class Backup(object):
""" Class object for normal-based backup network model.
Parameters
----------
nodes: set of nodes
links: set of links
capacity: capacities per link based based on random failures
mean: mean for failure random variable
std: standard deviation for failure random variable
invstd: inverse of Phi-normal distribution for (1-epsilon)
Returns
-------
solution: set of capacity assigned per backup link.
"""
# Private model object
__model = []
# Private model variables
__BackupCapacity = {}
__bBackupLink = {}
__ValidLink = {}
# Private model parameters
__links = []
__nodes = []
__capacity = []
__mean = []
__std = []
__invstd = 1
def __init__(self,nodes,links,capacity,mean,std,invstd):
'''
Constructor
'''
self.__links = links
self.__nodes = nodes
self.__capacity = capacity
self.__mean = mean
self.__std = std
self.__invstd = invstd
self.__loadModel()
def __loadModel(self):
# Create optimization model
self.__model = Model('Backup')
# Auxiliary variables for SOCP reformulation
U = {}
R = {}
# Create variables
for i,j in self.__links:
self.__BackupCapacity[i,j] = self.__model.addVar(lb=0, obj=1, name='Backup_Capacity[%s,%s]' % (i, j))
self.__model.update()
for i,j in self.__links:
for s,d in self.__links:
self.__bBackupLink[i,j,s,d] = self.__model.addVar(vtype=GRB.BINARY,obj=1,name='Backup_Link[%s,%s,%s,%s]' % (i, j, s, d))
self.__model.update()
for i,j in self.__links:
U[i,j] = self.__model.addVar(obj=1,name='U[%s,%s]' % (i, j))
self.__model.update()
for i,j in self.__links:
for s,d in self.__links:
R[i,j,s,d] = self.__model.addVar(obj=1,name='R[%s,%s,%s,%s]' % (i,j,s,d))
self.__model.update()
self.__model.modelSense = GRB.MINIMIZE
#m.setObjective(quicksum([fixedCosts[p]*open[p] for p in plants]))
self.__model.setObjective(quicksum(self.__BackupCapacity[i,j] for i,j in self.__links))
self.__model.update()
#------------------------------------------------------------------------#
# Constraints definition #
# #
# #
#------------------------------------------------------------------------#
# Link capacity constraints
for i,j in self.__links:
self.__model.addConstr(self.__BackupCapacity[i,j] >= quicksum(self.__mean[s,d]*self.__bBackupLink[i,j,s,d] for (s,d) in self.__links) + U[i,j]*self.__invstd,'[CONST]Link_Cap_%s_%s' % (i, j))
self.__model.update()
# SCOP Reformulation Constraints
for i,j in self.__links:
self.__model.addConstr(quicksum(R[i,j,s,d]*R[i,j,s,d] for (s,d) in self.__links) <= U[i,j]*U[i,j],'[CONST]SCOP1[%s][%s]' % (i, j))
self.__model.update()
# SCOP Reformulation Constraints
for i,j in self.__links:
for s,d in self.__links:
self.__model.addConstr(self.__std[s,d]*self.__bBackupLink[i,j,s,d] == R[i,j,s,d],'[CONST]SCOP2[%s][%s][%s][%s]' % (i, j,s,d))
self.__model.update()
for i in self.__nodes:
for s,d in self.__links:
# Flow conservation constraints
if i == s:
self.__model.addConstr(quicksum(self.__bBackupLink[i,j,s,d] for i,j in self.__links.select(i,'*')) -
quicksum(self.__bBackupLink[j,i,s,d] for j,i in self.__links.select('*',i)) == 1,'Flow1[%s,%s,%s,%s]' % (i,j,s, d))
# Flow conservation constraints
elif i == d:
self.__model.addConstr(quicksum(self.__bBackupLink[i,j,s,d] for i,j in self.__links.select(i,'*')) -
quicksum(self.__bBackupLink[j,i,s,d] for j,i in self.__links.select('*',i)) == -1,'Flow2[%s,%s,%s,%s]' % (i,j,s, d))
# Flow conservation constraints
else:
self.__model.addConstr(quicksum(self.__bBackupLink[i,j,s,d] for i,j in self.__links.select(i,'*')) -
quicksum(self.__bBackupLink[j,i,s,d] for j,i in self.__links.select('*',i)) == 0,'Flow3[%s,%s,%s,%s]' % (i,j,s, d))
self.__model.update()
def optimize(self,MipGap, TimeLimit):
self.__model.write('backup.lp')
if MipGap != None:
self.__model.params.timeLimit = TimeLimit
if TimeLimit != None:
self.__model.params.MIPGap = MipGap
# Compute optimal solution
self.__model.optimize()
# Print solution
if self.__model.status == GRB.Status.OPTIMAL:
solution = self.__model.getAttr('x', self.__BackupCapacity)
for i,j in self.__links:
if solution[i,j] > 0:
print('%s -> %s: %g' % (i, j, solution[i,j]))
else:
print('Optimal value not found!\n')
solution = []
return solution;
def reset(self):
'''
Reset model solution
'''
self.__model.reset()
def create_problem(cobra_model, objective_sense="maximize"):
lp = Model("cobra")
lp.Params.OutputFlag = 0
if objective_sense == 'maximize':
objective_sign = -1.0
elif objective_sense == 'minimize':
objective_sign = 1.0
else:
raise ValueError("objective_sense must be 'maximize' or 'minimize'")
# create metabolites/constraints
metabolite_constraints = {}
for metabolite in cobra_model.metabolites:
metabolite_constraints[metabolite] = \
lp.addConstr(0.0, sense_dict[metabolite._constraint_sense],
metabolite._bound, metabolite.id)
lp.update()
# create reactions/variables along with S matrix
for j, reaction in enumerate(cobra_model.reactions):
constraints = [metabolite_constraints[i] \
for i in reaction._metabolites]
stoichiometry = reaction._metabolites.values()
lp.addVar(
lb=float(reaction.lower_bound),
ub=float(reaction.upper_bound),
obj=objective_sign * reaction.objective_coefficient,
name=reaction.id,
vtype=variable_kind_dict[reaction.variable_kind],
column=Column(stoichiometry, constraints))
lp.update()
return lp
class MainProblem:
def __init__(self):
self.model = Model("main_problem")
self.x_1 = self.model.addVar(lb=0, name="x_1")
self.x_2 = self.model.addVar(lb=0, name="x_2")
self.x_3 = self.model.addVar(lb=0, name="x_3")
self.x_4 = self.model.addVar(lb=0, name="x_4")
self.x_5 = self.model.addVar(lb=0, name="x_5")
self.model.addConstr(self.x_1 + self.x_4 + self.x_5 <= 3)
self.model.addConstr(2 * self.x_2 + 3 * self.x_4 <= 12)
self.model.addConstr(self.x_3 - 7 * self.x_5 <= -16)
self.model.addConstr(-self.x_4 + self.x_5 <= 2)
self.x_hat_4 = None
self.x_hat_5 = None
self.model.setObjective(
-2 * self.x_1 - self.x_2 + self.x_3 + 3 * self.x_4 - 3 * self.x_5,
GRB.MINIMIZE,
)
def solve(self):
self.model.optimize()
return self.model.objVal
def build_model(plants, warehouses, capacity, demand, fixed_costs, trans_costs):
# decision variables
m = Model("facility")
is_open = []
for p in plants:
is_open.append(m.addVar(vtype=GRB.BINARY,
name="is_open[{}]".format(p)))
trans_qty = []
for w in warehouses:
trans_qty.append([])
for p in plants:
trans_qty[w].append(m.addVar(vtype=GRB.CONTINUOUS,
name="trans_qty[{}.{}]".format(p, w),
lb=0.0))
m.update()
# objective function
m.setObjective(quicksum(fixed_costs[p] * is_open[p]
for p in plants) +
quicksum(trans_costs[w][p] * trans_qty[w][p]
for w in warehouses
for p in plants),
GRB.MINIMIZE)
# constraints
for p in plants:
m.addConstr(quicksum(trans_qty[w][p] for w in warehouses) <= capacity[p] * is_open[p],
"Capacity({})".format(p))
for w in warehouses:
m.addConstr(quicksum(trans_qty[w][p] for p in plants) == demand[w],
"Demand({})".format(w))
m.update()
return m
class MasterProblem:
def __init__(self):
self.model = Model("benders_master_problem")
self.x_4 = self.model.addVar(lb=0, name="x_4")
self.x_5 = self.model.addVar(lb=0, name="x_5")
self.phi = self.model.addVar(lb=-100 * 100 * 100, name="phi")
self.model.addConstr(-self.x_4 + self.x_5 <= 2)
self.model.setObjective(
3 * self.x_4 - 3 * self.x_5 + self.phi,
GRB.MINIMIZE,
)
def add_cut(self, lhs, pi_1, pi_2):
self.model.addConstr(
lhs <= self.phi - self.x_4 * pi_1 - self.x_5 * pi_2, name="cut")
def solve(self):
self.model.optimize()
return (
self.model.objVal,
self.x_4.x,
self.x_5.x,
)
def solve_lp_knapsack_gurobi(scores, costs, budget):
from gurobipy import Model, LinExpr, GRB
n = len(scores)
# Create a new model.
m = Model("lp_knapsack")
# Create variables.
for i in range(n):
m.addVar(lb=0.0, ub=1.0)
m.update()
vars = m.getVars()
# Set objective.
obj = LinExpr()
for i in range(n):
obj += scores[i] * vars[i]
m.setObjective(obj, GRB.MAXIMIZE)
# Add constraint.
expr = LinExpr()
for i in range(n):
expr += costs[i] * vars[i]
m.addConstr(expr, GRB.LESS_EQUAL, budget)
# Optimize.
m.optimize()
assert m.status == GRB.OPTIMAL
x = np.zeros(n)
for i in range(n):
x[i] = vars[i].x
return x
def create_problem(cobra_model, objective_sense="maximize"):
lp = Model("cobra")
lp.Params.OutputFlag = 0
if objective_sense == "maximize":
objective_sign = -1.0
elif objective_sense == "minimize":
objective_sign = 1.0
else:
raise ValueError("objective_sense must be 'maximize' or 'minimize'")
# create metabolites/constraints
metabolite_constraints = {}
for metabolite in cobra_model.metabolites:
metabolite_constraints[metabolite] = lp.addConstr(
0.0, sense_dict[metabolite._constraint_sense], metabolite._bound, metabolite.id
)
lp.update()
# create reactions/variables along with S matrix
for j, reaction in enumerate(cobra_model.reactions):
constraints = [metabolite_constraints[i] for i in reaction._metabolites]
stoichiometry = reaction._metabolites.values()
lp.addVar(
lb=float(reaction.lower_bound),
ub=float(reaction.upper_bound),
obj=objective_sign * reaction.objective_coefficient,
name=reaction.id,
vtype=variable_kind_dict[reaction.variable_kind],
column=Column(stoichiometry, constraints),
)
lp.update()
return lp
def solve_optimal_gurobi(matrix):
"""
Solves a given tsp instance optimal using the python gurobi solver interface.
Returns a list of indices. The result list has a cardinality
of the length of the matrix.
"""
model = Model()
model.Params.OutputFlag = 0
n = len(matrix); N = list(range(n))
# Create variables
x = [[model.addVar(vtype=GRB.BINARY, ub=1.0, lb=0.0, name='x{}{}'.format(i,j)) for j in N] for i in range(n)]
u = [ model.addVar(vtype=GRB.CONTINUOUS, name='u{}'.format(i)) for i in N] # miller tucker vars
model.update()
# Set objective
sum_tour_length = [x[i][j] * matrix[i][j] for i in N for j in N]
model.setObjective(quicksum(sum_tour_length), GRB.MINIMIZE)
# Constraints for assignment problem:
[model.addConstr(quicksum([x[i][j] for j in range(n)]) == 1) for i in N]
[model.addConstr(quicksum([x[i][j] for i in range(n)]) == 1) for j in N]
# Constraints for subtour elimination:
[model.addConstr(2 <= u[i] <= n) for i in N[1:]]
[model.addConstr(u[i] - u[j] + 1 <= (n-1)*(1-x[i][j])) for i in N[1:] for j in N[1:]]
model.update()
#model.write('gurobi.lp')
model.optimize()
if model.status == GRB.Status.OPTIMAL:
return __grb_retrieve_tour(model, x)
class WheatSubProblem:
def __init__(self, cfg: Config):
self.cfg = cfg
# model.ModelSense is minimization by default
self.model = Model("wheat_sub_problem")
self.x_1 = self.model.addVar(ub=self.cfg.area, name="x_1")
probability = 1 / len(self.cfg.scenarios)
for index, scenario in enumerate(self.cfg.scenarios):
self._variables_constraint(index, scenario, probability)
def _variables_constraint(self, index, scenario, probability):
y_11 = self.model.addVar(name=f"y_11_{index}",
obj=self.cfg.wheat.buy_price * probability)
y_12 = self.model.addVar(name=f"y_12_{index}",
obj=-self.cfg.wheat.sell_price * probability)
self.model.addConstr(
self.cfg.wheat.requirement <=
self.x_1 * self.cfg.wheat.produce_rate *
(1 + scenario) + y_11 - y_12,
name="wheat_produce_constraint",
)
def solve(self, _lambda):
self.x_1.obj = _lambda + self.cfg.wheat.plant_cost
self.model.optimize()
return (
self.model.objVal,
self.x_1.x,
)
def solve(budget, buses, lines, u, c, b, S, D):
m = Model('inhibit')
w, v, y = {}, {}, {}
for i in buses:
w[i] = m.addVar(vtype=GRB.BINARY, name="w_%s" % i)
for i, j in lines:
v[i, j] = m.addVar(vtype=GRB.BINARY, name='v_%s_%s' % (i, j))
y[i, j] = m.addVar(vtype=GRB.BINARY, name='y_%s_%s' % (i, j))
m.update()
for i, j in lines:
m.addConstr(w[i] - w[j] <= v[i, j] + y[i, j],
'balance1_%s_%s' % (i, j))
m.addConstr(w[j] - w[i] <= v[i, j] + y[i, j],
'balance2_%s_%s' % (i, j))
m.addConstr(
quicksum(c[i, j] * y[i, j] for i, j in lines) <= budget, 'budget')
m.setObjective(
quicksum(u[i, j] * v[i, j] for i, j in lines) +
quicksum(b[i] * (1 - w[i]) for i in S) - quicksum(b[i] * w[i]
for i in D))
m.setParam('OutputFlag', 0)
m.optimize()
m.write('gurobi.lp')
return w, v, y, m
def solve_lp_knapsack_gurobi(scores, costs, budget):
from gurobipy import Model, LinExpr, GRB
n = len(scores)
# Create a new model.
m = Model("lp_knapsack")
# Create variables.
for i in range(n):
m.addVar(lb=0.0, ub=1.0)
m.update()
vars = m.getVars()
# Set objective.
obj = LinExpr()
for i in range(n):
obj += scores[i] * vars[i]
m.setObjective(obj, GRB.MAXIMIZE)
# Add constraint.
expr = LinExpr()
for i in range(n):
expr += costs[i] * vars[i]
m.addConstr(expr, GRB.LESS_EQUAL, budget)
# Optimize.
m.optimize()
assert m.status == GRB.OPTIMAL
x = np.zeros(n)
for i in range(n):
x[i] = vars[i].x
return x
def calculate_sample_weights(pred, c, D, prev_sample_weights=None):
# Dual problem
tree_count = len(pred)
sample_count = len(c)
m = Model("sample_weight_optimiser")
sample_weights = [
m.addVar(vtype=GRB.CONTINUOUS,
name="sample_weights " + str(i),
ub=D if D > 0 else 1) for i in range(sample_count)
]
# Set sample weights to given value
if prev_sample_weights is not None:
for i in range(min(len(prev_sample_weights), len(sample_weights))):
sample_weights[i].setAttr("Start", prev_sample_weights[i])
gamma = m.addVar(vtype=GRB.CONTINUOUS, name="gamma", lb=float("-inf"))
m.setObjective(gamma, GRB.MINIMIZE)
m.addConstr(quicksum(sample_weights) == 1, name="weights = 1")
for t in range(tree_count):
m.addConstr(quicksum([
c[i] * sample_weights[i] * pred[t][i] for i in range(sample_count)
]) <= gamma,
name="Constraint on tree " + str(t))
m.setParam("LogToConsole", 0)
m.optimize()
return [w.X for w in sample_weights], gamma.X
def compute_plane(self, batch, row, col, candidates, candidate_flows,
is_lower):
model = Model()
model.setParam('OutputFlag', False)
model.setParam('NumericFocus', 2)
a = model.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY)
b = model.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY)
c = model.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY)
differences = list()
for candidate, flow in zip(candidates, candidate_flows):
(x, y), z = flow[batch, row, col], candidate[batch, row, col]
x, y, z = x.item(), y.item(), z.item()
if is_lower:
model.addConstr(a + b * x + c * y <= z)
differences.append(z - a + b * x + c * y)
else:
model.addConstr(a + b * x + c * y >= z)
differences.append(a + b * x + c * y - z)
model.setObjective(quicksum(differences), sense=GRB.MINIMIZE)
model.optimize()
if model.status != GRB.OPTIMAL:
raise ValueError('Gurobi: objective not optimal')
return a.x, b.x, c.x
def add_set_flag(
m: gModel,
label: str,
x_var: gVar,
A: Sequence[Sequence[float]],
b: Sequence[float],
K: float,
) -> gVar:
if len(A) == 1:
delta = m.addVar(vtype=g.GRB.BINARY, name=label)
deltas = [delta]
else:
deltas = [
m.addVar(vtype=g.GRB.BINARY, name=delta_label(label, i))
for i in range(len(A))
]
delta = m.addVar(vtype=g.GRB.BINARY, name=label)
for i in range(len(A)):
m.addConstr(
g.quicksum(A[i][j] * x_var[j]
for j in range(len(x_var))) - deltas[i] * K <= b[i])
m.addConstr(
g.quicksum(A[i][j] * x_var[j] for j in range(len(x_var))) +
(1 - deltas[i]) * K >= b[i])
if len(A) > 1:
for i in range(len(A)):
m.addConstr(delta >= deltas[i])
m.addConstr(delta <= g.quicksum(deltas))
return delta
def q2():
from gurobipy import Model, GRB, quicksum, LinExpr
import numpy
from functions import open_data
# Creation of the model
m = Model('LR')
# Your code goes here
x, y = open_data()
N, n = len(x), len(x[0])
