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 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 retrieve_values(lp_problem: LpProblem, lp_variables: List[LpVariable],
model: gurobipy.Model) -> None:
""" Extract the value of variables from the gurobi model and set them into the Flipy objects
Parameters
----------
lp_problem:
The Flipy object into which the variable values will be set
lp_variables:
A list of LpVariables of the problem
model:
The gurobi model to grab the variable values from
"""
try:
var_name_to_values = dict(
zip(model.getAttr(gurobipy.GRB.Attr.VarName, model.getVars()),
model.getAttr(gurobipy.GRB.Attr.X, model.getVars())))
for var in lp_variables:
var.set_value(var_name_to_values[var.name])
for constraint in lp_problem.lp_constraints.values():
if constraint.slack:
constraint.slack_variable.set_value(
var_name_to_values[constraint.slack_variable.name])
except (gurobipy.GurobiError, AttributeError):
pass
def add_constraints(lp_problem: LpProblem, model: gurobipy.Model) -> None:
""" Add the constraints in a Flipy LpProblem to a gurobi model
Parameters
----------
lp_problem:
The Flipy object to grab the constraints from
model:
The gurobi model to add the constraints to
"""
for name, constraint in lp_problem.lp_constraints.items():
lhs_expr = [(coef, var.solver_var)
for var, coef in constraint.lhs.expr.items()]
if constraint.slack:
lhs_expr += [((-1 if constraint.sense == 'leq' else 1),
constraint.slack_variable.solver_var)]
lhs_expr = gurobipy.LinExpr(lhs_expr)
lhs_expr.addConstant(constraint.lhs.const)
rhs_expr = gurobipy.LinExpr([
(coef, var.solver_var)
for var, coef in constraint.rhs.expr.items()
])
rhs_expr.addConstant(constraint.rhs.const)
if constraint.sense.lower() == 'leq':
relation = gurobipy.GRB.LESS_EQUAL
elif constraint.sense.lower() == 'geq':
relation = gurobipy.GRB.GREATER_EQUAL
else:
relation = gurobipy.GRB.EQUAL
constraint.solver_constraint = model.addConstr(
lhs_expr, relation, rhs_expr, name)
model.update()
def __init__(self, index: int, scenario: float, probability: float,
cfg: Config):
self.cfg = cfg
self.probability = probability
self.index = index
self.scenario = scenario
self.objective = QuadExpr()
# model.ModelSense is minimization by default
self.model = Model(f"base_problem_{self.index}")
self.x_1 = self.model.addVar(ub=self.cfg.area, name="x_1")
self.x_2 = self.model.addVar(ub=self.cfg.area, name="x_2")
self.x_3 = self.model.addVar(ub=self.cfg.area, name="x_3")
self.model.addConstr(self.x_1 + self.x_2 + self.x_3 <= self.cfg.area)
self.objective.add(self.x_1 * self.cfg.wheat.plant_cost *
self.probability)
self.objective.add(self.x_2 * self.cfg.corn.plant_cost *
self.probability)
self.objective.add(self.x_3 * self.cfg.beet.plant_cost *
self.probability)
self._corn_variables_constraint()
self._wheat_variables_constraint()
self._beet_variables_constraint()
def __init__(self):
self.model = Model("benders_sub_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")
v_1 = self.model.addVar(lb=0, name="v_1")
self.model.addConstr(self.x_1 + self.x_4 + self.x_5 - v_1 <= 3)
v_2 = self.model.addVar(lb=0, name="v_2")
self.model.addConstr(2 * self.x_2 + 3 * self.x_4 - v_2 <= 12)
v_3 = self.model.addVar(lb=0, name="v_3")
self.model.addConstr(self.x_3 - 7 * self.x_5 - v_3 <= -16)
self.x_hat_4 = None
self.x_hat_5 = None
self.model.setObjective(
-2 * self.x_1 - self.x_2 + self.x_3 + BIG_M * v_1 + BIG_M * v_2 +
BIG_M * v_3,
GRB.MINIMIZE,
)
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 __init__(self, si: SolverInfo, budget, gurobi_params: Dict[str, Any] = None, ablation=False, overhead=False):
self.gurobi_params = gurobi_params
self.num_threads = self.gurobi_params.get('Threads', 1)
self.budget = int(budget * MEM_GCD_MULTIPLIER * GB_TO_KB)
self.si: SolverInfo = si
self.solve_time = None
self.ablation = ablation
self.overhead = overhead
V = self.si.loss + 1
T = len(self.si.nodes) - self.si.loss
Y = 3
budget = self.budget
