,
# we need additional constraint for non-zero output `ys`
# resulting in non-zero input `xs`
model += len(ys) * mip.xsum(xs) >= mip.xsum(ys)
def knapsack():
p = [10, 13, 18, 31, 7, 15]
w = [11, 15, 20, 35, 10, 33]
c, I = 47, range(len(w))
m = Model("knapsack")
x = [m.add_var(var_type=BINARY) for i in I]
m.objective = maximize(xsum(p[i] * x[i] for i in I))
m += xsum(w[i] * x[i] for i in I) <= c
print(m.optimize())
def do_matching_stable(graph, visualize=True, individual=1, communal=10000000):
print("Starting model")
weights = dict()
graph = {int(key): graph[key] for key in graph}
E = set()
V = graph.keys()
inputs = {v: [] for v in V}
outputs = {v: [] for v in V}
for v in V:
original = v
for u, weight in graph[original]:
s, t = (u, v) if u < v else (v, u)
edge = (s, t)
E.add(edge)
weights[(original, u)] = weight
outputs[original].append(u)
inputs[u].append(original)
if visualize:
graph = nx.Graph()
graph.add_nodes_from(V)
graph.add_edges_from(E)
nx.draw_kamada_kawai(graph)
plt.show()
model = Model("Rogue Couples based")
edge_vars = {e: model.add_var(var_type=BINARY) for e in E}
undirected = dict()
for e in E:
undirected[e] = edge_vars[e]
undirected[e[1], e[0]] = edge_vars[e]
rogue_vars = {e: model.add_var(var_type=BINARY) for e in E}
partners = dict()
for v in V:
partners[v] = model.add_var()
partners[v] = xsum(edge_vars[s, t] for s, t in E if v in [s, t])
model += partners[v] <= 1
for (u, v), rogue_var in rogue_vars.items():
v_primes = [
vp for vp in outputs[u] if weights[(u, vp)] < weights[(u, v)]
]
u_primes = [
up for up in outputs[v] if weights[(v, up)] < weights[(v, u)]
]
model += 1 - partners[v] - partners[u] + xsum(
undirected[u, vp]
for vp in v_primes) + xsum(undirected[up, v]
for up in u_primes) <= rogue_var
model.objective = maximize(individual * xsum(
((weights[edge] + weights[edge[1], edge[0]]) / 2) * edge_vars[edge]
for edge in E) - communal * xsum(rogue_vars[edge] for edge in E))
model.optimize(max_seconds=300)
return sorted([e for e in E if edge_vars[e].x > .01])
def test_queens(solver: str):
"""MIP model n-queens"""
n = 50
queens = Model("queens", MAXIMIZE, solver_name=solver)
queens.verbose = 0
x = [[
queens.add_var("x({},{})".format(i, j), var_type=BINARY)
for j in range(n)
] for i in range(n)]
# one per row
for i in range(n):
queens += xsum(x[i][j] for j in range(n)) == 1, "row({})".format(i)
# one per column
for j in range(n):
queens += xsum(x[i][j] for i in range(n)) == 1, "col({})".format(j)
# diagonal \
for p, k in enumerate(range(2 - n, n - 2 + 1)):
queens += (
xsum(x[i][j] for i in range(n)
for j in range(n) if i - j == k) <= 1,
"diag1({})".format(p),
)
# diagonal /
for p, k in enumerate(range(3, n + n)):
queens += (
xsum(x[i][j] for i in range(n)
for j in range(n) if i + j == k) <= 1,
"diag2({})".format(p),
)
queens.optimize()
assert queens.status == OptimizationStatus.OPTIMAL # "model status"
# querying problem variables and checking opt results
total_queens = 0
for v in queens.vars:
# basic integrality test
assert v.x <= TOL or v.x >= 1 - TOL
total_queens += v.x
# solution feasibility
rows_with_queens = 0
for i in range(n):
if abs(sum(x[i][j].x for j in range(n)) - 1) <= TOL:
rows_with_queens += 1
assert abs(total_queens - n) <= TOL # "feasible solution"
assert rows_with_queens == n # "feasible solution"
def possible(c, n, history):
model = Model()
model.verbose = 0
assign = [[model.add_var(var_type=BINARY) for j in range(c)]
for i in range(n)]
for i in range(n):
model += xsum(assign[i][j] for j in range(c)) == 1
for (tab, sc) in history:
model += xsum(assign[i][tab[i]] for i in range(n)) == sc
model.optimize()
tab = [max([(assign[i][j].x, j) for j in range(c)])[1] for i in range(n)]
return tab
def add_impos(self, pattern, X, Y):
"""
remove impossible case for a given pattern
"""
sz_i = len(X)
sz_o = len(Y)
self += xsum(X[i] * (1 - pattern.get(f"X{i}", 1)) +
(1 - X[i]) * pattern.get(f"X{i}", 0)
for i in range(sz_i)) + xsum(
Y[j] * (1 - pattern.get(f"Y{j}", 1)) +
(1 - Y[j]) * pattern.get(f"Y{j}", 0)
for j in range(sz_o)) >= 1