# The following example is here to help you build the model (you must adapt it !!!)
# Define decision variables
var = [] # w, b, z
for i in range(n):
var.append(m.addVar(lb = -GRB.INFINITY, vtype=GRB.CONTINUOUS, name = 'w_{}'.format(i), obj = 1))
var.append(m.addVar(lb = -GRB.INFINITY, vtype=GRB.CONTINUOUS, name = 'b'.format(i), obj = 1))
for i in range(N):
var.append(m.addVar(lb = 0, vtype=GRB.CONTINUOUS, name = 'z_{}'.format(i), obj = 1))
#m.update()
# Constraints
expr={}
for j in range(N):
expr = LinExpr()
for i in range(n):
expr += -var[i]*x[j][i]
expr += -var[n]
expr += -var[n+1+j]
m.addConstr(expr, GRB.LESS_EQUAL, -y[j])
expr = LinExpr()
for i in range(n):
expr.add(var[i], x[j][i])
expr += var[n]
expr += -var[n+1+j]
m.addConstr(expr, GRB.LESS_EQUAL, y[j])
# Define objective function:
obj=LinExpr()
for i in range(N):
obj += var[n+1+i]
m.setObjective(obj, GRB.MINIMIZE)
m.update()
m.optimize()
m.write('q2.lp')
# Your code goes here
#if m.status == GRB.Status.OPTIMAL:
z = m.objVal
b = var[n].x
w = [v.x for v in var[:n]]
#print([v.x for v in var[n+1:]])
return ([z, b, w])
def re_verification_tree_extension(s, x, G, i, state_end, factor=0.99):
"""
This is a method to deal with numerical inaccuracies in high dimensioanl MILPs that are terminated early.
Requires solving a linear program. If feasible, the computed control startegy is recomputed.
If infeasible, report back, raise a flag, and abort the tree extention
Inputs: state_X, state_end
Output: flag, u, theta
"""
model = Model("verifying tree extention")
G_dynamic = np.empty((s.n, s.n), dtype='object')
theta = np.empty((s.m, s.n), dtype='object')
u = np.empty((s.m, 1), dtype='object')
x_bar = np.empty((s.n, 1), dtype='object')
for row in range(s.n):
for column in range(s.n):
G_dynamic[row, column] = model.addVar(lb=-GRB.INFINITY,
ub=GRB.INFINITY)
for row in range(s.m):
u[row, 0] = model.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY)
for column in range(s.n):
theta[row, column] = model.addVar(lb=-GRB.INFINITY,
ub=GRB.INFINITY)
for row in range(s.n):
x_bar[row, 0] = model.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY)
model.update()
for row in range(s.n):
for column in range(s.n):
AG = LinExpr()
for k in range(s.n):
AG.add(s.A[i][row, k] * G[k, column])
for k in range(s.m):
AG.add(s.B[i][row, k] * theta[k, column])
model.addConstr(G_dynamic[row, column] == AG * factor)
for row in range(s.n):
Bu = LinExpr()
for k in range(s.m):
Bu.add(s.B[i][row, k] * u[k, 0])
model.addConstr(x_bar[row, 0] == np.dot(s.A[i], x)[row, 0] + Bu +
s.c[i][row, 0])
eps = subset_eps(model, G_dynamic, s.Pi, state_end.polytope.H,
state_end.polytope.h, x_bar)
subset(model, theta, s.Pi, s.F[i], s.f[i], u)
model.setParam("OutputFlag", False)
model.optimize()
if model.Status == 2:
print("eps=", valuation(eps).T)
if np.amax(valuation(eps)) > 10**-3:
print(
"\n-" * 10, "Too large of Epsilon: %d Tree extention failed!" %
np.amax(valuation(eps)), "\n-" * 10)
return None
else:
print("Tree extention verified succesuflly!")
return (valuation(u), valuation(theta), valuation(eps))
else:
print("\n-" * 10, "Infeasible! Tree extention failed!", "\n-" * 10)
return None
def repair(self):
this = self
data_size = self.instance.size()
def get_cj(j, x_vars):
x_list = [x_vars[i][j] for i in xrange(data_size)]
multi_list = list()
for k in xrange(data_size):
if k not in self.neighbor_map[j]:
continue
for i in xrange(data_size):
multi_list.append(x_vars[i][k])
return quicksum(x_list) + quicksum(multi_list)
def build_objective(x_vars):
result = list()
for i, record1 in enumerate(this.instance.data):
for j, record2 in enumerate(this.instance.data):
result.append(record1.distance(record2) * x_vars[i][j])
return result
try:
m = Model('mip1')
x = list()
y = list()
for i, record in enumerate(self.instance.data):
variables = [m.addVar(vtype=GRB.BINARY, name='x_%d_%d' % (i, j)) for j in xrange(data_size)]
x.append(variables)
y.append(m.addVar(vtype=GRB.BINARY, name='y_%d' % i))
m.addConstr(quicksum(x[i]) == 1, name='sum_%d' % i)
for j, record in enumerate(self.instance.data):
c_j = get_cj(j, x)
m.addConstr(c_j - self.k * y[j] >= 0, name='constr_1_%d' % j)
m.addConstr(y[j] * data_size - c_j >= 1 - self.k, name='constr_2_%d' % j)
m.addConstr(y[j] +
quicksum([y[i] if i in self.neighbor_map[j] else 0 for i in xrange(data_size)]) -
quicksum([x[k][j] for k in xrange(data_size)]) / float(data_size)
>= 0, name='constr_3_%d' % j)
m.setObjective(quicksum(build_objective(x)))
print '---- Begin to solve the ILP ----'
m.optimize()
repair_result = list()
for v in m.getVars():
if v.varName.startswith('x') and v.x == 1:
_, record_id, candidate_id = v.varName.split('_')
repair_result.append((int(record_id), int(candidate_id)))
print('Obj: %g' % m.objVal)
return repair_result
except GurobiError as e:
print('Error code ' + str(e.errno) + ": " + str(e))
except AttributeError:
import traceback;
traceback.print_exc()
print('Encountered an attribute error')
def VRPSol(n, K, C, Ps, Ds, d, F, TimeLimit):
m = Model()
m.setParam(GRB.Param.TimeLimit, TimeLimit)
# Create variables
x = {}
for i in Ps:
for j in Ps:
if i != j :
x[i,j] = m.addVar(obj=F(Ps[i], Ps[j]), vtype=GRB.BINARY,
name='x'+str(i)+'_'+str(j))
# Create Miller variables (subtour elimination)
u = {}
for i in Ds:
if i != d:
u[i] = m.addVar(obj=0.0, vtype=GRB.CONTINUOUS,
lb=Ds[i], ub=C, name='u'+str(i))
m.update()
# Add outdegree constraint
for j in Ps:
if j != d:
Ls = list(filter(lambda z: z!=j, Ps))
m.addConstr(quicksum(x[i,j] for i in Ls) == 1)
# Add indegree constraint
for i in Ps:
if i != d:
Ls = filter(lambda z: z!=i, Ps)
m.addConstr(quicksum(x[i,j] for j in Ls) == 1)
# Number of vehicles
Ls = list(filter(lambda z: z!=d, Ps))
m.addConstr(quicksum(x[i,d] for i in Ls) == K)
m.addConstr(quicksum(x[d,j] for j in Ls) == K)
# Subtour elimination constraints
for i in Ls:
for j in Ls:
if i != j:
m.addConstr( u[i] - u[j] +C*x[i,j] <= C - Ds[j] )
m.update()
# Solve the model
m.optimize()
solution = m.getAttr('x', x)
selected = [(i,j) for (i,j) in solution if solution[i,j] > 0.5]
# Xs = [p for p in Ps.values()]
# Ws = [w for w in Ds.values()]
# for i,j in selected:
# DisegnaSegmento(Ps[i], Ps[j])
# plt.scatter([i for i,j in Xs[1:]], [j for i,j in Xs[1:]],
# s=Ws[1:], alpha=0.3, cmap='viridis')
# plt.plot([Xs[0][0]], [Xs[0][1]], marker='s', color='red', alpha=0.5)
# plt.axis('square')
# plt.axis('off')
return m.objVal, selected
def markovitz_dro_wasserstein(data,
delta_param,
alpha_param,
wasserstein_norm=1):
'''
Model from Blanchet et al. 2017
DRO Markovitz reformulation from Wasserstein distance.
'''
r = np.mean(data, axis=0)
cov = np.cov(data, rowvar=False)
k = len(r)
n = len(data)
m = Model('opt_profolio')
m.params.OutputFlag = 0
m.params.NumericFocus = 3
x = m.addVars(k, lb=0, ub=1, vtype=GRB.CONTINUOUS, name='x')
norm_p = m.addVar(lb=0, ub=1, vtype=GRB.CONTINUOUS, name='norm')
p_SD = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name='p_var')
m.update()
sqrt_delta = np.sqrt(delta_param)
m.addConstr((x.sum() == 1), 'portfolio_ctr')
m.addConstr(
(quicksum(x[j] * r[j]
for j in range(k)) >= alpha_param - sqrt_delta * norm_p),
'return_ctr')
m.addConstr((p_SD * p_SD >= quicksum(cov[i, j] * x[i] * x[j]
for i in range(k)
for j in range(k))), 'SD_def')
objfun = p_SD * p_SD + 2 * p_SD * sqrt_delta * norm_p + delta_param * norm_p * norm_p
m.setObjective(objfun, GRB.MINIMIZE)
if wasserstein_norm == 1:
regularizer_norm = 'inf'
m.addConstrs((norm_p >= x[j] for j in range(k)), 'norm_def')
elif wasserstein_norm == 2:
regularizer_norm = 2
m.addConstr((norm_p * norm_p >=
(quicksum(x[j] * x[j] for j in range(k)))), 'norm_def')
elif wasserstein_norm == 'inf':
regularizer_norm = 1
#Note: this works since x>=0
m.addConstr((norm_p == (quicksum(x[j] for j in range(k)))), 'norm_def')
else:
raise 'wasserstain norm should be 1,2, or inf'
m.optimize()
x_sol = np.array([x[j].X for j in range(k)])
p_mean = r.dot(x_sol)
p_var = x_sol.dot(cov.dot(x_sol))
#print(x_sol, p_mean, p_var)
#print('norms' , np.linalg.norm(x_sol) , norm_p.X)
return x_sol, p_mean, p_var
def fair_l1_solution(old_solutions, num_patients):
solutions = process_solutions(old_solutions)
num_solutions = len(solutions)
patient_to_solutions = [[] for _ in range(num_patients)]
for s, solution in enumerate(solutions):
for p in solution:
patient_to_solutions[p].append(s)
model = Model()
model.params.OutputFlag = 0
solution_probs = [
model.addVar(lb=0.0, ub=1.0, vtype=GRB.CONTINUOUS)
for _ in range(num_solutions)
]
model.addConstr(quicksum(solution_probs), GRB.EQUAL, 1.0)
patient_probs = [
model.addVar(lb=0.0, ub=1.0, vtype=GRB.CONTINUOUS)
for _ in range(num_patients)
]
for i in range(num_patients):
expr = quicksum(solution_probs[j] for j in patient_to_solutions[i])
model.addConstr(patient_probs[i], GRB.EQUAL, expr)
m = model.addVar(lb=0.0, ub=1.0, vtype=GRB.CONTINUOUS)
model.addConstr(quicksum(patient_probs), GRB.EQUAL, num_patients * m)
distance_to_mean = [
model.addVar(lb=0.0, ub=1.0, vtype=GRB.CONTINUOUS)
for _ in range(num_patients)
]
for i in range(num_patients):
model.addConstr(distance_to_mean[i], GRB.GREATER_EQUAL,
patient_probs[i] - m)
model.addConstr(distance_to_mean[i], GRB.GREATER_EQUAL,
m - patient_probs[i])
model.setObjective(quicksum(distance_to_mean), GRB.MINIMIZE)
model.optimize()
#return [solution_probs[i].x for i in range(num_solutions)]
if (model.status == GRB.Status.OPTIMAL):
solution_prob_dict = {}
for i in range(num_solutions):
solution_prob_dict[i] = solution_probs[i].x
return solution_prob_dict
else:
return {}
def fair_maxmin_solution(solutions, num_patients):
model = Model('maximin_fair')
model.params.outputflag = 0
solutions = process_solutions(solutions)
solution_size = len(solutions)
solution_dict = {}
dict_array = []
solution_vars = []
for i in range(solution_size):
p = model.addVar(lb=0, ub=1, vtype=GRB.CONTINUOUS)
solution_dict[i] = p
solution_vars.append(p)
solution_exprt = quicksum(solution_vars)
model.addConstr(solution_exprt, GRB.EQUAL, 1.0)
node_prob_dict = {}
for i in range(solution_size):
for item in solutions[i]:
if int(item) in node_prob_dict.keys():
node_prob_dict[int(item)].append(i)
else:
node_prob_dict[int(item)] = [i]
y = model.addVar(lb=0, ub=1.0, vtype=GRB.CONTINUOUS)
for key, value in node_prob_dict.items():
tmp = []
for solution in value:
tmp.append(solution_dict[solution])
expr = quicksum(tmp)
#expr_constant = float(len(value))
model.addConstr(expr, GRB.GREATER_EQUAL, y)
model.update()
model.setObjective(y, GRB.MAXIMIZE)
model.update()
try:
model.optimize()
except e:
print(e)
if (model.status == GRB.Status.OPTIMAL):
solution_prob_dict = {}
for key, value in solution_dict.items():
solution_prob_dict[key] = value.x
return solution_prob_dict
else:
return {}
class MasterProblem:
def __init__(self):
self.model = Model("benders_master_problem")
self.x_1 = self.model.addVar(lb=0, name="x_1", vtype=GRB.BINARY)
self.x_2 = self.model.addVar(lb=0, name="x_2", vtype=GRB.BINARY)
self.phi = self.model.addVar(lb=-100, name="phi")
self.model.addConstr(self.x_1 + self.x_2 <= 1)
self.model.setObjective(
3 * self.x_1 + 5 * self.x_2 + self.phi,
GRB.MINIMIZE,
)
def add_cut(self, lhs, x_hat_1, x_hat_2):
if x_hat_1 == 1 and x_hat_2 == 0:
self.model.addConstr(
lhs + BIG_M * (self.x_1 - 1) - BIG_M * (self.x_2) <= self.phi,
name="cut",
)
if x_hat_1 == 0 and x_hat_2 == 1:
self.model.addConstr(
lhs - BIG_M * (self.x_1) + BIG_M * (self.x_2 - 1) <= self.phi,
name="cut",
)
if x_hat_1 == 0 and x_hat_2 == 0:
self.model.addConstr(
lhs - BIG_M * (self.x_1) - BIG_M * (self.x_2) <= self.phi,
name="cut",
)
if x_hat_1 == 1 and x_hat_2 == 1:
self.model.addConstr(
lhs + BIG_M * (self.x_1 - 1) + BIG_M *
(self.x_2 - 1) <= self.phi,
name="cut",
)
def solve(self):
self.model.optimize()
print()
print(f"PHI: {self.phi.x}")
print(f"X_1: {self.x_1.x}")
print(f"X_2: {self.x_2.x}")
print()
return (
self.model.objVal,
self.x_1.x,
self.x_2.x,
)
def mip_gurobipy(x, y0, n, m, N):
from gurobipy import Model, GRB, quicksum
# set big M
M = 100
# generate model
model = Model('linear regression_mip')
# variables
r = [
model.addVar(name='r({})'.format(i), vtype=GRB.CONTINUOUS)
for i in range(n)
]
t = [
model.addVar(name='t({})'.format(i), vtype=GRB.CONTINUOUS)
for i in range(n)
]
q = [
model.addVar(name='q({})'.format(i), vtype=GRB.BINARY)
for i in range(n)
]
b = [
model.addVar(name='b({})'.format(j), lb=-inf, vtype=GRB.CONTINUOUS)
for j in range(m)
]
# objective
model.setObjective(quicksum(r[i] - t[i] for i in range(n)), GRB.MINIMIZE)
# constraints
for i in range(n):
model.addConstr(r[i] >= y0[i] - quicksum(x[j, i] * b[j]
for j in range(m)))
model.addConstr(r[i] >= quicksum(x[j, i] * b[j]
for j in range(m)) - y0[i])
model.addConstr(t[i] <= M * (1 - q[i]))
model.addConstr(t[i] <= r[i])
model.addConstr(quicksum(q[i] for i in range(n)) >= N)
# optimize
model.optimize()
# get results
r_sol = [r[i].x for i in range(n)]
q_sol = [round(q[i].x) for i in range(n)]
b_sol = [b[j].x for j in range(m)]
t_sol = [t[i].x for i in range(n)]
return r_sol, q_sol, b_sol
class MasterProblem:
"""
Benders's master problem.