self.m = Model("monet{}".format(self.budget))
if gurobi_params is not None:
for k, v in gurobi_params.items():
setattr(self.m.Params, k, v)
self.ram = np.array([math.ceil(self.si.nodes[i].mem*MEM_GCD_MULTIPLIER/1024) for i in self.si.nodes]) # Convert to KB
self.cpu = dict(( i, [math.ceil(val*CPU_GCD_MULTIPLIER) for val in self.si.nodes[i].workspace_compute] ) for i in self.si.nodes)
self.cpu_recompute = dict(( i, [math.ceil(val*CPU_GCD_MULTIPLIER) for val in self.si.nodes[i].recompute_workspace_compute] ) for i in self.si.nodes)
self.cpu_inplace = dict(( i, [math.ceil(val*CPU_GCD_MULTIPLIER) for val in self.si.nodes[i].inplace_workspace_compute] ) for i in self.si.nodes)
self.R = self.m.addVars(T, V, name="R", vtype=GRB.BINARY) # Recomputation
self.P = self.m.addVars(T, V, name="P", vtype=GRB.BINARY) # In-memory
self.S = self.m.addVars(T+1, V, name="S", vtype=GRB.BINARY) # Stored
self.M = self.m.addVars(T, Y, name="M", vtype=GRB.BINARY) # Backward operator implementation
self.SM = self.m.addVars(T, V, Y, name="SM", vtype=GRB.BINARY) # Linearization of S * M
if self.si.select_conv_algo:
self.RF = self.m.addVars(T, len(self.si.conv_list), self.si.num_conv_algos, name="RF", vtype=GRB.BINARY) # Conv operator implementations
if self.si.do_inplace:
self.IP = self.m.addVars(T, V, name="IP", vtype=GRB.BINARY) # In-place
class IandPModel:
def __init__(self, instance):
self.model = Model()
self.vars = dict()
self._set_model(instance)
def _set_model(self, instance):
T = instance.periods
c = instance.c
h = instance.h
d = instance.d
model = self.model
x = model.addVars(range(T))
z = model.addVars(range(T))
model.addConstrs(z[t] == z[t - 1] + x[t] - d[t] for t in range(1, T))
model.addConstr(z[0] == x[0] - d[0])
obj = quicksum(c[t] * x[t] + h[t] * z[t] for t in range(T))
model.setObjective(obj, sense=GRB.MINIMIZE)
self.vars = {'x': x, 'z': z}
def solve(self):
self.model.optimize()
def __build_base_model_for_hitting_set( self ) :
if self._use_pulp:
self.base_model = pulp.LpProblem( "min-cost-hitting-set", pulp.LpMinimize )
else:
self.base_model = Model( "min-cost-hitting-set" )
self.base_model.setParam( "OutputFlag", 0 )
# variables -> one per action
self.hs_vars = []
self.hs_coeffs = {}
for idx in xrange( len(self.task.actions) ) :
var_name = 'a_%d'%idx
if self._use_pulp:
self.hs_vars.append( pulp.LpVariable( var_name, 0, 1, cat = 'Integer' ) )
else:
self.hs_vars.append( self.base_model.addVar( name=var_name, vtype=GRB.BINARY ) )
self.hs_coeffs[ var_name ] = self.task.actions[idx].cost
if not self._use_pulp:
self.base_model.update()
# objective functions
if self._use_pulp:
obj = 0
for var in self.hs_vars:
obj = (self.hs_coeffs[var.getName()] * var) + obj
self.base_model.setObjective(obj)
else:
# MRJ: Support for non-unit costs, makes heuristic admissible if there are action costs
self.base_model.setObjective( quicksum( self.hs_coeffs[a.getAttr('VarName')] * a for a in self.hs_vars ), GRB.MINIMIZE )
# MRJ: Assumes action have unit costs, makes heuristic inadmissible if there are action costs
#self.base_model.setObjective( quicksum( a for a in self.hs_vars ), GRB.MINIMIZE )
self.base_model.update()
class RegressionModel:
def __init__(self, instance):
self.model = Model()
self.vars = dict()
self._set_model(instance)
def _set_model(self, instance):
model = self.model
factors = range(instance.factors)
obs = range(instance.obs)
X = instance.X
Y = instance.Y
beta_0 = model.addVar(lb=-GRB.INFINITY)
beta_1 = model.addVars(factors, lb=-GRB.INFINITY)
error = quicksum((Y[i] - beta_0 - quicksum(beta_1[j] * X[i][j] for j in factors)) ** 2 for i in obs)
model.setObjective(error, sense=GRB.MINIMIZE)
self.vars['beta_0'] = beta_0
self.vars['beta_1'] = beta_1
def solve(self):
self.model.optimize()
m = list(map(lambda x: x.X, self.vars['beta_1'].values()))
n = self.vars['beta_0'].X
return m, n
def set_solution_size(model: Model, size: int) -> None:
""" Set the number of solutions to be computed by optimizing the given model.