In each iteration a new cut will be added into this.
"""
def __init__(self, cfg: Config):
self.model = Model("benders_master_porblem")
self.cfg = cfg
self.x_1 = self.model.addVar(vtype=GRB.CONTINUOUS, lb=0, name="x_1")
self.x_2 = self.model.addVar(vtype=GRB.CONTINUOUS, lb=0, name="x_2")
self.x_3 = self.model.addVar(vtype=GRB.CONTINUOUS, lb=0, name="x_3")
self.phi = self.model.addVar(vtype=GRB.CONTINUOUS,
lb=-100 * 100 * 100,
name="phi")
self.model.addConstr(self.x_1 + self.x_2 + self.x_3 <= cfg.area,
name="area_constraint")
self.model.setObjective(
self.x_1 * cfg.wheat.plant_cost + self.x_2 * cfg.corn.plant_cost +
self.x_3 * cfg.beet.plant_cost + self.phi,
GRB.MINIMIZE,
)
def add_cut(self, lhs, pi_1, pi_2, pi_3):
"""
add_cut adds new cuts to master problem based
on given dual values and constant.
these parameters come from the sub problem
optimal solution in each benders iteration.
"""
self.model.addConstr(
lhs <=
self.phi - self.x_1 * pi_1 - self.x_2 * pi_2 - self.x_3 * pi_3,
name="cut",
)
def solve(self):
"""
solve solves master problem and returns the optimal solution
"""
self.model.optimize()
return (
self.model.objVal,
self.x_1.x,
self.x_2.x,
self.x_3.x,
)
def build_gurobi_model(case):
G, B = case.G, case.B
P = real(case.demands)
Q = imag(case.demands)
branches = case.branch_list
n = len(case.demands)
vhat = case.vhat
s2 = 2**.5
gens = {bus: gen.v for bus, gen in case.gens.items()}
del gens[0]
m = GurobiModel("jabr")
u = [m.addVar(name='u_%d' % i) for i in range(n)]
R = {(i, j): m.addVar(name='R_%d_%d' % (i, j)) for i, j in branches}
I = {(i, j): m.addVar(lb=-GRB.INFINITY, name='I_%d_%d' % (i, j))
for i, j in branches}
for i, j in branches:
R[j, i] = R[i, j]
I[j, i] = I[i, j]
m.update()
m.addConstr(u[0] == vhat * vhat / s2, 'u0')
for gen, v in gens.iteritems():
m.addConstr(u[gen] == v * v / s2, 'u%d' % gen)
for i, j in branches:
m.addQConstr(2 * u[i] * u[j] >= R[i, j] * R[i, j] + I[i, j] * I[i, j],
'cone_%d_%d' % (i, j))
k = lambda i: (j for j in B[i, :].nonzero()[1])
s = lambda i, j: 1 if i < j else -1
for i in range(1, n):
m.addConstr(
-s2 * u[i] * G[i, :].sum() +
quicksum(G[i, j] * R[i, j] + B[i, j] * s(i, j) * I[i, j]
for j in k(i)) == P[i], 'real_flow_%d_%d' % (i, j))
if i in gens:
continue
m.addConstr(
s2 * u[i] * B[i, :].sum() +
quicksum(-B[i, j] * R[i, j] + G[i, j] * s(i, j) * I[i, j]
for j in k(i)) == Q[i], 'reac_flow_%d_%d' % (i, j))
m.setObjective(quicksum(R[i, j] for i, j in branches), sense=GRB.MAXIMIZE)
m.params.outputFlag = 0
#m.params.barQCPConvTol = 5e-10
m.optimize()
if m.status != 2:
raise ValueError("gurobi failed to converge: %s (check log)" %
m.status)
u_opt = [x.getAttr('x') for x in u]
R_opt = {(i, j): x.getAttr('x') for (i, j), x in R.items()}
I_opt = {(i, j): x.getAttr('x') for (i, j), x in I.items()}
return u_opt, R_opt, I_opt
def generateInstance(self):
def euc_dist(bor, sh):
dx = bor["x_coord"] - sh["x_coord"]
dy = bor["y_coord"] - sh["y_coord"]
return math.sqrt(dx * dx + dy * dy)
model = Model('FireSolver')
# Generate variables
x = {}
for bor in self.boroughs:
# New firehouses
for fh in self.new_firehouses + self.old_firehouses:
name = "x_" + fh["loc_id"] + "_" + bor["loc_id"]
x[bor["loc_id"], fh["loc_id"]] = model.addVar(name=name, vtype ="b", obj=self.cost_coef * euc_dist(bor, fh))
# Open variables
openfh = {}
for fh in self.new_firehouses:
openfh[fh["loc_id"]] = model.addVar(name = "open_" + fh["loc_id"], vtype ="b", obj=fh["construction_cost"])
# Close variables
closefh = {}
for fh in self.old_firehouses:
closefh[fh["loc_id"]] = model.addVar(name = "close_" + fh["loc_id"], vtype ="b", obj=fh["destruction_cost"])
model.modelSense = GRB.MINIMIZE
model.update()
# Constraints: one firehouse / borough
for bor in self.boroughs:
model.addConstr(quicksum(x[key] for key in x if key[0] == bor["loc_id"]) == 1)
# capacity of firehouses
for fh in self.new_firehouses:
model.addConstr(quicksum(x[key] for key in x if key[1] == fh["loc_id"]) <= self.capacity * openfh[fh["loc_id"]])
# If it is not removed, the initial assignment needs to be respected
for fh in self.old_firehouses:
for bor in self.boroughs:
if bor["currently_protected_by"] == fh["loc_id"]:
model.addConstr(x[bor["loc_id"], fh["loc_id"]] == 1 - closefh[fh["loc_id"]])
else:
model.addConstr(x[bor["loc_id"], fh["loc_id"]] == 0)
# solve it
model.optimize()
self.model = model
def build_ilp(g, eqs, forbidden, simple_cycles, match):
m = Model()
m.setAttr('ModelSense', GRB.MAXIMIZE)
edges = sorted(g.edges(eqs))
# y: is edge e in the matching? The worth of each allowed match is 1.
obj_coeff = {e: (1 if e not in forbidden else 0) for e in edges}
y = {e: m.addVar(vtype=GRB.BINARY, obj=obj_coeff[e]) for e in edges}
m.update()
# An equation is matched at most once
for eq in eqs:
add_matched_at_most_once_con(m, y, g.edges(eq))
# A variable is matched at most once
set_eqs = set(eqs)
vrs = sorted(v for v in g if v not in set_eqs)
for v in vrs:
add_matched_at_most_once_con(m, y, list(
(eq, v) for v, eq in g.edges(v)))
#
break_each_cycle_at_least_once(eqs, m, y, simple_cycles)
#
set_lower_bound_if_any(g, eqs, m, y)
#
# Set feasible solution from the matching, if any
if match is not None:
match = set(match)
for edge, var in iteritems(y):
var.setAttr('Start', 1 if edge in match else 0)
return m, y
def createInstance(self):
model = Model()
modelVars = {}
# x variables are assigned.
for i in range(self.m):
for j in range(self.n):
Vname = 'x_{}_{}'.format(i, j)
modelVars[Vname] = model.addVar(vtype=GRB.BINARY, name=Vname)
# Term 2: Objective Function
obj = quicksum(self.v[j] * modelVars['x_{}_{}'.format(i, j)]
for i in range(self.m) for j in range(self.n))
# Term 3: Each job is assigned to at most 1 machine.
model.addConstrs(
quicksum(modelVars['x_{}_{}'.format(i, j)]
for i in range(self.m)) <= 1 for j in range(self.n))
# Term 4: Allows the assignment of at most R resources to a machine.
model.addConstrs(
quicksum(modelVars['x_{}_{}'.format(i, j)] * self.r[j]
for j in self.J[h]) <= self.R for i in range(self.m)
for h in range(1, self.k + 1))
# Term 5: Implicit in varaible definition.
# Objective Function is set.
model._vars = modelVars
model.setObjective(obj, GRB.MAXIMIZE)
#print(model.getAttr('ModelSense') == GRB.MINIMIZE)
return model
def gurobi_qp(self, qp):
n = qp.H.shape[1]
model = Model()
x = {
i: model.addVar(
vtype=GRB.CONTINUOUS,
name='x_%d' % i,
lb=qp.lb,
ub=qp.ub)
for i in range(n)
}
model.update()
obj = QuadExpr()
rows, cols = qp.H.nonzero()
for i, j in zip(rows, cols):
obj += 0.5 * x[i] * qp.H[i, j] * x[j]
for i in range(n):
obj += qp.f[i] * x[i]
model.setObjective(obj, GRB.MINIMIZE)
if qp.A is not None:
A_nonzero_rows = get_nonzero_rows(qp.A)
for i, row in A_nonzero_rows.items():
model.addConstr(quicksum(qp.A[i, j] * x[j] for j in row) <= qp.b[i])
if qp.Aeq is not None:
A_nonzero_rows = get_nonzero_rows(qp.Aeq)
for i, row in A_nonzero_rows.items():
model.addConstr(quicksum(qp.Aeq[i, j] * x[j] for j in row) == qp.beq[i])
model.optimize()
self.solution = empty(n)
for i in range(n):
self.solution[i] = model.getVarByName('x_%d' % i).x
def sample_from_polytope(polytope):
"""
A random point in H,h
"""
model=Model("Polytope Sampling")
n=polytope.H.shape[1]
alpha=np.random.random((n,1))-0.5
theta=model.addVar(lb=-GRB.INFINITY,ub=GRB.INFINITY)
model.update()
Hx_Anchor=np.dot(polytope.H,polytope.anchor)
H_alpha=np.dot(polytope.H,alpha)
for row in range(polytope.H.shape[0]):
model.addConstr(H_alpha[row,0]*theta+Hx_Anchor[row,0]<=polytope.h[row])
model.setObjective(theta,GRB.MINIMIZE)
model.setParam('OutputFlag',False)
model.optimize()
theta_min=theta.X
model.reset()
model.setObjective(theta,GRB.MAXIMIZE)
model.optimize()
theta_max=theta.X
c=rand()
x_sample=(polytope.anchor+alpha*theta_min)*c+(polytope.anchor+alpha*theta_max)*(1-c)
polytope.anchor=x_sample
return x_sample
def construct_lp_model(c, A, d):
from gurobipy import Model, LinExpr, GRB
# A = numpy.array (matrix)
# c = numpy.array (vector)
# d = numpy.array (vector)
k, n = A.shape
# Creation of the gurobi model
m = Model("sp")
# Variables
x = list()
for i in range(n):
x.append(m.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY, name='x_%d' % i))
# Objective Function
objExpr = LinExpr()
for i in range(n):
objExpr.add(x[i], c[i])
m.setObjective(objExpr, GRB.MAXIMIZE)
# Constraints
expr = {}
for j in range(k):
expr = LinExpr()
for i in range(n):
expr.add(x[i], A[j, i])
m.addConstr(expr, GRB.LESS_EQUAL, d[j])
# Update the model to add new entries
m.update()
return m
def _construct_smore_lp(self, G, edge_to_paths, num_total_paths):
m = Model('min-edge-util')
# Create variables: one for each path
path_vars = m.addVars(num_total_paths,
vtype=GRB.CONTINUOUS,
lb=0.0,
ub=1.0,
name='f')
max_link_util_var = m.addVar(vtype=GRB.CONTINUOUS, lb=0.0, name='z')
m.update()
m.setObjective(max_link_util_var, GRB.MINIMIZE)
# Add demand constraints
for k, d_k, path_ids in self.commodities:
m.addConstr(quicksum(path_vars[p] for p in path_ids) == 1)
# Add edge util constraints
for u, v, c_e in G.edges.data('capacity'):
paths = edge_to_paths[(u, v)]
constr_vars = [
path_vars[p] * self.commodities[self._path_to_commod[p]][-2]
for p in paths
]
m.addConstr(quicksum(constr_vars) / c_e <= max_link_util_var)
return LpSolver(m, None, self.DEBUG, self.VERBOSE, self.out)
def max_return(r, risk_threshold, cvar_alpha=0.95):
r_bar = np.mean(r, axis=0)
cov = np.cov(r, rowvar=False)
n = len(r)
k = len(r[0])
m = Model('opt_profolio')
m.params.OutputFlag = 0
m.params.NumericFocus = 3
x = m.addVars(k, lb=0, ub=1, vtype=GRB.CONTINUOUS, name='x')
z = m.addVars(n, lb=0, vtype=GRB.CONTINUOUS, name='z')
eta = m.addVar(lb=-GRB.INFINITY, vtype=GRB.CONTINUOUS, name='eta')
m.update()
#Portfolio contraint
m.addConstr((x.sum() == 1), 'portfolio_ctr')
#Risk constraint
m.addConstr(
(eta + (1.0 / (n * (1 - cvar_alpha))) * z.sum() <= risk_threshold),
'cvar_ctr')
#CVaR linearlization
m.addConstrs((z[i] >= quicksum(-r[i, j] * x[j] for j in range(k)) - eta
for i in range(n)), 'cvar_linear')
m.setObjective(quicksum(r_bar[j] * x[j] for j in range(k)), GRB.MAXIMIZE)
m.update()
m.optimize()
x_sol = np.array([x[j].X for j in range(k)])
p_mean = r_bar.dot(x_sol)
p_var = x_sol.dot(cov.dot(x_sol))
cvar_loss = (eta + (1.0 / (n * (1 - cvar_alpha))) * z.sum()).getValue()
#print(m.status, eta.X, (-1+(1+eta.X)**365), cvar_loss , (-1+(1+cvar_loss)**365))
return x_sol, p_mean, p_var
def check_redundancy_row(H, h, ROW, atol=10**-8):
model = Model("Row Redundancy Check")
n = H.shape[1]
x = np.empty((n, 1), dtype='object')
for row in range(n):
x[row, 0] = model.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY)
model.update()
for row in [r for r in range(H.shape[0]) if r != ROW]:
Hx = LinExpr()
for column in range(n):
Hx.add(H[row, column] * x[column, 0])
model.addConstr(Hx <= h[row, 0])
J = LinExpr()
for column in range(n):
J.add(H[ROW, column] * x[column, 0])
model.setObjective(J, GRB.MAXIMIZE)
model.setParam('OutputFlag', False)
model.optimize()
if model.Status == 2:
if J.getValue() > h[ROW, 0] + atol:
return False # It is NOT redundant
else:
return True # It is redudant
else:
return False
def ilp(costMatrix):
#Invalid_Connections : -1
if costMatrix.shape==(0,0):
return []
dist_mat=numpy.copy(costMatrix)
dist_mat[costMatrix==-1]=10e10
size_x = dist_mat.shape[0]
size_y = dist_mat.shape[1]
size_min = int(numpy.amin([size_x,size_y]))
from gurobipy import Model, quicksum, GRB
m=Model("mip1")
COS,VAR={},{}
for i in range(size_x):
x_cos, x_var = [],[]
for j in range(size_y):
COS[i,j]=dist_mat[i,j]
VAR[i,j]=m.addVar(vtype='B',name="["+str(i)+","+str(j)+"]")
m.update()
# Set objective
m.setObjective( quicksum(\
COS[x,y]*VAR[x,y]
for x in range(size_x) \
for y in range(size_y) \
),GRB.MINIMIZE)
# Constrains HORIZONTAL
for i in range(size_x):
m.addConstr( quicksum\
(VAR[i,y] for y in range(size_y)) <= 1)
# Constrains VERTICAL
for i in range(size_y):
m.addConstr( quicksum\
(VAR[x,i] for x in range(size_x)) <= 1)
m.addConstr(quicksum(\
VAR[x,y] for x in range(size_x) for y in range(size_y)) == int(size_min))
m.setParam("OutputFlag",False)
m.optimize()
res=numpy.zeros(dist_mat.shape,dtype=bool)
for i in range(size_x):
for j in range(size_y):
res[i,j]=VAR[i,j].x
binMatrix = numpy.zeros( costMatrix.shape,dtype=bool )
binMatrix[res==1]=1
binMatrix[costMatrix==-1]=0
return binMatrix
def build_gurobi_model(case):
G, B = case.G, case.B
P = real(case.demands)
Q = imag(case.demands)
branches = case.branch_list
n = len(case.demands)
vhat = case.vhat
s2 = 2**.5
gens = {bus: gen.v for bus, gen in case.gens.items()}
del gens[0]
m = GurobiModel("jabr")
u = [m.addVar(name='u_%d'%i) for i in range(n)]
R = {(i, j): m.addVar(name='R_%d_%d' % (i, j)) for i, j in branches}
I = {(i, j): m.addVar(lb=-GRB.INFINITY, name='I_%d_%d' % (i, j)) for i, j in branches}