For Gurobi only.
"""
if args.use_gurobi:
model.setParam(GRB.param.PoolSearchMode, 2)
model.setParam(GRB.param.PoolSolutions, size)
def init(self, lp):
lp.build_original_model(data)
lp.model.optimize()
if lp.model.status == GRB.OPTIMAL:
lp.get_value()
number_of_invalid_paths = 0
for i in range(len(lp.routes)):
if len(lp.routes[i]) == 2:
number_of_invalid_paths += 1
if number_of_invalid_paths == 0:
self.data.veh_num -= 1
lp.model = Model("original_model")
lp = Bab_Vrptw(self.data)
return self.init(lp)
else:
self.data.veh_num -= number_of_invalid_paths
lp.model = Model("original_model")
lp = Bab_Vrptw(self.data)
return self.init(lp)
else:
data.veh_num += 1
lp.model = Model("original_model")
lp = Bab_Vrptw(data)
lp.build_original_model(data)
lp.model.optimize()
if lp.model.status == GRB.OPTIMAL:
lp.get_value()
return lp
else:
print("发现错误")
return None
def get_iis_weight(self, gmodel: Model,
iis_constrains: List[Constr]) -> int:
weight_a, weight_b = 0, 0
for c in iis_constrains:
weight_a += abs(gmodel.getCoeff(c, self.alpha_var))
weight_b += abs(gmodel.getCoeff(c, self.beta_var))
return weight_a + weight_b
def build_milp(self, model, **options):
self.milp = Model(self.name)
for param, value in options.items():
self.milp.setParam(param, value)
# ...
return self.milp
def __init__(self, name):
Model.__init__(self, name)
print str(self)
self.testVar = 4
self.createVars()
self.update()
self.createObjectiveFunction()
self.createConstraints()
def parse_results(model: gp.Model) -> None:
objVal = model.getObjective().getValue()
print("Get optimal Obj: {}".format(objVal))
print("Solution:")
for name, val in zip(model.getAttr("varName"), model.getAttr("x")):
print("Var {}: {}".format(name, val))
for con, val in zip(model.getAttr("constrName"), model.getAttr("Pi")):
print("Dual var of {}: {}".format(con, val))
def analizar(subcarpeta: str):
print(f"Analizando {subcarpeta}")
if not os.path.exists(os.path.join(os.getcwd(), 'output')):
os.makedirs(os.path.join(os.getcwd(), 'output'))
if not os.path.exists(os.path.join(os.getcwd(), 'output', subcarpeta)):
os.makedirs(os.path.join(os.getcwd(), 'output', subcarpeta))
if not os.path.exists(
os.path.join(os.getcwd(), 'output', subcarpeta, 'restricciones')):
os.makedirs(
os.path.join(os.getcwd(), 'output', subcarpeta, 'restricciones'))
if not os.path.exists(
os.path.join(os.getcwd(), 'output', subcarpeta, 'resultados')):
os.makedirs(
os.path.join(os.getcwd(), 'output', subcarpeta, 'resultados'))
if not os.path.exists(
os.path.join(os.getcwd(), 'output', subcarpeta, 'variables')):
os.makedirs(
os.path.join(os.getcwd(), 'output', subcarpeta, 'variables'))
if not os.path.exists(
os.path.join(os.getcwd(), 'output', subcarpeta, 'valores')):
os.makedirs(os.path.join(os.getcwd(), 'output', subcarpeta, 'valores'))
# cargamos los parámetros. Estos deben venir de los datos.
# Usamos pandas
parametros_dict = cargar_datos(subcarpeta)
# creamos el modelo
m = Model()
# cargamos las variables
variables_dict = cargar_variables(m, parametros_dict)
m.update()
# cargamos las restricciones
restricciones_dict = cargar_restricciones(m, variables_dict,
parametros_dict)
m.update()
# cargamos la función objetivo
cargar_funcion_objetivo(m, variables_dict, parametros_dict)
m.update()
# optimizamos
m.optimize()
guardar_variables(variables_dict, subcarpeta)
guardar_restricciones(restricciones_dict, subcarpeta)
guardar_fo(m.ObjVal, subcarpeta)
# tabla de que contenido se libera que semana
generar_graficos(subcarpeta)
print(f"Analizado {subcarpeta}!")
print("\n\n\n\n\n")
return m
def __init__(self, model=None, env=None):
Solver.__init__(self)
if env:
self.problem = GurobiModel(env=env)
else:
self.problem = GurobiModel()
self.set_logging(False)
self.set_parameters(default_parameters)
if model:
self.build_problem(model)
def def_PL(self):
"""
Definie le PL, variables/contraintes/objectifs
"""
model = Model("MR")
self.set_vars(model)
self.set_constraints(model)
self.set_objectif(model)
model.setParam("OutputFlag", False)
return model
def OptimalTransportGurobi(H1, H2):
n = len(H1)
m = len(H2)
mod = Model()
# Parameters
I = list(range(n))
J = (range(m))
# Variables
x = {}
for i in I:
for j in J:
x[i,j] = mod.addVar(obj=D(H1[i], H2[j]))
# Constraints on the supports
for i in I:
mod.addConstr(quicksum(x[i,j] for j in J) == 1)
for j in J:
mod.addConstr(quicksum(x[i,j] for i in I) == 1)
# Train: Solve the model
mod.optimize()
ColMap = []
for i in I:
for j in J:
if x[i,j].X > 0.5:
ColMap.append(j)
return ColMap
def optimizeGEM(GEM, obj_rxn):
"""
Plain old FBA using cobra model with gurobi. I made this function because the cobra
optimize function gives error when used on split, irreversible model
"""
model = Model('FBA_model')
GEM_rxn_ids = [rxn.id for rxn in GEM.reactions]
S = cobra.util.array.create_stoichiometric_matrix(GEM, array_type='dense')
# Add variables
v = {}
for rxn in GEM.reactions:
var_id = f'v_{rxn.id}'
x = model.addVar(lb=rxn.lower_bound,
ub=rxn.upper_bound,
obj=0.0,
vtype=GRB.CONTINUOUS,
name=var_id)
v[var_id] = x
# Add constraints
for i, row in enumerate(S):
c = ''
for j, coeff in enumerate(row):
rxn_id = GEM_rxn_ids[j]
if coeff != 0:
c += f'{coeff} * v["v_{rxn_id}"] +'
c = c[:-1]
c += '== 0'
model.addConstr(eval(c), f'mass_balance_{GEM.metabolites[i].id}')
# Set Objective
model.setObjective(v['v_' + obj_rxn], GRB.MAXIMIZE)
model.optimize()
return model
def generate_row_model(row_matrix, b, v, c):
"""
rows_matrix: The matrix, represented as a list of rows
b: List of variables in b
v: The target vector
c: The weights of each column
"""
# Initializes a model
mdl = Model('persistenthomologylocalization')
# Add matrix variables
x = mdl.addVars(list(b), vtype=GRB.BINARY)
# Add the dummy variable needed to do arithmetics mod 2
y = mdl.addVars(list(range(len(row_matrix))), vtype=GRB.INTEGER)
# Set model to minimization
mdl.modelSense = GRB.MINIMIZE
# Set objective function to minimize
mdl.setObjective(quicksum(x[j] * c[j] for j in b))
# Set the constrains
for i in list(range(len(row_matrix))):
mdl.addConstr(quicksum(x[j] for j in row_matrix[i]) + v[i] == y[i] * 2)
return mdl, x, y
def _construct_max_flow_lp(self, G, edge_to_paths, num_total_paths):