for i, j in branches:
R[j, i] = R[i, j]
I[j, i] = I[i, j]
m.update()
m.addConstr(u[0] == vhat*vhat/s2, 'u0')
for gen, v in gens.iteritems():
m.addConstr(u[gen] == v*v/s2, 'u%d' % gen)
for i, j in branches:
m.addQConstr(2*u[i]*u[j] >= R[i,j]*R[i,j] + I[i,j]*I[i,j], 'cone_%d_%d' % (i, j))
k = lambda i: (j for j in B[i, :].nonzero()[1])
s = lambda i, j: 1 if i < j else -1
for i in range(1, n):
m.addConstr(-s2*u[i]*G[i, :].sum() + quicksum(G[i,j]*R[i,j] + B[i,j]*s(i,j)*I[i,j] for j in k(i)) == P[i],
'real_flow_%d_%d' % (i, j))
if i in gens:
continue
m.addConstr(s2*u[i]*B[i, :].sum() + quicksum(-B[i,j]*R[i,j] + G[i,j]*s(i,j)*I[i,j] for j in k(i)) == Q[i],
'reac_flow_%d_%d' % (i, j))
m.setObjective(quicksum(R[i,j] for i, j in branches), sense=GRB.MAXIMIZE)
m.params.outputFlag = 0
#m.params.barQCPConvTol = 5e-10
m.optimize()
if m.status != 2:
raise ValueError("gurobi failed to converge: %s (check log)" % m.status)
u_opt = [x.getAttr('x') for x in u]
R_opt = {(i, j): x.getAttr('x') for (i, j), x in R.items()}
I_opt = {(i, j): x.getAttr('x') for (i, j), x in I.items()}
return u_opt, R_opt, I_opt
def create_problem(cobra_model, quadratic_component=None, **kwargs):
"""Solver-specific method for constructing a solver problem from
a cobra.Model. This can be tuned for performance using kwargs
"""
lp = Model("")
the_parameters = parameter_defaults
if kwargs:
the_parameters = parameter_defaults.copy()
the_parameters.update(kwargs)
# Set verbosity first to quiet infos on parameter changes
if "verbose" in the_parameters:
set_parameter(lp, "verbose", the_parameters["verbose"])
for k, v in iteritems(the_parameters):
set_parameter(lp, k, v)
# Create variables
#TODO: Speed this up
variable_list = [lp.addVar(_float(x.lower_bound),
_float(x.upper_bound),
float(x.objective_coefficient),
variable_kind_dict[x.variable_kind],
str(i))
for i, x in enumerate(cobra_model.reactions)]
reaction_to_variable = dict(zip(cobra_model.reactions,
variable_list))
# Integrate new variables
lp.update()
#Constraints are based on mass balance
#Construct the lin expression lists and then add
#TODO: Speed this up as it takes about .18 seconds
#HERE
for i, the_metabolite in enumerate(cobra_model.metabolites):
constraint_coefficients = []
constraint_variables = []
for the_reaction in the_metabolite._reaction:
constraint_coefficients.append(_float(the_reaction._metabolites[the_metabolite]))
constraint_variables.append(reaction_to_variable[the_reaction])
#Add the metabolite to the problem
lp.addConstr(LinExpr(constraint_coefficients, constraint_variables),
sense_dict[the_metabolite._constraint_sense.upper()],
the_metabolite._bound,
str(i))
# Set objective to quadratic program
if quadratic_component is not None:
set_quadratic_objective(lp, quadratic_component)
lp.update()
return(lp)
def global_model(N, k_choices, distance_matrix):
if k_choices >= N:
raise ValueError("k_choices must be less than N")
model = Model("distance1")
trajectories = range(N)
distance_matrix = np.array(
distance_matrix / distance_matrix.max(), dtype=np.float64)
dm = distance_matrix ** 2
y, x = {}, {}
for i in trajectories:
y[i] = model.addVar(vtype="B", obj=0, name="y[%s]" % i)
for j in range(i + 1, N):
x[i, j] = model.addVar(
vtype="B", obj=1.0, name="x[%s,%s]" % (i, j))
model.update()
model.setObjective(quicksum([x[i, j] * dm[j][i]
for i in trajectories
for j in range(i + 1, N)]))
# Add constraints to the model
model.addConstr(quicksum([y[i]
for i in trajectories]) <= k_choices, "27")
for i in trajectories:
for j in range(i + 1, N):
model.addConstr(x[i, j] <= y[i], "28-%s-%s" % (i, j))
model.addConstr(x[i, j] <= y[j], "29-%s-%s" % (i, j))
model.addConstr(y[i] + y[j] <= 1 + x[i, j],
"30-%s-%s" % (i, j))
model.addConstr(quicksum([x[i, j] for i in trajectories
for j in range(i + 1, N)])
<= nchoosek(k_choices, 2), "Cut_1")
model.update()
return model
def find_feasible_start(n_colors, h, statespace, conflicts, verbose=False):
model = Model("TimeFeasibility")
p = len(h)
y = {}
# y[i,k] = if color i gets slot l
for i in range(n_colors):
for l in range(p):
y[i,l] = model.addVar(vtype=GRB.BINARY, name="y_%s_%s" % (i,l))
model.update()
# Building constraints...
# c1: all get one
for i in range(n_colors):
model.addConstr( quicksum([ y[i, l] for l in range(p) ]) == 1, "c1")
# c2: each slot needs to be used tops once
for l in range(p):
model.addConstr( quicksum([ y[i, l] for i in range(n_colors) ]) <= 1, "c2")
### c3: statespace constraints
for i in range(n_colors):
#print l, h[l], i, [s for s in statespace]
model.addConstr( quicksum([ y[i, l] for l in range(p) if h[l] not in statespace[i] ]) == 0, "c3")
# objective: minimize conflicts
#obj = quicksum([ y[i,l] * y[j,l] for l in range(p) for i in range(n_colors) for j in range(i+1, n_colors) ])
obj = quicksum([ sum(y[i,l] for i in range(n_colors)) for l in range(p) ])
#obj = 0
model.setObjective(obj, GRB.MINIMIZE)
if not verbose:
model.params.OutputFlag = 0
model.optimize()
# return best room schedule
color_schedule = []
if model.status == GRB.INFEASIBLE:
return color_schedule
for i in range(n_colors):
for l in range(p):
v = model.getVarByName("y_%s_%s" % (i,l))
if v.x == 1:
color_schedule.append(h[l])
break
return color_schedule
def check_feasability_ILP(exams_to_schedule, period, data, verbose=False):
# More precise but by far to slow compared to heuristic
r = data['r']
T = data['T']
s = data['s']
z = {}
model = Model("RoomFeasability")
# z[i,k] = if exam i is written in room k
for k in range(r):
# print k, period
if T[k][period] == 1:
for i in exams_to_schedule:
z[i, k] = model.addVar(vtype=GRB.BINARY, name="z_%s_%s" % (i, k))
model.update()
# Building constraints...
# c1: seats for all students
for i in exams_to_schedule:
expr = LinExpr()
for k in range(r):
if T[k][period] == 1:
expr.addTerms(1, z[i, k])
model.addConstr(expr >= s[i], "c1")
# c2: only one exam per room
for k in range(r):
if T[k][period] == 1:
expr = LinExpr()
for i in exams_to_schedule:
expr.addTerms(1, z[i, k])
model.addConstr(expr <= 1, "c2")
model.setObjective(0, GRB.MINIMIZE)
if not verbose:
model.params.OutputFlag = 0
model.params.heuristics = 0
model.params.PrePasses = 1
model.optimize()
# return best room schedule
try:
return model.objval
except GurobiError:
logging.warning('check_feasability_ILP: model has no objVal')
return None
def solve(budget, buses, lines, u, c, b, S, D):
m = Model('inhibit')
w, v, y = {}, {}, {}
for i in buses:
w[i] = m.addVar(vtype=GRB.BINARY, name="w_%s" % i)
for i, j in lines:
v[i, j] = m.addVar(vtype=GRB.BINARY, name='v_%s_%s' % (i, j))
y[i, j] = m.addVar(vtype=GRB.BINARY, name='y_%s_%s' % (i, j))
m.update()
for i, j in lines:
m.addConstr(w[i]-w[j] <= v[i, j] + y[i, j], 'balance1_%s_%s' % (i, j))
m.addConstr(w[j]-w[i] <= v[i, j] + y[i, j], 'balance2_%s_%s' % (i, j))
m.addConstr(quicksum(c[i, j]*y[i, j] for i, j in lines) <= budget, 'budget')
m.setObjective(quicksum(u[i, j]*v[i, j] for i, j in lines) +
quicksum(b[i]*(1-w[i]) for i in S) -
quicksum(b[i]*w[i] for i in D))
m.setParam('OutputFlag', 0)
m.optimize()
m.write('gurobi.lp')
return w, v, y, m
def _cut(self, model, val_func, cut_func):
'''Returns true if a cut was added to the master'''
problem = self.problem
theta = self.theta
x = self.x
# Create subproblem.
sub = Model()
# y[ip,iq,s,c] = 1 if images ip & iq have a shared path through stage
# s by running command c during s, 0 otherwise
y = {}
for (ip, iq), cmds in problem.shared_cmds.items():
for s, c in product(problem.shared_stages[ip, iq], cmds):
y[ip,iq,s,c] = sub.addVar(name='y[%s,%s,%s,%s]' % (ip,iq,s,c))
sub.update()
# Find shared paths among image pairs.
constraints = defaultdict(list)
for (ip, iq), cmds in problem.shared_cmds.items():
for s in problem.shared_stages[ip,iq]:
for c in cmds:
constraints[ip,s,c].append(sub.addConstr(y[ip,iq,s,c] <= val_func(model, x[ip,s,c])))
constraints[iq,s,c].append(sub.addConstr(y[ip,iq,s,c] <= val_func(model, x[iq,s,c])))
if s > 1:
sub.addConstr(sum(y[ip,iq,s,c] for c in cmds) <= sum(y[ip,iq,s-1,c] for c in cmds))
sub.setObjective(
-sum(problem.commands[c] * y[ip,iq,s,c] for ip,iq,s,c in y),
GRB.MINIMIZE
)
sub.optimize()
# Add the dual prices for each variable
pi = defaultdict(float)
for isp, cons in constraints.iteritems():
for c in cons:
pi[isp] += c.pi
# Detect optimality
if val_func(model, theta) >= sub.objVal:
return False # no cuts to add
# Optimality cut
cut_func(model, theta >= sum(pi[isp]*x[isp] for isp in pi if pi[isp]))
return True
def two_cycle(A, C, gap):
"""
Solve high-vertex dense graphs by reduction to
weighted matching ILP.
"""
_ = '*'
m = Model()
m.modelsense = GRB.MAXIMIZE
m.params.mipgap = gap
m.params.timelimit = 60 * 60
n = A.shape[0]
vars = {}
edges = tuplelist()
# model as undirected graph
for i in range(n):
for j in range(i+1, n):
if A[i, j] == 1 and A[j, i] == 1:
e = (i, j)
edges.append(e)
w_i = 2 if i in C else 1
w_j = 2 if j in C else 1
w = w_i + w_j
var = m.addVar(vtype=GRB.BINARY, obj=w)
vars[e] = var
m.update()
# 2 cycle constraint <=> undirected flow <= 1
for i in range(n):
lhs = LinExpr()
lhs_vars = [vars[e] for e in chain(edges.select(i, _), edges.select(_, i))]
ones = [1.0]*len(lhs_vars)
lhs.addTerms(ones, lhs_vars)
m.addConstr(lhs <= 1)
m.optimize()
m.update()
cycles = [list(e) for e in edges if vars[e].x == 1.0]
return cycles, m.objval
def build_model(data, n_cliques = 0, verbose = True):
# Load Data Format
n = data['n']
r = data['r']
p = data['p']
s = data['s']
c = data['c']
h = data['h']
w = data['w']
location = data['location']
conflicts = data['conflicts']
locking_times = data['locking_times']
T = data['T']
similarp = data['similarp']
model = Model("ExaminationScheduling")
if verbose:
print("Building variables...")
# x[i,k,l] = 1 if exam i is at time l in room k
x = {}
for k in range(r):
for l in range(p):
if T[k][l] == 1:
for i in range(n):
if location[k] in w[i]:
x[i,k,l] = model.addVar(vtype=GRB.BINARY, name="x_%s_%s_%s" % (i,k,l))
# y[i,l] = 1 if exam i is at time l
y = {}
for i in range(n):
for l in range(p):
y[i, l] = model.addVar(vtype=GRB.BINARY, name="y_%s_%s" % (i,l))
# integrate new variables
model.update()
# for i in range(p+5):
# for l in range(i-5):
# y[i, l].setAttr("BranchPriority", s[i])
# model.update()
start = timeit.default_timer()
# not very readable but same constraints as in GurbiLinear_v_10: speeded up model building by 2 for small problems (~400 exams) and more for huger problem ~1500 exams
if verbose:
print("Building constraints...")
s_sorted = sorted(range(len(c)), key = lambda k: c[k])
obj = LinExpr()
sumconflicts = {}
maxrooms = {}
for i in range(n):
sumconflicts[i] = sum(conflicts[i])
if s[i] <= 50:
maxrooms[i] = 1
elif s[i] <= 100:
maxrooms[i] = 2
elif s[i] <= 400:
maxrooms[i] = 7
elif s[i] <= 700:
maxrooms[i] = 9
else:
maxrooms[i] = 12
c2 = LinExpr()
c4 = LinExpr()
for l in range(p):
c1 = LinExpr()
c1 = LinExpr()
c3 = LinExpr()
for k in range(r):
if T[k][l] == 1 and location[k] in w[i]:
# print k, c[k], 1-(1/(pow(2,s_sorted.index(k))))
obj.addTerms( 1-(1/(pow(2,s_sorted.index(k)))) , x[i, k, l])
c1.addTerms(1, x[i,k,l])
c4.addTerms(c[k],x[i,k,l])
model.addConstr(c1 <= maxrooms[i]* y[i,l], "c1a")
model.addConstr(c1 >= y[i,l], "C1b")
for j in conflicts[i]:
c3.addTerms(1,y[j,l])
model.addConstr(c3 <= (1 - y[i,l])*sumconflicts[i], "c3")
c2.addTerms(1,y[i,l])
model.addConstr( c2 == 1 , "c2")
model.addConstr(c4 >= s[i], "c4")
sumrooms = {}
for l in range(p):
sumrooms[l] = 0
cover_inequalities = LinExpr()
for k in range(r):
if T[k][l] == 1:
sumrooms[l] += 1
c5 = LinExpr()
for i in range(n):
if location[k] in w[i]:
c5.addTerms(1,x[i,k,l])
model.addConstr( c5 <= 1, "c5")
cover_inequalities += c5
model.addConstr(cover_inequalities <= sumrooms[l], "cover_inequalities")
# Break Symmetry
# First only use small rooms in a period if all bigger rooms are already used
# TODO Do for every location
if similarp[0] >= 0:
for i in range(i-1):
for l in range(p):
model.addConstr(y[i,l] <= quicksum( y[i+1,sim] for sim in similarp), "s1")
# for l in range(p):
# for index, k in enumerate(s_sorted):
# #print k, index
# s1 = LinExpr()
# if index < len(s_sorted)-1:
# if T[k][l] == 1:
# for k2 in range(r-index):
# if T[s_sorted[index+k2]][l] == 1:
# for i in range(n):
# # if location[k] in w[i]:
# s1.addTerms([1,-1], [x[i,k,l], x[i,s_sorted[index+k2],l]])
# break
# model.addConstr( s1 <= 0 , "s1")
#if p <= n:
# for l in range(p):
# model.addConstr( quicksum(y[l,i] for i in range(l)) >= 1, "s1")
# for l in range(p-1):
# for i in range(n):
# model.addConstr( y[i,l] - quicksum(y[i,l+1] for i in range(l,n)) <= 0, "l1")
model.setObjective( obj, GRB.MINIMIZE)
print timeit.default_timer()-start
if verbose:
print("All constrained and objective built - OK")
if not verbose:
model.params.OutputFlag = 0
# Set Parameters
#print("Setting Parameters...")