m = Model('max-flow')
# Create variables: one for each path
path_vars = m.addVars(num_total_paths,
vtype=GRB.CONTINUOUS,
lb=0.0,
name='f')
obj = quicksum(path_vars)
m.setObjective(obj, GRB.MAXIMIZE)
# Add demand constraints
commod_id_to_path_inds = {}
for k, d_k, path_inds in self.commodities:
commod_id_to_path_inds[k] = path_inds
m.addConstr(quicksum(path_vars[p] for p in path_inds) <= d_k)
# Add edge capacity constraints
for u, v, c_e in G.edges.data('capacity'):
paths = edge_to_paths[(u, v)]
constr_vars = [path_vars[p] for p in paths]
m.addConstr(quicksum(constr_vars) <= c_e)
return LpSolver(m, None, self.DEBUG, self.VERBOSE, self.out)
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 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 optimization_model:
def __init__(self, scenario):
self.scenario = scenario
self.model = Model('network_optimization')
def create_start_time_variables(self):
self.S = self.model.addVars(self.scenario.settings.number_of_tasks,
vtype = GRB.INTEGER,
lb = 0,
ub = self.scenario.settings.number_of_time_periods,
name = 'S')
def create_end_time_variables(self):
self.C = self.model.addVars(self.scenario.settings.number_of_tasks,
vtype = GRB.INTEGER,
lb = 0,
ub = self.scenario.settings.number_of_time_periods,
name = 'C')
def create_work_time_variables(self):
self.X = self.model.addVars(self.scenario.settings.number_of_tasks,self.scenario.settings.number_of_modes,self.scenario.settings.number_of_time_periods,
vtype = GRB.BINARY,
name = 'X')
def create_tech_assignment_variables(self):
self.V = self.model.addVars(self.scenario.settings.number_of_techs,self.scenario.settings.number_of_tasks,self.scenario.settings.number_of_time_periods,
vtype = GRB.BINARY,
name = 'V')
def add_precedence_constraints(self):
for task in self.scenario.task_list:
for successor in task.successor_list:
self.model.addConstr(self.S[successor] - self.C[task.task_index],
GRB.GREATER_EQUAL,
1,
name = "Precedence.%d.%d" % (successor,task.task_index))
def set_objective_makespan(self):
self.model.setObjective(self.C[self.scenario.task_list[-1].task_index],
sense = GRB.MINIMIZE)
def create_model_variables(self):
self.create_start_time_variables()
self.create_end_time_variables()
self.create_work_time_variables()
self.create_tech_assignment_variables()
def add_model_constraints(self):
self.add_precedence_constraints()
def set_model_objective(self):
self.set_objective_makespan()
def write_model(self):
self.model.write("/Users/yashpatil/Desktop/Personal Github Projects/Multimode_Network_Assignment/model_optimizationFiles/model_formulation.lp")
def __init__(self, cfg: Config):
self.cfg = cfg
# model.ModelSense is minimization by default
self.model = Model("beet_sub_problem")
self.x_3 = self.model.addVar(ub=self.cfg.area, name="x_3")
probability = 1 / len(self.cfg.scenarios)
for index, scenario in enumerate(self.cfg.scenarios):
self._variables_constraint(index, scenario, probability)
def __init__(
self,
g: DFGraph,
budget: int,
eps_noise=None,
model_file=None,
remote=False,
gurobi_params: Dict[str, Any] = None,
cpu_fwd_factor: int = 2,
):
self.cpu_fwd_factor = cpu_fwd_factor
self.logger = logging.getLogger(__name__)
self.remote = remote
self.profiler = functools.partial(Timer, print_results=True)
self.gurobi_params = gurobi_params
self.num_threads = self.gurobi_params.get("Threads", 1)
self.model_file = model_file
self.eps_noise = eps_noise
self.budget = budget
self.g = g
self.solve_time = None
self.init_constraints = [] # used for seeding the model
self.m = Model("checkpointmip_gc_maxbs_{}_{}".format(self.g.size, self.budget))
if gurobi_params is not None:
for k, v in gurobi_params.items():
setattr(self.m.Params, k, v)
T = self.g.size
CPU_VALS = list(self.g.cost_cpu.values())
RAM_VALS = list(self.g.cost_ram.values())
self.logger.info(
"RAM: [{:.2E}, {:.2E}], {:.2E} +- {:.2E}".format(
np.min(RAM_VALS), np.max(RAM_VALS), np.mean(RAM_VALS), np.std(RAM_VALS)
)
)
self.logger.info(
"CPU: [{:.2E}, {:.2E}], {:.2E} +- {:.2E}".format(
np.min(CPU_VALS), np.max(CPU_VALS), np.mean(CPU_VALS), np.std(CPU_VALS)
)
)
self.ram_gcd = int(max(self.g.ram_gcd(self.budget), 1))
self.cpu_gcd = int(max(self.g.cpu_gcd(), 1))
self.logger.info("ram_gcd = {} cpu_gcd = {}".format(self.ram_gcd, self.cpu_gcd))
self.batch_size = self.m.addVar(lb=1, ub=1024 * 16, name="batch_size")
self.R = self.m.addVars(T, T, name="R", vtype=GRB.BINARY)
self.S = self.m.addVars(T, T, name="S", vtype=GRB.BINARY)
self.Free_E = self.m.addVars(T, len(self.g.edge_list), name="FREE_E", vtype=GRB.BINARY)
self.U = self.m.addVars(T, T, name="U", lb=0.0, ub=self.budget)
for x in range(T):
for y in range(T):
self.m.addLConstr(self.U[x, y], GRB.GREATER_EQUAL, 0)
self.m.addLConstr(self.U[x, y], GRB.LESS_EQUAL, float(budget) / self.ram_gcd)
def __init__(self, samples, delta=1.0):
self.n_nodes = samples.n_nodes
self.n_samples = samples.n_samples
self.delta = delta
self.B = samples.B
self.T = samples.T
self.F = samples.F
self.model = Model('DPSL')
self.create_model()
def ilp_node_reachability(reachability_dic, max_delay=180, log_path=None):
# List of nodes ids
node_ids = sorted(list(reachability_dic.keys()))
#node_ids = node_ids[:100]
try:
# Create a new model
m = Model("region_centers")
if log_path:
m.Params.LogFile = '{}/region_centers_{}.log'.format(
log_path, max_delay)
# xi = 1, if vertex Vi is used as a region center and 0 otherwise
x = m.addVars(node_ids, vtype=GRB.BINARY, name="x")
# Ensures that every node in the road network graph is reachable
# within 'max_delay' travel time by at least one region center
# selected from the nodes in the graph.
# To extract the region centers, we select from V all vertices
# V[i] such that x[i] = 1.
for d in node_ids:
m.addConstr(
quicksum(x[o] * is_reachable(reachability_dic, o, d, max_delay)
for o in node_ids) >= 1)
# Set objective
m.setObjective(quicksum(x), GRB.MINIMIZE)
# Solve
m.optimize()
region_centers = list()
if m.status == GRB.Status.OPTIMAL:
var_x = m.getAttr('x', x)
for n in node_ids:
if var_x[n] > 0.0001:
region_centers.append(n)
return region_centers
else:
print('No solution')
return None
except GurobiError as e:
print('Error code ' + str(e.errno) + ": " + str(e))
except AttributeError as e:
print('Encountered an attribute error:' + str(e))
def add_binary_switch(m: gModel, label: str, v1: float, v2: float, delta: gVar,
K: float) -> gVar:
y = m.addVar(lb=-GRB.INFINITY, ub=GRB.INFINITY, name=label)
m.addConstr(y <= v1 + delta * K)
m.addConstr(y >= v1 - delta * K)
m.addConstr(y <= v2 + (1 - delta) * K)
m.addConstr(y >= v2 - (1 - delta) * K)
return y
def __init__(self, Data):
"""Formulate the master problem.
INPUTS
Data :: object, classes.Data; problem data.