# max presolve agressivity
#model.params.presolve = 2
# Choosing root method 3= concurrent = run barrier and dual simplex in parallel
model.params.method = 3
#model.params.MIPFocus = 1
model.params.OutputFlag = 1
#model.params.MIPFocus = 1
# cuts
#model.params.cuts = 0
#model.params.coverCuts = 2
#model.params.CutPasses = 4
# heuristics
#model.params.heuristics = 0
#model.params.symmetry = 2
# # Tune the model
# model.tune()
# if model.tuneResultCount > 0:
# # Load the best tuned parameters into the model
# model.getTuneResult(0)
# # Write tuned parameters to a file
# model.write('tune1.prm')
# return
return(model)
def cycle_milp(A, C, k, gap):
n = A.shape[0]
t_0 = time.clock()
_ = '*'
m = Model()
m.modelsense = GRB.MAXIMIZE
m.params.mipgap = gap
cycles = []
vars = []
cycles_grouped = [[] for i in range(n)]
vars_grouped = [[] for i in range(n)]
print('[%.1f] Generating variables...' % (time.clock() - t_0))
print('i = ', end='')
for i in range(n):
for cycle in dfs_cycles(i, A, k):
w = sum([2 if j in C else 1 for j in cycle])
var = m.addVar(vtype=GRB.BINARY, obj=w)
vars.append(var)
cycles.append(cycle)
cycles_grouped[i].append(cycle)
vars_grouped[i].append(var)
for j in cycle:
if j > i:
vars_grouped[j].append(var)
cycles_grouped[j].append(cycle)
if (i + 1) % 10 == 0:
print(i + 1)
m.update()
print('[%.1f] Generated variables...' % (time.clock() - t_0))
print('[%.1f] Generating constraints...' % (time.clock() - t_0))
for i in range(n):
vars_i = vars_grouped[i]
lhs = LinExpr()
ones = [1.0]*len(vars_i)
lhs.addTerms(ones, vars_i)
m.addConstr(lhs <= 1.0)
print('[%.1f] Generated constraints...' % (time.clock() - t_0))
print('[%.1f] Begin Optimizing %d vertex %d cycle model' % (time.clock() - t_0, n, len(cycles)))
m.update()
m.optimize()
m.update()
print('[%.1f] Finished Optimizing' % (time.clock() - t_0))
print('[%.1f] Building cycles...' % (time.clock() - t_0))
final_cycles = []
for i in range(len(vars)):
var = vars[i]
if var.x == 1.0:
cycle = cycles[i]
final_cycles.append(cycle)
print('[%.1f] Finished building cycles' % (time.clock() - t_0))
return final_cycles, m.objval
class BFPBackupNetwork_Continuous(object):
""" Class object for buffered failure probability-based model.
Parameters
----------
Gamma: importance sampling vector
Nodes: set of nodes
Links: set of links
Capacity: capacities per link based based on random failures
Survivability: desired survivabiliy factor (epsilon)
K: number of random scenarios
Returns
-------
BackupCapacity: set of capacity per backup link.
BackupRoutes: set of backup links
"""
# Private model object
model = []
# Private model variables
BackupCapacity = {}
bBackupLink = {}
z0 = {}
z = {}
def __init__(self):
"""
Constructor
"""
def LoadModel(self, Gamma, Nodes, Links, Capacity, Survivability, NumSamples):
""" Load model.
Parameters
----------
Gamma : importance sampling vector
"""
self.Links = tuplelist(Links)
self.Capacity = Capacity
# Create optimization model
self.model = Model("Backup")
# Create variables
for i, j in self.Links:
self.BackupCapacity[i, j] = self.model.addVar(
vtype=GRB.CONTINUOUS, lb=0, name="Backup_Capacity[%s,%s]" % (i, j)
)
# self.BackupCapacity[i,j] = self.model.addVar(lb=0, name='Backup_Capacity[%s,%s]' % (i, j))
self.model.update()
for i, j in self.Links:
for s, d in self.Links:
self.bBackupLink[i, j, s, d] = self.model.addVar(
vtype=GRB.BINARY, name="Backup_Link[%s,%s,%s,%s]" % (i, j, s, d)
)
self.model.update()
for i, j in self.Links:
for k in range(NumSamples):
self.z[k, i, j] = self.model.addVar(lb=0, name="z[%s][%s][%s]" % (k, i, j))
self.model.update()
for i, j in self.Links:
self.z0[i, j] = self.model.addVar(lb=-GRB.INFINITY, name="z0[%s][%s]" % (i, j))
self.model.update()
self.model.modelSense = GRB.MINIMIZE
self.model.setObjective(quicksum(self.BackupCapacity[i, j] for i, j in self.Links))
self.model.update()
# ------------------------------------------------------------------------#
# Constraints definition #
# #
# #
# ------------------------------------------------------------------------#
# Buffer probability I
for i, j in self.Links:
self.model.addConstr(
self.z0[i, j]
+ 1 / (NumSamples * Survivability) * quicksum(self.z[k, i, j] for (k) in range(NumSamples))
<= 0,
"[CONST]Buffer_Prob_I[%s][%s]" % (i, j),
)
self.model.update()
# Link capacity constraints
for i, j in self.Links:
for k in range(NumSamples):
if Gamma == None:
self.model.addConstr(
(
quicksum(self.bBackupLink[i, j, s, d] * Capacity[k, s, d] for s, d in self.Links)
- self.BackupCapacity[i, j]
- self.z0[i, j]
)
<= self.z[k, i, j],
"[CONST]Buffer_Prob_II[%s][%s][%s]" % (k, i, j),
)
else:
self.model.addConstr(
(
quicksum(self.bBackupLink[i, j, s, d] * Capacity[k, s, d] for s, d in self.Links)
- self.BackupCapacity[i, j]
- self.z0[i, j]
)
* Gamma[k]
<= self.z[k, i, j],
"[CONST]Buffer_Prob_II[%s][%s][%s]" % (k, i, j),
)
self.model.update()
# Link capacity constraints
for i, j in self.Links:
for k in range(NumSamples):
self.model.addConstr(self.z[k, i, j] >= 0, "[CONST]Buffer_Prob_III[%s][%s][%s]" % (k, i, j))
self.model.update()
for i in Nodes:
for s, d in self.Links:
# Flow conservation constraints
if i == s:
self.model.addConstr(
quicksum(self.bBackupLink[i, j, s, d] for i, j in self.Links.select(i, "*"))
- quicksum(self.bBackupLink[j, i, s, d] for j, i in self.Links.select("*", i))
== 1,
"Flow1[%s,%s,%s]" % (i, s, d),
)
# Flow conservation constraints
elif i == d:
self.model.addConstr(
quicksum(self.bBackupLink[i, j, s, d] for i, j in self.Links.select(i, "*"))
- quicksum(self.bBackupLink[j, i, s, d] for j, i in self.Links.select("*", i))
== -1,
"Flow2[%s,%s,%s]" % (i, s, d),
)
# Flow conservation constraints
else:
self.model.addConstr(
quicksum(self.bBackupLink[i, j, s, d] for i, j in self.Links.select(i, "*"))
- quicksum(self.bBackupLink[j, i, s, d] for j, i in self.Links.select("*", i))
== 0,
"Flow3[%s,%s,%s]" % (i, s, d),
)
self.model.update()
def Optimize(self, MipGap=None, TimeLimit=None, LogLevel=None):
""" Optimize the defined model.
Parameters
----------
MipGap : desired gap
TimeLimit : time limit
LogLevel: log level 1 for printing all optimal variables and None otherwise
Returns
-------
BackupCapacity: The total capacity assigned per backup link
BackupRoutes: The set of selected backup links
A tuple list with all paths for edge (s,d) that uses (i,j).
"""
self.model.write("bpbackup.lp")
if MipGap != None:
self.model.params.MIPGap = MipGap
if TimeLimit != None:
self.model.params.timeLimit = TimeLimit
# Compute optimal solution
self.model.optimize()
# Print solution
if self.model.status == GRB.Status.OPTIMAL:
if LogLevel == 1:
for v in self.model.getVars():
print("%s %g" % (v.varName, v.x))
self.BackupCapacitySolution = self.model.getAttr("x", self.BackupCapacity)
self.BackupRoutesSolution = self.model.getAttr("x", self.bBackupLink)
self.BackupLinksSolution = {}
self.HatBackupCapacity = {}
for link in self.BackupCapacitySolution:
if self.BackupCapacitySolution[link] < 1 and self.BackupCapacitySolution[link] > 0.001:
self.HatBackupCapacity[link] = math.ceil(self.BackupCapacitySolution[link])
else:
self.HatBackupCapacity[link] = math.floor(self.BackupCapacitySolution[link])
if self.HatBackupCapacity[link] > 0:
if len(self.BackupLinksSolution) == 0:
self.BackupLinksSolution = [link]
else:
self.BackupLinksSolution = self.BackupLinksSolution + [link]
else:
print("Optimal value not found!\n")
self.BackupCapacitySolution = []
self.BackupRoutesSolution = {}
self.BackupLinksSolution = {}
return self.BackupCapacitySolution, self.BackupRoutesSolution, self.BackupLinksSolution, self.HatBackupCapacity
def SaveBakupNetwork(self, file_name):
"""Save the optimal backup network to the file ``file_name``."""
data = {
"links": [i for i in self.BackupCapacitySolution],
"capacities": [self.BackupCapacitySolution[i] for i in self.BackupCapacitySolution],
"routes": [i for i in self.BackupRoutesSolution],
"status": [self.BackupRoutesSolution[i] for i in self.BackupRoutesSolution],
}
f = open(file_name, "w")
json.dump(data, f)
f.close()
def LoadBackupNetwork(self, file_name):
"""Load a backup network from the file ``file_name``.
Returns the backup network solution saved in the file.
"""
f = open(file_name, "r")
data = json.load(f)
f.close()
self.BackupCapacitySolution = {}
self.BackupRoutesSolution = {}
self.BackupLinksSolution = {}
links = [i for i in data["links"]]
capacities = [i for i in data["capacities"]]
routes = [i for i in data["routes"]]
status = [i for i in data["status"]]
IndexAux = 0
for i, j in links:
self.BackupCapacitySolution[i, j] = capacities[IndexAux]
IndexAux = IndexAux + 1
self.HatBackupCapacity = {}
for link in self.BackupCapacitySolution:
if self.BackupCapacitySolution[link] < 1 and self.BackupCapacitySolution[link] > 0.001:
self.HatBackupCapacity[link] = math.ceil(self.BackupCapacitySolution[link])
else:
self.HatBackupCapacity[link] = math.floor(self.BackupCapacitySolution[link])
if self.HatBackupCapacity[link] > 0:
if len(self.BackupLinksSolution) == 0:
self.BackupLinksSolution = [link]
else:
self.BackupLinksSolution = self.BackupLinksSolution + [link]
IndexAux = 0
for i, j, s, d in routes:
self.BackupRoutesSolution[i, j, s, d] = status[IndexAux]
IndexAux = IndexAux + 1
return self.BackupCapacitySolution, self.BackupRoutesSolution, self.BackupLinksSolution, self.HatBackupCapacity
def ResetModel(self):
"""
Reset model solution.
"""
self.BackupCapacity = {}
self.bBackupLink = {}
self.z0 = {}
self.z = {}
if self.model:
self.model.reset()
class SolveSC1GuMIP:
"""
Solve the initial marking problem optimally using Guroby (it must be install).
The computation time can be quite long for big instances.
"""
def __init__(self, dataflow, verbose, lp_filename):
"""
Constructor
"""
self.dataflow = dataflow
self.verbose = verbose
self.lp_filename = lp_filename
self.col_v = {} # dict use for storing gamma's variable column
self.col_m0 = {} # dict use for storing bds's variable column
self.col_fm0 = {} # dict use for storing FM0's variable column
def compute_initial_marking(self):
"""launch the computation. This function return the objective value of the MILP problem
The initial marking of the graph in parameter is modify.
"""
self.__init_prob() # Modify parameters
self.__create_col() # Add Col on prob
self.__create_row() # Add Row (constraint) on prob
self.__create_obj() # Add objectif function
self.__solve_prob() # Launch the solver and set preload of the graph
del self.prob # Del prob
return self.Z # Return the total amount find by the solver
def __init_prob(self): # Modify parameters
logging.info("Generating initial marking problem")
self.prob = Model("SC1_MIP")
# Gurobi parameters:
if not self.verbose:
self.prob.params.OutputFlag = 0
try:
os.remove("gurobi.log")
except OSError:
pass
self.prob.params.Threads = 2
self.prob.params.intfeastol = 0.000001
def __create_col(self): # Add Col on prob
# Create column bds (M0)
for arc in self.dataflow.get_arc_list():
self.__add_col_m0(arc)
# Create column bds (FM0)
for arc in self.dataflow.get_arc_list():
self.__add_col_fm0(arc)
# Create column lambda (v)
for task in self.dataflow.get_task_list():
phase_count = self.__get_range_phases(task)
for i in xrange(phase_count):
self.__add_col_v(str(task) + "/" + str(i))
# Integrate new variables
self.prob.update()
def __create_row(self): # Add Row (constraint) on prob
# BEGUIN FILL ROW
########################################################################
# Constraint FM0*step - M0 = 0 #
########################################################################
for arc in self.dataflow.get_arc_list():
if not self.dataflow.is_arc_reentrant(arc):
arc_gcd = self.dataflow.get_gcd(arc)
self.__add_frow(arc, arc_gcd)
########################################################################
# Constraint u-u'+M0 >= W1+1 #
########################################################################
for arc in self.dataflow.get_arc_list():
source = self.dataflow.get_source(arc)
target = self.dataflow.get_target(arc)
if not self.dataflow.is_arc_reentrant(arc):
range_source = self.__get_range_phases(source)
range_target = self.__get_range_phases(target)
prod_list = self.__get_prod_rate_list(arc)
cons_list = self.__get_cons_rate_list(arc)
if self.dataflow.is_pcg:
threshold_list = self.__get_threshold_list(arc)
arc_gcd = self.dataflow.get_gcd(arc)
pred_prod = 0
for sourcePhase in xrange(range_source): # source/prod/out normaux
if sourcePhase > 0:
pred_prod += prod_list[sourcePhase - 1]
pred_cons = 0
cons = 0
for targetPhase in xrange(range_target): # target/cons/in normaux
cons += cons_list[targetPhase]
if targetPhase > 0:
pred_cons += cons_list[targetPhase - 1]
w = cons - pred_prod - arc_gcd
if self.dataflow.is_pcg:
w += pred_cons + threshold_list[targetPhase] - cons
str_v1 = str(source) + "/" + str(sourcePhase)
str_v2 = str(target) + "/" + str(targetPhase)
self.__add_row(str_v1, str_v2, arc, w)
# END FILL ROW
def __create_obj(self):
obj = QuadExpr()
for arc in self.dataflow.get_arc_list():
obj += self.col_m0[arc]
self.prob.setObjective(obj, GRB.MINIMIZE)
def __solve_prob(self): # Launch the solver and set preload of the graph
logging.info("loading matrix ...")
self.prob.update()
if self.lp_filename is not None:
problem_location = str(self.prob.write(self.lp_filename))
logging.info("Writing problem: " + str(problem_location))
logging.info("solving problem ...")
self.prob.optimize()
logging.info("Integer solving done !")
self.Z = self.prob.objVal
for arc in self.dataflow.get_arc_list():
if not self.dataflow.is_arc_reentrant(arc):
self.dataflow.set_initial_marking(arc, int(self.col_m0[arc].x))
logging.info("SC1 MIP Mem tot (no reentrant): " + str(self.Z))
# Add a variable lamda
def __add_col_v(self, name):
var = self.prob.addVar(vtype=GRB.CONTINUOUS, name=name)
self.col_v[name] = var
# Add a variable M0
def __add_col_m0(self, arc):
var = self.prob.addVar(lb=0, vtype=GRB.INTEGER)
self.col_m0[arc] = var
# Add a variable FM0
def __add_col_fm0(self, arc):
var = self.prob.addVar(lb=0, vtype=GRB.INTEGER)
self.col_fm0[arc] = var
# Add a constraint: lambda1 - lambda2 + M0 > W1
def __add_row(self, str_v1, str_v2, arc, w):
expr = LinExpr()
if not self.dataflow.is_arc_reentrant(arc):
expr += self.col_v[str_v1]
expr -= self.col_v[str_v2]
expr += self.col_m0[arc]
self.prob.addConstr(expr, GRB.GREATER_EQUAL, w + 0.00001)
# Add a constraint: FM0*step = M0
def __add_frow(self, arc, step):
expr = LinExpr()
expr += self.col_fm0[arc]*float(step)
expr -= self.col_m0[arc]
self.prob.addConstr(expr, GRB.EQUAL, 0)
def __get_range_phases(self, task):
if self.dataflow.is_sdf:
return 1
range_task = self.dataflow.get_phase_count(task)
if self.dataflow.is_pcg:
range_task += self.dataflow.get_ini_phase_count(task)
return range_task
def __get_prod_rate_list(self, arc):
if self.dataflow.is_sdf:
return [self.dataflow.get_prod_rate(arc)]
prod_list = self.dataflow.get_prod_rate_list(arc)
if self.dataflow.is_pcg:
prod_list = self.dataflow.get_ini_prod_rate_list(arc) + prod_list
return prod_list
def __get_cons_rate_list(self, arc):
if self.dataflow.is_sdf:
return [self.dataflow.get_cons_rate(arc)]
cons_list = self.dataflow.get_cons_rate_list(arc)
if self.dataflow.is_pcg:
cons_list = self.dataflow.get_ini_cons_rate_list(arc) + cons_list
return cons_list
def __get_threshold_list(self, arc):
return self.dataflow.get_ini_threshold_list(arc) + self.dataflow.get_threshold_list(arc)
[ 8, 9, 5]
]
a = [
[ 5, 7, 2],
[14, 8, 7],
[10, 6, 12],
[ 8, 4, 15],
[ 6, 12, 5]
]
# x[i][j] = 1 if i is assigned to j
x = []
for i in range(len(c)):
x_i = []
for j in c[i]:
x_i.append(model.addVar(vtype=GRB.BINARY))
x.append(x_i)
# As stated, the GAP has these following constraints. We dualize these into
# penalties instead, using variables so we can easily extract their values.
penalties = [model.addVar() for _ in x]
model.update()
# Dualized constraints: sum j: x_ij <= 1 for all i
for p, x_i in zip(penalties, x):
model.addConstr(p == 1 - sum(x_i))
# sum i: a_ij * x_ij <= b[j] for all j
for j in range(len(b)):
model.addConstr(sum(a[i][j] * x[i][j] for i in range(len(x))) <= b[j])
def __objective_function(self, x, q):
m = Model("Overall_Model")
CT = {}
DT = {}
TD = {}
#### Add Variable ####
for j in range(self.project_n):
## solve individual model get Project complete date
CT[j] = self.__optmize_single_project(x, j)
## Project Tadeness,construction completion time
DT[j] = m.addVar(obj=0, vtype=GRB.CONTINUOUS, name="(DT%d)" % j)
TD[j] = m.addVar(obj=0, vtype=GRB.CONTINUOUS, name="(TD%d)" % j)
DT[-1] = m.addVar(obj=0, vtype=GRB.CONTINUOUS, name="(DT-1)")
## Review Sequence z_ij
z = {}
for i in range(self.project_n):
for j in range(self.project_n):
if i != j:
z[i, j] = m.addVar(obj=0, vtype=GRB.BINARY, name="(z%d,%d)" % (i, j))
for j in range(self.project_n):
z[-1, j] = m.addVar(obj=0, vtype=GRB.BINARY, name="(z%d,%d)" % (-1, j))
m.update();
#### Add Constraint ####
## Constrain 2: project complete data>due data ##
for j in range(self.project_n):
m.addConstr(DT[j] - TD[j], GRB.LESS_EQUAL, self.DD[j], name="constraint_2_project_%d" % j)
## Constraint 13
for j in range(self.project_n):
m.addConstr(DT[j], GRB.GREATER_EQUAL, CT[j] + self.review_duration[j], name="constraint_13_project_%d" % j)
## Constraint 14
for i in range(-1, self.project_n):
for j in range(self.project_n):
if i != j:
m.addConstr(DT[j], GRB.GREATER_EQUAL, DT[i] - self.M * (1 - z[i, j]) + self.review_duration[j],
name="constraint_14_project_%d_project_%d" % (i, j))
## Constrain 15
for j in range(self.project_n):
m.addConstr(quicksum(z[i, j] for i in range(-1, self.project_n) if i != j), GRB.EQUAL, 1,
name="constraint_15_project_%d" % j)
## Constrain 16
m.addConstr(quicksum(z[-1, j] for j in range(self.project_n)), GRB.EQUAL, 1, name="constraint_16")
## Constrain 17
for i in range(self.project_n):
m.addConstr(quicksum(z[i, j] for j in range(self.project_n) if j != i), GRB.LESS_EQUAL, 1,
name="constraint_17_project_%d" % i)
m.update()
# Set optimization objective - minimize sum of
expr = LinExpr()
for j in range(self.project_n):
expr.add(self.w[j] * TD[j])
m.setObjective(expr, GRB.MINIMIZE)
m.update()
m.params.presolve = 1
m.update()
m.optimize()
m.write(join(self.output_dir, "heuristic_whole.lp"))
m.write(join(self.output_dir, "heuristic_whole.sol"))
print([self.w[j] * TD[j].X for j in range(self.project_n)])
return m.objVal, argmax([self.w[j] * TD[j].X for j in range(self.project_n)])
def build_model(data, n_cliques = 0, verbose = True):
# Load Data Format
n = data['n']
r = data['r']
p = data['p']
s = data['s']
c = data['c']
h = data['h']
w = data['w']
location = data['location']
conflicts = data['conflicts']
locking_times = data['locking_times']
T = data['T']
model = Model("ExaminationScheduling")
if verbose:
print("Building variables...")
# x[i,k,l] = 1 if exam i is at time l in room k
x = {}
for k in range(r):
for l in range(p):
if T[k][l] == 1:
for i in range(n):
if location[k] in w[i]:
x[i,k,l] = model.addVar(vtype=GRB.BINARY, name="x_%s_%s_%s" % (i,k,l))
# y[i,l] = 1 if exam i is at time l
y = {}
for i in range(n):
for l in range(p):
y[i, l] = model.addVar(vtype=GRB.BINARY, name="y_%s_%s" % (i,l))
# integrate new variables
model.update()
start = timeit.default_timer()
# not very readable but same constraints as in GurbiLinear_v_10: speeded up model building by 2 for small problems (~400 exams) and more for huger problem ~1500 exams
if verbose:
print("Building constraints...")
obj = LinExpr()
sumconflicts = {}
maxrooms = {}
for i in range(n):
sumconflicts[i] = sum(conflicts[i])
if s[i] <= 50:
maxrooms[i] = 1
elif s[i] <= 100:
maxrooms[i] = 2
elif s[i] <= 400:
maxrooms[i] = 7
elif s[i] <= 700:
maxrooms[i] = 9
else:
maxrooms[i] = 12
c2 = LinExpr()
c4 = LinExpr()
for l in range(p):
c1 = LinExpr()
c1 = LinExpr()
c3 = LinExpr()
for k in range(r):
if T[k][l] == 1 and location[k] in w[i]:
c1.addTerms(1, x[i, k, l])
c4.addTerms(c[k],x[i,k,l])
obj += c1
model.addConstr(c1 <= maxrooms[i]* y[i,l], "c1a")
model.addConstr(c1 >= y[i,l], "C1b")
for j in conflicts[i]:
c3.addTerms(1,y[j,l])
model.addConstr(c3 <= (1 - y[i,l])*sumconflicts[i], "c3")
c2.addTerms(1,y[i,l])
model.addConstr( c2 == 1 , "c2")
model.addConstr(c4 >= s[i], "c4")
sumrooms = {}
for l in range(p):
sumrooms[l] = 0
cover_inequalities = LinExpr()
for k in range(r):
if T[k][l] == 1:
sumrooms[l] += 1
c5 = LinExpr()
for i in range(n):
if location[k] in w[i]:
c5.addTerms(1,x[i,k,l])
model.addConstr( c5 <= 1, "c5")
cover_inequalities += c5
model.addConstr(cover_inequalities <= sumrooms[l], "cover_inequalities")
model.setObjective( obj, GRB.MINIMIZE)
print timeit.default_timer()-start
if verbose:
print("All constrained and objective built - OK")
if not verbose:
model.params.OutputFlag = 0
# Set Parameters
#print("Setting Parameters...")
# max presolve agressivity
#model.params.presolve = 2
# Choosing root method 3= concurrent = run barrier and dual simplex in parallel
#model.params.method = 1
#model.params.MIPFocus = 1
model.params.OutputFlag = 1
model.params.Method = 3
# cuts
model.params.cuts = 0
model.params.cliqueCuts = 0
model.params.coverCuts = 0
model.params.flowCoverCuts = 0
model.params.FlowPathcuts = 0
model.params.GUBCoverCuts = 0
model.params.impliedCuts = 0
model.params.MIPSepCuts = 0
model.params.MIRCuts = 0
model.params.ModKCuts = 0
model.params.NetworkCuts = 2
model.params.SUBMIPCuts = 0
model.params.ZeroHalfCuts = 0
model.params.TimeLimit = 30
# # Tune the model
# model.tune()
# if model.tuneResultCount > 0:
# # Load the best tuned parameters into the model
# model.getTuneResult(0)
# # Write tuned parameters to a file
# model.write('tune1.prm')
# return
return(model)
def __optmize_single_project(self, x, j):
'''
Given the generated x for single project, try to optimize the tardiness of the project.
:param x: the assignment of resource supplier to project
:param j: index of project
:return:
'''
m = Model("SingleProject_%d" % j)
#### Create variables ####
project = self.project_list[j]
## Project complete data,Project Tadeness,construction completion time
CT = m.addVar(obj=0, vtype=GRB.CONTINUOUS, name="(CT%d)" % j)
## Activity start time
ST = {}
project_activities = self.project_activity[project]
# print(project_activities.nodes())
for row in project_activities.nodes():
ST[row] = m.addVar(obj=0, vtype=GRB.CONTINUOUS, name="(ST%d,%s)" % (j, row))
## Review sequence z_ij
## move to annealing objective function
# y
y = {}
for activity_i in project_activities.nodes():
for activity_j in project_activities.nodes():
# print(project_activities.node[activity_i])
# print(dir(project_activities.node[activity_i]))
if activity_i != activity_j and len(list(
set(project_activities.node[activity_i]['rk_resources']).intersection(
project_activities.node[activity_j]['rk_resources']))) > 0:
y[activity_i, activity_j] = m.addVar(obj=0, vtype=GRB.BINARY,
name="(y%d,%s,%s)" % (j, activity_i, activity_j))
m.update()
#### Create constrains ####
## Constrain 2: project complete data>due data
## move to annealing objective function
## Constrain 3: supplier capacity limit
## move to annealing neighbor & random generator
## Constrain 4,6: project demand require; each project receive from one supplier for each resource
## move to annealing neighbor & random generator
## constrain 5: shipping constrain
## move to annealing neighbor & random generator
## Constrain 7:budget limit
## move to annealing constraint valid
## Constrain 8: activity starting constrain
for a in project_activities.nodes():
for r in project_activities.node[a]['resources']:
resource_delivered_days = 0
for s in self.resource_supplier_list[r]:
resource_delivered_days += x.get((r, s, project), 0) * \
(self.resource_supplier_release_time[r, s] +
self.supplier_project_shipping[
r, s, project])
m.addConstr(resource_delivered_days, GRB.LESS_EQUAL, ST[a],
name="constraint_8_project_%d_activity_%s_resource_%s" % (j, a, r))
## Constrain 9 activity sequence constrain
for row1, row2 in project_activities.edges():
# print(row1, '#', row2, '#', j)
# print(ST)
m.addConstr(ST[row1] + project_activities.node[row1]['duration'], GRB.LESS_EQUAL,
ST[row2], name="constraint_9_project_%d_activity_%s_activity_%s" % (j, row1, row2))
## Constrain 10,11
for row1 in project_activities.nodes():
for row2 in project_activities.nodes():
if row1 != row2 and len(list(
set(project_activities.node[row1]['rk_resources']).intersection(
project_activities.node[row2]['rk_resources']))) > 0:
m.addConstr(ST[row1] + project_activities.node[row1]['duration'] - self.M * (
1 - y[row1, row2]), GRB.LESS_EQUAL, ST[row2],
name="constraint_10_project_%d_activity_%s_activity_%s" % (j, row1, row2))
m.addConstr(
ST[row2] + project_activities.node[row2]['duration'] - self.M * (y[row1, row2]),
GRB.LESS_EQUAL, ST[row1],
name="constraint_11_project_%d_activity_%s_activity_%s" % (j, row1, row2))
# m.addConstr(y[j,row1,row2]+y[j,row2,row1],GRB.LESS_EQUAL,1)
## Constrain 12
for row in project_activities.nodes():
# print(project_activities.node[row]['duration'])
m.addConstr(CT, GRB.GREATER_EQUAL, ST[row] + project_activities.node[row]['duration'],
name="constraint_12_project_%d_activity_%s" % (j, row))
## Constrain 13
## move to anealing objective function
## Constrain 14
## move to anealing objective function
## Constrain 15
## move to anealing objective function
## Constrain 16
## move to anealing objective function
## Constrain 17
## move to anealing objective function
m.update()
# Set optimization objective - minimize completion time
expr = LinExpr()
expr.add(CT)
m.setObjective(expr, GRB.MINIMIZE)
m.update()
##########################################
m.params.presolve = 1
m.update()
# Solve
# m.params.presolve=0
m.optimize()
m.write(join(self.output_dir, "heuristic_%d.lp" % j))
m.write(join(self.output_dir, "heuristic_%d.sol" % j))
return m.objVal
def lazy_cycle_constraint(A, C, k, gap):
"""
Lazily generate cycle constraints as potential feasible solutions
are generated.