"""
self.Data = Data
self.duals = []
self.master = Model("master LP") # Init master model
self.master.Params.OutputFlag = 0 # No output
self._formulate_master()
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 __loadModel(self):
# Create optimization model
self.__model = Model('PathBackup')
# 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 p in self.__paths:
#LP Relaxation
#self.__bPath[self.__paths.index(p)] = self.__model.addVar(lb=0,obj=1,name='Backup_Path[%s]' % (self.__paths.index(p)))
self.__bPath[self.__paths.index(p)] = self.__model.addVar(vtype=GRB.BINARY,obj=1,name='Backup_Path[%s]' % (self.__paths.index(p)))
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
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]*quicksum(self.__bPath[self.__paths.index(p)] for p in self.__Pij[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]*quicksum(self.__bPath[self.__paths.index(p)] for p in self.__Pij[i,j,s,d]) == R[i,j,s,d],'[CONST]SCOP2[%s][%s][%s][%s]' % (i,j,s,d))
self.__model.update()
# Unique path
for s,d in self.__links:
self.__model.addConstr(quicksum(self.__bPath[self.__paths.index(p)] for p in self.__Psd[s,d]) == 1,'UniquePath[%s,%s]' % (s, d))
self.__model.update()
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 __init_prob(self): # Modify parameters
logging.info("Generating initial marking problem")
self.prob = Model("SC1")
# Gurobi parameters:
if not self.verbose:
self.prob.params.OutputFlag = 0
try:
os.remove("gurobi.log")
except OSError:
pass
self.prob.params.Threads = 4
def _init_LP(self):
if self._lp_inited:
return
logging.debug('Init LP')
self.lp = LPModel('estep')
self.lp.setAttr("modelSense", 1) # minimzation
self.alpha = {}
beta2 = {}
beta3 = {}
# instantiate vars
logging.debug('Init LP - create vars')
for a in self.author_graph:
self.alpha[a] = {}
for p in self.parts:
self.alpha[a][p] = self.lp.addVar(lb=0.0)
for a, b in self.author_graph.edges():
beta2[(a, b)] = self.lp.addVar()
beta3[(a, b)] = {}
for p in self.parts:
beta3[(a, b)][p] = self.lp.addVar(lb=0.0)
# integrate added variables into the model
self.lp.update()
# add constraints once during this init
# alphas are indicator vars
logging.debug('Init LP - indiv constraints')
ones_arr = [1.0] * len(self.parts)
for a in self.author_graph:
self.lp.addConstr(LinExpr(ones_arr, self.alpha[a].values()), GRB.EQUAL, 1.0)
# beta2 is the sum of beta3s
logging.debug('Init LP - pair constraints')
pt_five_array = [0.5] * len(self.parts)
for a, b in self.author_graph.edges():
self.lp.addConstr(LinExpr(pt_five_array, beta3[(a, b)].values()), GRB.EQUAL, beta2[(a, b)])
for p in self.parts:
self.lp.addConstr(LinExpr([1.0, -1.0], [self.alpha[a][p], self.alpha[b][p]]), GRB.LESS_EQUAL, beta3[(a, b)][p])
self.lp.addConstr(LinExpr([-1.0, 1.0], [self.alpha[a][p], self.alpha[b][p]]), GRB.LESS_EQUAL, beta3[(a, b)][p])
self.lp.update()
# calculate pairwise potentials part of the objective
# the optimization is to minimize negated log-likelihood = maximize the log-likelihood
logging.debug('Obj func - pair potentials')
s = np.log(1 - self.TAU) - np.log(self.TAU)
lpcoeffs, lpvars = [], []
for a, b in self.author_graph.edges():
lpcoeffs.append(-self.author_graph[a][b]['weight'] * s)
lpvars.append(beta2[(a, b)])
self.objF_pair = LinExpr(list(lpcoeffs), list(lpvars))
self._lp_inited = True
logging.debug('Init LP Done')
def __loadModel(self,imp_samp, backup_link,link_capacity):
# Create optimization model
self.__model = Model('Backup')
for i,j in self.__links:
for k in range(self.__N):
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()
for i,j in self.__links:
self.__q[i,j] = self.__model.addVar(lb=-GRB.INFINITY,name='q[%s][%s]' %(i,j))
self.__model.update()
self.__model.modelSense = GRB.MINIMIZE
self.__model.setObjective(quicksum(self.__q[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/(self.__N*self.__epsilon)*quicksum(self.__z[k,i,j]*imp_samp[k] for (k) in range(self.__N)) <= self.__q[i,j],'[CONST]Buffer_Prob_I[%s][%s]'%(i,j))
self.__model.update()
# Link capacity constraints
for i,j in self.__links:
for k in range(self.__N):
self.__model.addConstr((quicksum(backup_link[i,j,s,d]*self.__capacity[k,s,d] for s,d in self.__links) - link_capacity[i,j] - self.__z0[i,j]) <= 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(self.__N):
self.__model.addConstr(self.__z[k,i,j] >= 0,'[CONST]Buffer_Prob_III[%s][%s][%s]' % (k,i,j))
self.__model.update()
def __init__(self, length):
"""Initialize model, note and chord variables, and constraints for notes
and chord constraints."""