"""
_ = '*'
m = Model()
m.modelsense = GRB.MAXIMIZE
m.params.mipgap = gap
m.params.timelimit = 5 * 60 * 60
m.params.lazyconstraints = 1
n = A.shape[0]
edges = tuplelist()
vars = {}
for i in range(n):
for j in range(n):
if A[i, j] == 1:
e = (i, j)
edges.append(e)
w = 2 if j in C else 1
var = m.addVar(vtype=GRB.BINARY, obj=w)
vars[e] = var
m.update()
# flow constraints
for i in range(n):
out_vars = [vars[e] for e in edges.select(i, _)]
out_ones = [1.0]*len(out_vars)
out_expr = LinExpr()
out_expr.addTerms(out_ones, out_vars)
in_vars = [vars[e] for e in edges.select(_, i)]
in_ones = [1.0]*len(in_vars)
in_expr = LinExpr()
in_expr.addTerms(in_ones, in_vars)
m.addConstr(in_expr <= 1)
m.addConstr(out_expr == in_expr)
m.update()
ith_cycle = 0
def callback(model, where):
if where == GRB.Callback.MIPSOL:
sols = model.cbGetSolution([vars[e] for e in edges])
c_edges = [edges[i] for i in range(len(edges)) if sols[i] > 0.5]
cycles = cycles_from_edges(c_edges)
for cycle in cycles:
len_cycle = len(cycle)
if len_cycle > k:
cycle_vars = [vars[(cycle[i], cycle[(i+1) % len_cycle])] for i in range(len_cycle)]
ones = [1.0]*len(cycle_vars)
expr = LinExpr()
expr.addTerms(ones, cycle_vars)
model.cbLazy(expr <= len_cycle - 1)
m.optimize(callback)
m.update()
c_edges = [e for e in edges if vars[e].x == 1.0]
cycles = cycles_from_edges(c_edges)
return cycles, m.objval
def gurobi(wanted_parts, available_parts, stores, shipping_cost=10.0):
from gurobipy import Model, GRB, LinExpr
kf1 = lambda x: (x['item_id'], x['wanted_color_id'])
kf2 = lambda x: (x['ItemID'], x['ColorID'])
available_by_store = utils.groupby(available_parts, lambda x: x['store_id'])
store_by_id = dict( (s['store_id'], s) for s in stores )
m = Model()
store_variables = {} # store id to variable indicating store is used
quantity_variables = [] # list of all lot variables + metadata
# for every store
for (store_id, inventory) in available_by_store.iteritems():
# a variable for if anything was bought from this store. if 1, then pay
# shipping cost and all store inventory is available; if 0, then don't pay
# for shipping and every lot in it has 0 quantity available
store_variables[store_id] = m.addVar(0.0, 1.0, shipping_cost, GRB.BINARY,
"use-store=%s" % (store_id,))
for lot in inventory:
store_id = lot['store_id']
quantity = lot['quantity_available']
unit_cost= lot['cost_per_unit']
item_id = lot['item_id']
color_id = lot['color_id']
# a variable for how much to buy of this lot
v = m.addVar(0.0, quantity, unit_cost, GRB.CONTINUOUS,
"quantity-store=%s-item=%s-color=%s" % (store_id, item_id, color_id))
# keep a list of all lots
quantity_variables.append({
'store_id': store_id,
'item_id': lot['item_id'],
'wanted_color_id': lot['wanted_color_id'],
'color_id': lot['color_id'],
'variable': v,
'quantity_available': quantity,
'cost_per_unit': unit_cost
})
# actually put the variables into the model
m.update()
# for every lot in every store
for lot in quantity_variables:
use_store = store_variables[lot['store_id']]
quantity = lot['quantity_available']
unit_cost = lot['cost_per_unit']
v = lot['variable']
# a constraint for how much can be bought
m.addConstr(LinExpr([1.0, -1 * quantity], [v, use_store]),
GRB.LESS_EQUAL, 0.0,
"maxquantity-store=%s-item=%s-color-%d" % (lot['store_id'], lot['item_id'], lot['color_id']))
# for every wanted lot
variables_by_id = utils.groupby(quantity_variables, kf1)
for lot in wanted_parts:
# a constraint saying amount bought >= wanted amount
variables = map(lambda x: x['variable'], variables_by_id[kf2(lot)])
constants = len(variables) * [1.0]
m.addConstr(LinExpr(constants, variables),
GRB.GREATER_EQUAL, lot['Qty'],
"wantedamount-item=%s-color=%s" % (lot['ItemID'], lot['ColorID']))
# for every store
variables_by_store = utils.groupby(quantity_variables, lambda x: x['store_id'])
for (store_id, variables) in variables_by_store.iteritems():
use_store = store_variables[store_id]
minimum_purchase = store_by_id[store_id]['minimum_buy']
# a constraint saying "if I purchased from this store, I bought the minimum amount or more"
constants = [v['cost_per_unit'] for v in variables] + [-1 * minimum_purchase]
variables = [v['variable'] for v in variables] + [use_store]
m.addConstr(LinExpr(constants, variables),
GRB.GREATER_EQUAL, 0.0,
"minbuy-store=%d" % (store_id,))
# minimize sum of costs of items bought + shipping costs
m.setParam(GRB.param.MIPGap, 0.01) # stop when duality gap <= 1%
m.optimize()
# get results
if m.ObjVal < float('inf'):
result = []
for lot in quantity_variables:
# get variable out
v = lot['variable']
del lot['variable']
# lot variables are continuous, so they might not actually be integral.
# If they're not, check that they're "almost" integral, so we can just
# round. Otherwise, print this warning. According to theory the optimal
# solution is for all continuous variables to be integral.
if v.X != int(v.X) and abs(v.X - round(v.X)) > 1e-3:
print 'Uh oh. Variable %s has value %f. This is a little close for comfort.' % (v.VarName, v.X)
# save quantity to buy if it's > 0
lot['quantity'] = int(round(v.X))
if lot['quantity'] > 0:
result.append(lot)
cost = sum(e['quantity'] * e['cost_per_unit'] for e in result)
store_ids = list(set(e['store_id'] for e in result))
return [{
'cost': cost,
'allocation': result,
'store_ids': store_ids
}]
else:
print 'No solution :('
return []
def constantino(A, C, k, gap):
"""
Polynomial-sized CCMcP Edge-Extended Model
See Constantino et al. (2013)
"""
t_0 = time.clock()
_ = '*'
m = Model()
m.modelsense = GRB.MAXIMIZE
m.params.mipgap = gap
# m.params.timelimit = 60 * 60
# m.params.nodefilestart = 1.0
# m.params.nodefiledir = './.nodefiledir'
# m.params.presparsify = 0
# m.params.presolve = 0
n = A.shape[0]
vars = {}
edges = tuplelist()
print('[%.1f] Generating variables...' % (time.clock() - t_0))
# Variables
for l in range(n):
for i in range(l, n):
for j in range(l, n):
if A[i, j] == 1:
e = (l, i, j)
edges.append(e)
w = 2 if j in C else 1
var = m.addVar(vtype=GRB.BINARY, obj=w)
vars[e] = var
if l % 100 == 0 and l != 0:
print('[%.1f] l = %d' % (time.clock() - t_0, l))
m.update()
print('[%.1f] Generated variables' % (time.clock() - t_0))
print('[%.1f] Adding flow constraints...' % (time.clock() - t_0))
# Constraint (2): Flow in = Flow out
for l in range(n):
for i in range(l, n):
# Flow in
lhs_vars = [vars[e] for e in edges.select(l, _, i)]
ones = [1.0]*len(lhs_vars)
lhs = LinExpr()
lhs.addTerms(ones, lhs_vars)
# Flow out
rhs_vars = [vars[e] for e in edges.select(l, i, _)]
ones = [1.0]*len(rhs_vars)
rhs = LinExpr()
rhs.addTerms(ones, rhs_vars)
# Flow in = Flow out
m.addConstr(lhs == rhs)
if l % 100 == 0 and l != 0:
print('[%.1f] l = %d' % (time.clock() - t_0, l))
print('[%.1f] Added flow constraints' % (time.clock() - t_0))
print('[%.1f] Adding cycle vertex constraints...' % (time.clock() - t_0))
# Constraint (3): Use a vertex only once per cycle
for i in range(n):
c_vars = [vars[e] for e in edges.select(_, i, _)]
ones = [1.0]*len(c_vars)
expr = LinExpr()
expr.addTerms(ones, c_vars)
m.addConstr(expr <= 1.0)
if i % 100 == 0 and i != 0:
print('[%.1f] V_i = %d' % (time.clock() - t_0, i))
print('[%.1f] Added cycle vertex constraints' % (time.clock() - t_0))
print('[%.1f] Adding cycle cardinality constraints...' % (time.clock() - t_0))
# Constraint (4): Limit cardinality of cycles to k
for l in range(n):
c_vars = [vars[e] for e in edges.select(l, _, _)]
ones = [1.0]*len(c_vars)
expr = LinExpr()
expr.addTerms(ones, c_vars)
m.addConstr(expr <= k)
if l % 100 == 0 and l != 0:
print('[%.1f] l = %d' % (time.clock() - t_0, l))
print('[%.1f] Added cycle cardinality constraints' % (time.clock() - t_0))
print('[%.1f] Adding cycle index constraints...' % (time.clock() - t_0))
# Constraint (5): Cycle index is smallest vertex-index
for l in range(n):
rhs_vars = [vars[e] for e in edges.select(l, l, _)]
ones = [1.0]*len(rhs_vars)
rhs = LinExpr()
rhs.addTerms(ones, rhs_vars)
for i in range(l+1, n):
lhs_vars = [vars[e] for e in edges.select(l, i, _)]
if len(lhs_vars) > 0:
ones = [1.0]*len(lhs_vars)
lhs = LinExpr()
lhs.addTerms(ones, lhs_vars)
m.addConstr(lhs <= rhs)
if l % 100 == 0 and l != 0:
print('[%.1f] l = %d' % (time.clock() - t_0, l))
print('[%.1f] Added cycle index constraints...' % (time.clock() - t_0))
print('[%.1f] Begin Optimizing %d vertex model' % (time.clock() - t_0, n))
m.optimize()
m.update()
print('[%.1f] Finished Optimizing' % (time.clock() - t_0))
print('[%.1f] Building cycles...' % (time.clock() - t_0))
cycles = []
for l in range(n):
c_edges = [(e[1], e[2]) for e in edges.select(l, _, _) if vars[e].x == 1.0]
cycles.extend(cycles_from_edges(c_edges))
print('[%.1f] Finished building cycles' % (time.clock() - t_0))
return cycles, m.objval
def _optimize_gurobi(cobra_model, new_objective=None, objective_sense='maximize',
min_norm=0, the_problem=None,
tolerance_optimality=1e-6, tolerance_feasibility=1e-6,
tolerance_barrier=None, tolerance_integer=1e-9, error_reporting=None,
print_solver_time=False, copy_problem=False, lp_method=0,
relax_b=None, quad_precision=False, quadratic_component=None,
reuse_basis=True, lp_parallel=None, update_problem_reaction_bounds=True):
"""Uses the gurobi (http://gurobi.com) optimizer to perform an optimization on cobra_model
for the objective_coefficients in cobra_model._objective_coefficients based
on objective sense.
cobra_model: A cobra.Model object
new_objective: Reaction, String, or Integer referring to a reaction in
cobra_model.reactions to set as the objective. Currently, only supports single
objective coeffients. Will expand to include mixed objectives.
objective_sense: 'maximize' or 'minimize'
min_norm: not implemented
the_problem: None or a problem object for the specific solver that can be used to hot
start the next solution.
tolerance_optimality: Solver tolerance for optimality.
tolerance_feasibility: Solver tolerance for feasibility.
quad_precision: Boolean. Whether or not to used quad precision in calculations
error_reporting: None or True to disable or enable printing errors encountered
when trying to find the optimal solution.
print_solver_time: False or True. Indicates if the time to calculate the solution
should be displayed.
quadratic_component: None or
scipy.sparse.dok of dim(len(cobra_model.reactions),len(cobra_model.reactions))
If not None:
Solves quadratic programming problems for cobra_models of the form:
minimize: 0.5 * x' * quadratic_component * x + cobra_model._objective_coefficients' * x
such that,
cobra_model._lower_bounds <= x <= cobra_model._upper_bounds
cobra_model._S * x (cobra_model._constraint_sense) cobra_model._b
NOTE: When solving quadratic problems it may be necessary to disable quad_precision
and use lp_method = 0 for gurobi.
reuse_basis: Boolean. If True and the_problem is a model object for the solver,
attempt to hot start the solution.
update_problem_reaction_bounds: Boolean. Set to True if you're providing the_problem
and you've modified reaction bounds on your cobra_model since creating the_problem. Only
necessary for CPLEX
lp_parallel: Not implemented
lp.optimize() with Salmonella model:
cold start: 0.063 seconds
hot start: 0.057 seconds (Slow due to copying the LP)
"""
if relax_b is not None:
raise Exception('Need to reimplement constraint relaxation')
from numpy import array, nan, zeros
#TODO: speed this up
if objective_sense == 'maximize':
objective_sense = -1
else:
objective_sense = 1
from gurobipy import Model, LinExpr, GRB, QuadExpr
sense_dict = {'E': GRB.EQUAL,
'L': GRB.LESS_EQUAL,
'G': GRB.GREATER_EQUAL}
from cobra.flux_analysis.objective import update_objective
from cobra.solvers.legacy import status_dict, variable_kind_dict
variable_kind_dict = eval(variable_kind_dict['gurobi'])
status_dict = eval(status_dict['gurobi'])
#Update objectives if they are new.
if new_objective and new_objective != 'update problem':
update_objective(cobra_model, new_objective)
#Create a new problem
if not the_problem or the_problem in ['return', 'setup'] or \
not isinstance(the_problem, Model):
lp = Model("cobra")
lp.Params.OutputFlag = 0
lp.Params.LogFile = ''
# Create variables
#TODO: Speed this up
variable_list = [lp.addVar(lb=float(x.lower_bound),
ub=float(x.upper_bound),
obj=objective_sense*float(x.objective_coefficient),
name=x.id,
vtype=variable_kind_dict[x.variable_kind])
for x in cobra_model.reactions]
reaction_to_variable = dict(zip(cobra_model.reactions,
variable_list))
# Integrate new variables
lp.update()
#Set objective to quadratic program
if quadratic_component is not None:
if not hasattr(quadratic_component, 'todok'):
raise Exception('quadratic component must be a scipy.sparse type array')
quadratic_objective = QuadExpr()
for (index_0, index_1), the_value in quadratic_component.todok().items():
quadratic_objective.addTerms(the_value,
variable_list[index_0],
variable_list[index_1])
lp.setObjective(quadratic_objective, sense=objective_sense)
#Constraints are based on mass balance
#Construct the lin expression lists and then add
#TODO: Speed this up as it takes about .18 seconds
#HERE
for the_metabolite in cobra_model.metabolites:
constraint_coefficients = []
constraint_variables = []
for the_reaction in the_metabolite._reaction:
constraint_coefficients.append(the_reaction._metabolites[the_metabolite])
constraint_variables.append(reaction_to_variable[the_reaction])
#Add the metabolite to the problem
lp.addConstr(LinExpr(constraint_coefficients, constraint_variables),
sense_dict[the_metabolite._constraint_sense.upper()],
the_metabolite._bound,
the_metabolite.id)
else:
#When reusing the basis only assume that the objective coefficients or bounds can change
if copy_problem:
lp = the_problem.copy()
else:
lp = the_problem
if not reuse_basis:
lp.reset()
for the_variable, the_reaction in zip(lp.getVars(),
cobra_model.reactions):
the_variable.lb = float(the_reaction.lower_bound)
the_variable.ub = float(the_reaction.upper_bound)
the_variable.obj = float(objective_sense*the_reaction.objective_coefficient)
if the_problem == 'setup':
return lp
if print_solver_time:
start_time = time()
lp.update()
lp.setParam("FeasibilityTol", tolerance_feasibility)
lp.setParam("OptimalityTol", tolerance_optimality)
if tolerance_barrier:
lp.setParam("BarConvTol", tolerance_barrier)
if quad_precision:
lp.setParam("Quad", 1)
lp.setParam("Method", lp_method)
#Different methods to try if lp_method fails
the_methods = [0, 2, 1]
if lp_method in the_methods:
the_methods.remove(lp_method)
if not isinstance(the_problem, Model):
lp.optimize()
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
#Try to find a solution using a different method
lp.setParam("MarkowitzTol", 1e-2)
for lp_method in the_methods:
lp.setParam("Method", lp_method)
lp.optimize()
if status_dict[lp.status] == 'optimal':
break
else:
lp.setParam("TimeLimit", 0.6)
lp.optimize()
lp.setParam("TimeLimit", "default")
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp.setParam("MarkowitzTol", 1e-2)
#Try to find a solution using a different method
for lp_method in the_methods:
lp.setParam("Method", lp_method)
lp.optimize()
if status_dict[lp.status] == 'optimal':
break
if status_dict[lp.status] != 'optimal':
lp = optimize_gurobi(cobra_model, new_objective=new_objective, objective_sense=objective_sense,
min_norm=min_norm, the_problem=None,
print_solver_time=print_solver_time)['the_problem']
if print_solver_time:
print 'optimize time: %f'%(time() - start_time)
x_dict = {}
y_dict = {}
y = None
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status == 'optimal':
objective_value = objective_sense*lp.ObjVal
[x_dict.update({v.VarName: v.X}) for v in lp.getVars()]
x = array([x_dict[v.id] for v in cobra_model.reactions])
if lp.isMIP:
y = y_dict = None #MIP's don't have duals
else:
[y_dict.update({c.ConstrName: c.Pi})
for c in lp.getConstrs()]
y = array([y_dict[v.id] for v in cobra_model.metabolites])
else:
y = y_dict = x = x_dict = None
objective_value = None
if error_reporting:
print 'gurobi failed: %s'%lp.status
the_solution = Solution(objective_value, x=x, x_dict=x_dict,
y=y, y_dict=y_dict,
status=status)
solution = {'the_problem': lp, 'the_solution': the_solution}
return solution
def build_model(data, n_cliques = 0, verbose = True):
# Load Data Format
n = data['n']
r = data['r']
p = data['p']
s = data['s']
c = data['c']
h = data['h']
w = data['w']
location = data['location']
conflicts = data['conflicts']
locking_times = data['locking_times']
T = data['T']
model = Model("ExaminationScheduling")
if verbose:
print("Building variables...")
# x[i,k,l] = 1 if exam i is at time l in room k
x = {}
for k in range(r):
for l in range(p):
if T[k][l] == 1:
for i in range(n):
if location[k] in w[i]:
x[i,k,l] = model.addVar(vtype=GRB.BINARY, name="x_%s_%s_%s" % (i,k,l))
# y[i,l] = 1 if exam i is at time l
y = {}
for i in range(n):
for l in range(p):
y[i, l] = model.addVar(vtype=GRB.BINARY, name="y_%s_%s" % (i,l))
# integrate new variables
model.update()
start = timeit.default_timer()
# adding constraints as found in MidTerm.pdf
if verbose:
print("Building constraints...")
if verbose:
print("c1: connecting variables x and y")
for i in range(n):
for l in range(p):
model.addConstr( quicksum([ x[i, k, l] for k in range(r) if T[k][l] == 1 and location[k] in w[i] ]) <= 12 * y[i, l], "c1a")
model.addConstr( quicksum([ x[i, k, l] for k in range(r) if T[k][l] == 1 and location[k] in w[i] ]) >= y[i, l], "c1b")
if verbose:
print("c2: each exam at exactly one time")
for i in range(n):
model.addConstr( quicksum([ y[i, l] for l in range(p) ]) == 1 , "c2")
"""
Idea: -instead of saving a conflict Matrix, save Cliques of exams that cannot be written at the same time
-then instead of saying of one exam is written in a given period all conflicts cannot be written in the same period we could say
-for all exams in a given clique only one can be written
"""
if verbose:
print("c3: avoid conflicts")
for i in range(n):
for l in range(p):
# careful!! Big M changed!
model.addConstr(quicksum([ y[j,l] for j in conflicts[i] ]) <= (1 - y[i, l]) * sum(conflicts[i]), "c3")
if verbose:
print("c4: seats for all students")
for i in range(n):
model.addConstr( quicksum([ x[i, k, l] * c[k] for k in range(r) for l in range(p) if T[k][l] == 1 and location[k] in w[i] ]) >= s[i], "c4")
if verbose:
print("c5: only one exam per room per period")
for k in range(r):
for l in range(p):
if T[k][l] == 1:
model.addConstr( quicksum([ x[i, k, l] for i in range(n) if location[k] in w[i] ]) <= 1, "c5")
if verbose:
print("All constrained built - OK")
# objective: minimize number of used rooms
if verbose:
print("Building Objective...")
obj1 = quicksum([ x[i,k,l] for i,k,l in itertools.product(range(n), range(r), range(p)) if T[k][l] == 1 and location[k] in w[i]])
model.setObjective( obj1, GRB.MINIMIZE)
print timeit.default_timer()-start
if not verbose:
model.params.OutputFlag = 0
# Set Parameters
#print("Setting Parameters...")
# max presolve agressivity
#model.params.presolve = 2
# Choosing root method 3= concurrent = run barrier and dual simplex in parallel
#model.params.method = 1
#model.params.MIPFocus = 1
#model.params.cuts = 0
model.params.OutputFlag = 1
# # Tune the model
# model.tune()
# if model.tuneResultCount > 0:
# # Load the best tuned parameters into the model
# model.getTuneResult(0)
# # Write tuned parameters to a file
# model.write('tune1.prm')
# return
return(model)
class GurobiSolver(Solver):
""" Implements the solver interface using gurobipy. """
def __init__(self):
Solver.__init__(self)
self.problem = GurobiModel()
def __getstate__(self):
tmp_file = tempfile.mktemp(suffix=".lp")
self.problem.update()
self.problem.write(tmp_file)
cplex_form = open(tmp_file).read()
repr_dict = {'var_ids': self.var_ids, 'constr_ids': self.constr_ids, 'cplex_form': cplex_form}
return repr_dict
def __setstate__(self, repr_dict):
tmp_file = tempfile.mktemp(suffix=".lp")
open(tmp_file, 'w').write(repr_dict['cplex_form'])
self.problem = read(tmp_file)
self.var_ids = repr_dict['var_ids']
self.constr_ids = repr_dict['constr_ids']
def add_variable(self, var_id, lb=None, ub=None, vartype=VarType.CONTINUOUS, persistent=True, update_problem=True):
""" Add a variable to the current problem.
Arguments:
var_id : str -- variable identifier
lb : float -- lower bound
ub : float -- upper bound
vartype : VarType -- variable type (default: CONTINUOUS)
persistent : bool -- if the variable should be reused for multiple calls (default: true)
update_problem : bool -- update problem immediately (default: True)
"""
lb = lb if lb is not None else -GRB.INFINITY
ub = ub if ub is not None else GRB.INFINITY
map_types = {VarType.BINARY: GRB.BINARY,
VarType.INTEGER: GRB.INTEGER,
VarType.CONTINUOUS: GRB.CONTINUOUS}
if var_id in self.var_ids:
var = self.problem.getVarByName(var_id)
var.setAttr('lb', lb)
var.setAttr('ub', ub)
var.setAttr('vtype', map_types[vartype])
else:
self.problem.addVar(name=var_id, lb=lb, ub=ub, vtype=map_types[vartype])
self.var_ids.append(var_id)
if not persistent:
self.temp_vars.add(var_id)
if update_problem:
self.problem.update()
def add_constraint(self, constr_id, lhs, sense='=', rhs=0, persistent=True, update_problem=True):
""" Add a variable to the current problem.
Arguments:
constr_id : str -- constraint identifier
lhs : list [of (str, float)] -- variables and respective coefficients
sense : {'<', '=', '>'} -- default '='
rhs : float -- right-hand side of equation (default: 0)
persistent : bool -- if the variable should be reused for multiple calls (default: True)
update_problem : bool -- update problem immediately (default: True)
"""
grb_sense = {'=': GRB.EQUAL,
'<': GRB.LESS_EQUAL,
'>': GRB.GREATER_EQUAL}
if constr_id in self.constr_ids:
constr = self.problem.getConstrByName(constr_id)
self.problem.remove(constr)
expr = quicksum([coeff * self.problem.getVarByName(r_id) for r_id, coeff in lhs if coeff])
self.problem.addConstr(expr, grb_sense[sense], rhs, constr_id)
self.constr_ids.append(constr_id)
if not persistent:
self.temp_constrs.add(constr_id)
if update_problem:
self.problem.update()
def remove_variable(self, var_id):
""" Remove a variable from the current problem.
Arguments:
var_id : str -- variable identifier
"""
if var_id in self.var_ids:
self.problem.remove(self.problem.getVarByName(var_id))
self.var_ids.remove(var_id)
def remove_constraint(self, constr_id):
""" Remove a constraint from the current problem.
Arguments:
constr_id : str -- constraint identifier
"""
if constr_id in self.constr_ids:
self.problem.remove(self.problem.getConstrByName(constr_id))
self.constr_ids.remove(constr_id)
def update(self):
""" Update internal structure. Used for efficient lazy updating. """
self.problem.update()
def solve_lp(self, objective, model=None, constraints=None, get_shadow_prices=False, get_reduced_costs=False):
""" Solve an LP optimization problem.
Arguments:
objective : dict (of str to float) -- reaction ids in the objective function and respective
coefficients, the sense is maximization by default
model : ConstraintBasedModel -- model (optional, leave blank to reuse previous model structure)
constraints : dict (of str to (float, float)) -- environmental or additional constraints (optional)
get_shadow_prices : bool -- return shadow price information if available (optional, default: False)
get_reduced_costs : bool -- return reduced costs information if available (optional, default: False)
Returns:
Solution
"""
return self._generic_solve(None, objective, GRB.MAXIMIZE, model, constraints, get_shadow_prices,
get_reduced_costs)
def solve_qp(self, quad_obj, lin_obj, model=None, constraints=None, get_shadow_prices=False,
get_reduced_costs=False):
""" Solve an LP optimization problem.
Arguments:
quad_obj : dict (of (str, str) to float) -- map reaction pairs to respective coefficients
lin_obj : dict (of str to float) -- map single reaction ids to respective linear coefficients
model : ConstraintBasedModel -- model (optional, leave blank to reuse previous model structure)
constraints : dict (of str to (float, float)) -- overriding constraints (optional)
get_shadow_prices : bool -- return shadow price information if available (default: False)
get_reduced_costs : bool -- return reduced costs information if available (default: False)
Returns:
Solution
"""
return self._generic_solve(quad_obj, lin_obj, GRB.MINIMIZE, model, constraints, get_shadow_prices,
get_reduced_costs)
def _generic_solve(self, quad_obj, lin_obj, sense, model=None, constraints=None, get_shadow_prices=False,
get_reduced_costs=False):
if model:
self.build_problem(model)
problem = self.problem
if constraints:
old_constraints = {}
for r_id, (lb, ub) in constraints.items():
lpvar = problem.getVarByName(r_id)
old_constraints[r_id] = (lpvar.lb, lpvar.ub)
lpvar.lb = lb if lb is not None else -GRB.INFINITY
lpvar.ub = ub if ub is not None else GRB.INFINITY
problem.update()
#create objective function
quad_obj_expr = [q * problem.getVarByName(r_id1) * problem.getVarByName(r_id2)
for (r_id1, r_id2), q in quad_obj.items() if q] if quad_obj else []
lin_obj_expr = [f * problem.getVarByName(r_id)
for r_id, f in lin_obj.items() if f] if lin_obj else []
obj_expr = quicksum(quad_obj_expr + lin_obj_expr)
problem.setObjective(obj_expr, sense)
problem.update()
# from datetime import datetime
# self.problem.write("problem_{}.lp".format(str(datetime.now())))
#run the optimization
problem.optimize()
status = status_mapping[problem.status] if problem.status in status_mapping else Status.UNKNOWN
message = str(problem.status)
if status == Status.OPTIMAL:
fobj = problem.ObjVal
values = OrderedDict([(r_id, problem.getVarByName(r_id).X) for r_id in self.var_ids])
#if metabolite is disconnected no constraint will exist
shadow_prices = OrderedDict([(m_id, problem.getConstrByName(m_id).Pi)
for m_id in self.constr_ids
if problem.getConstrByName(m_id)]) if get_shadow_prices else None
reduced_costs = OrderedDict([(r_id, problem.getVarByName(r_id).RC)
for r_id in self.var_ids]) if get_reduced_costs else None
solution = Solution(status, message, fobj, values, shadow_prices, reduced_costs)
else:
solution = Solution(status, message)
#reset old constraints because temporary constraints should not be persistent
if constraints:
for r_id, (lb, ub) in old_constraints.items():
lpvar = problem.getVarByName(r_id)
lpvar.lb, lpvar.ub = lb, ub
problem.update()
return solution
def tsp_gurobi(edges):
"""
Modeled using GUROBI python example.
"""
from gurobipy import Model, GRB, quicksum
edges = populate_edge_weights(edges)
incoming, outgoing, nodes = node_to_edge(edges)
idx = dict((n, i) for i, n in enumerate(nodes))
nedges = len(edges)
n = len(nodes)
m = Model()
step = lambda x: "u_{0}".format(x)
# Create variables
vars = {}
for i, (a, b, w) in enumerate(edges):
vars[i] = m.addVar(obj=w, vtype=GRB.BINARY, name=str(i))
for u in nodes[1:]:
u = step(u)
vars[u] = m.addVar(obj=0, vtype=GRB.INTEGER, name=u)
m.update()
# Bounds for step variables
for u in nodes[1:]:
u = step(u)
vars[u].lb = 1
vars[u].ub = n - 1
# Add degree constraint
for v in nodes:
incoming_edges = incoming[v]
outgoing_edges = outgoing[v]
m.addConstr(quicksum(vars[x] for x in incoming_edges) == 1)
m.addConstr(quicksum(vars[x] for x in outgoing_edges) == 1)
# Subtour elimination
edge_store = dict(((idx[a], idx[b]), i) for i, (a, b, w) in enumerate(edges))
# Given a list of edges, finds the shortest subtour
def subtour(s_edges):
visited = [False] * n
cycles = []
lengths = []
selected = [[] for i in range(n)]
for x, y in s_edges:
selected[x].append(y)
while True:
current = visited.index(False)
thiscycle = [current]
while True:
visited[current] = True
neighbors = [x for x in selected[current] if not visited[x]]
if len(neighbors) == 0:
break
current = neighbors[0]
thiscycle.append(current)
cycles.append(thiscycle)
lengths.append(len(thiscycle))
if sum(lengths) == n:
break
return cycles[lengths.index(min(lengths))]
def subtourelim(model, where):
if where != GRB.callback.MIPSOL:
return
selected = []
# make a list of edges selected in the solution
sol = model.cbGetSolution([model._vars[i] for i in range(nedges)])
selected = [edges[i] for i, x in enumerate(sol) if x > .5]
selected = [(idx[a], idx[b]) for a, b, w in selected]
# find the shortest cycle in the selected edge list
tour = subtour(selected)
if len(tour) == n:
return
# add a subtour elimination constraint
c = tour
incident = [edge_store[a, b] for a, b in pairwise(c + [c[0]])]
model.cbLazy(quicksum(model._vars[x] for x in incident) <= len(tour) - 1)
m.update()
m._vars = vars
m.params.LazyConstraints = 1
m.optimize(subtourelim)
selected = [v.varName for v in m.getVars() if v.x > .5]
selected = [int(x) for x in selected if x[:2] != "u_"]
results = sorted(x for i, x in enumerate(edges) if i in selected) \
if selected else None
return results
def run_algorithm(self):
old_M = self.M
old_items = [i.copy() for i in self.items]
map_name_to_old_item = dict()
for i in old_items:
map_name_to_old_item[i.name] = i
self.scale_items_by_cost()
from gurobipy import Model, GRB
model = Model("NP-Hard")
print("Setting Model Parameters")
# set timeout
model.setParam('TimeLimit', 1600)
model.setParam('MIPFocus', 3)
model.setParam('PrePasses', 1)
model.setParam('Heuristics', 0.01)
model.setParam('Method', 0)
map_name_to_item = dict()
map_name_to_cost = dict()
map_name_to_weight = dict()
map_name_to_profit = dict()
map_class_to_name = dict()
item_names = list()
print("Preprocessing data for model...")
for item in self.items:
item_names.append(item.name)
map_name_to_item[item.name] = item
map_name_to_cost[item.name] = item.cost
map_name_to_weight[item.name] = item.weight
map_name_to_profit[item.name] = item.profit
if item.classNumber not in map_class_to_name:
map_class_to_name[item.classNumber] = list()
map_class_to_name[item.classNumber].append(item.name)
class_numbers = list(map_class_to_name.keys())
print("Setting model variables...")
# binary variables =1, if use>0
items = model.addVars(item_names, vtype=GRB.BINARY, name="items")
classes = model.addVars(class_numbers, vtype=GRB.BINARY, name="class numbers")
print("Setting model objective...")
# maximize profit
objective = items.prod(map_name_to_profit)
model.setObjective(objective, GRB.MAXIMIZE)
# constraints
print("Setting model constraints")
model.addConstr(items.prod(map_name_to_weight) <= self.P,"weight capacity")
model.addConstr(items.prod(map_name_to_cost) <= self.M,"cost capacity")
# if any item from a class is chosen, that class variable has to be a binary of 1
for num in class_numbers:
model.addGenConstrOr(classes[num], [items[x] for x in map_class_to_name[num]] ,name="class count")
for c in self.raw_constraints:
count = model.addVar()
for n in c:
if n in classes:
count += classes[n]
model.addConstr(count <= 1, name="constraint")
print("Start optimizing...")
model.optimize()
print("Done! ")
# Status checking
status = model.Status
if status == GRB.Status.INF_OR_UNBD or \
status == GRB.Status.INFEASIBLE or \
status == GRB.Status.UNBOUNDED:
print('The model cannot be solved because it is infeasible or unbounded')
if status != GRB.Status.OPTIMAL:
print('Optimization was stopped with status ' + str(status))
Problem = True
try:
model.write("mps_model/" + self.filename + ".sol")
except Exception as e:
pass
print("Generating solution file...")
# Display solution
solution_names = list()
for i, v in enumerate(items):
try:
if items[v].X > 0.9:
solution_names.append(item_names[i])
except Exception as e:
pass
self.M = old_M
self.items = old_items
solution = [map_name_to_old_item[i] for i in solution_names]
return solution