self.model = Model("harmony")
self.length = length
config = load_source("config",
join(abspath(dirname(__file__)), "config.py"))
config.length = self.length
config.model = self.model
self.notes = Notes(config)
config.notes = self.notes
self.chords = Chords(config)
def __init__(self, json_data):
self.m = Model('mip1.log')
self.solution_matrix = None
# Load from JSON
self.all_data = json_data
self.student_ids = [int(k) for k in json_data['students'].keys()]
self.course_ids = [int(k) for k in json_data['courses'].keys()]
self.semester_ids = [int(k) for k in json_data['semesters'].keys()]
self.dependencies = [(d['first_course'], d['second_course']) for d in json_data['course_dependencies']]
self.student_demand = defaultdict(lambda: False)
for sd in json_data['student_demand']:
self.student_demand[sd['student_id'], sd['course_id'], sd['semester_id']] = True
self.instructor_availability = defaultdict(lambda: False)
for ia in json_data['instructor_pool']:
self.instructor_availability[ia['instructor_id'], ia['course_id'], ia['semester_id']] = True
self.instructor_ids = [s['instructor_id'] for s in json_data['instructor_pool']]
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 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
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 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 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
#!/usr/bin/env python
# This is the GAP per Wolsey, pg 182, using Lagrangian Relaxation
from gurobipy import GRB, Model
model = Model('GAP per Wolsey with Lagrangian Relaxation')
model.modelSense = GRB.MAXIMIZE
model.setParam('OutputFlag', False) # turns off solver chatter
b = [15, 15, 15]
c = [
[ 6, 10, 1],
[12, 12, 5],
[15, 4, 3],
[10, 3, 9],
[ 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]:
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 global_model(N, k_choices, distance_matrix):
if k_choices >= N:
raise ValueError("k_choices must be less than N")
model = Model("distance1")
I = range(N)
distance_matrix = np.array(
distance_matrix / distance_matrix.max(), dtype=np.float64)
dm = distance_matrix ** 2
y, x = {}, {}
for i in I:
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 I for j in range(i + 1, N)]))
# Add constraints to the model
model.addConstr(quicksum([y[i] for i in I]) <= k_choices, "27")
for i in I:
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 I
for j in range(i + 1, N)])
<= nchoosek(k_choices, 2), "Cut_1")
model.update()
return model
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 __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 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()
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)
def _initialize_model(self):
problem = Model()
problem.setParam('OutputFlag', False)
# edges from source to reviewers, capacity controls maximum reviewer load
self._source_vars = problem.addVars(self.numrev, vtype=GRB.CONTINUOUS, lb=0.0,
ub=self.ability, name='reviewers')
# edges from papers to sink, capacity controls a number of reviewers per paper
self._sink_vars = problem.addVars(self.numpapers, vtype=GRB.CONTINUOUS, lb=0.0,
ub=self.demand, name='papers')
# edges between reviewers and papers. Initially capacities are set to 0 (no edge is added in the network)
self._mix_vars = problem.addVars(self.numrev, self.numpapers, vtype=GRB.CONTINUOUS,
lb=0.0, ub=0.0, name='assignment')
problem.update()
# flow balance equations for reviewers' nodes
self._balance_reviewers = problem.addConstrs((self._source_vars[i] == self._mix_vars.sum(i, '*')
for i in range(self.numrev)))
# flow balance equations for papers' nodes
self._balance_papers = problem.addConstrs((self._sink_vars[i] == self._mix_vars.sum('*', i)
for i in range(self.numpapers)))
problem.update()
self._problem = problem
def __init__(self):
Solver.__init__(self)
self.problem = GurobiModel()
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)
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 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
