def history_routes_load(rmp, routes):
# hwo to store the route generated
with open('../problem1_route.pkl', 'rb') as pkl2:
new_routes = pickle.load(pkl2)
n = len(new_routes)
for i in range(51, n):
v = new_routes[i]
m = len(routes) + 1
routes[m] = {}
routes[m]['demand'] = v['demand']
routes[m]['column'] = v['column']
routes[m]['distance'] = v['distance']
routes[m]['route'] = v['route']
added_column = gp.Column(routes[m]['column'], rmp.getConstrs())
routes[m]['var'] = rmp.addVar(column=added_column,
obj=routes[m]['distance'])
rmp.update()
return rmp, routes
def add_balance_slack(self):
""" add slack variables to balance constraints """
#constr_list = [self.m.getConstrByName("balance1[%s]" %(i)) for i in range(self.node_num)]
#constr_list += [self.m.getConstrByName("balance2[%s]" %(i)) for i in range(self.node_num)]
constr_list = [self.bound_const1[i] for i in range(self.node_num)]
constr_list += [self.bound_const2[i] for i in range(self.node_num)]
self.slack1 = {}
self.slack2 = {}
for n in range(self.node_num):
self.slack1[n] = self.m.addVar(column=gb.Column(
coeffs=[1 for i in range(2)],
constrs=[self.bound_const1[n], self.bound_const2[n]]),
name="slack1[%s]" % (n))
self.slack2[n] = self.m.addVar(column=gb.Column(
coeffs=[-1 for i in range(2)],
constrs=[self.bound_const1[n], self.bound_const2[n]]),
name="slack2[%s]" % (n))
def addColumn(self, objective, newPattern):
ctName = ('PatternUseVar[%s]' % len(self.model.getVars()))
newColumn = gu.Column(newPattern, self.model.getConstrs())
self.model.addVar(vtype=gu.GRB.INTEGER,
lb=0,
obj=objective,
column=newColumn,
name=ctName)
self.model.update()
def add_variables(model, variables, data):
"""
Adds a variable to the existing master model
:param model: Master model object
:param variables: A deque with variable objects (named tuples that hold: arc, no, objective, flow)
:return: Nothing
"""
nodes, periods, commodities, arcs = data.nodes, data.periods, data.commodities, data.arcs
constraints = model.getConstrs()
for count_arc, arc in enumerate(data.arcs):
for count_col, variable in enumerate(variables[count_arc]):
no, obj = model.numvars + count_arc + count_col, variable.objective
flow = variable.flow
coefficients = np.zeros(shape=2 * np.sum(flow > 10e-6) + 1,
dtype=float)
node_in, node_out = get_2d_index(arc, nodes)
constrs = []
for c in xrange(commodities):
for t in xrange(periods):
# node_out goes first
if flow[t, c] > 1e-6:
idx = len(constrs)
coefficients[idx] = -flow[t, c]
idx = len(constrs) + 1
coefficients[idx] = +flow[t, c]
# node_out index of constraint of (c,t)
idx = get_1d_index(idx1=node_out,
idx2=c + 1,
idx3=t,
width2=commodities,
width3=periods)
constrs.append(constraints[idx])
idx = get_1d_index(idx1=node_in,
idx2=c + 1,
idx3=t,
width2=commodities,
width3=periods)
constrs.append(constraints[idx])
idx = nodes * periods * commodities + count_arc
coefficients[len(constrs)] = 1.
constrs.append(constraints[idx])
column = grb.Column(coefficients, constrs)
model.addVar(lb=0.,
ub=1.,
obj=obj,
column=column,
name='col_{}_{}'.format(count_arc, no))
model.update()
def add_column(self, routes):
for route in routes:
fea = self.path_eva_vrptw(route[1:])
if not fea:
print('unfeasibile', route[1:])
continue
temp_length = len(self.routes)
added_column = gp.Column(self.routes[temp_length]['column'],
self.rmp.getConstrs())
self.routes[temp_length]['var'] = self.rmp.addVar(
column=added_column,
obj=self.routes[temp_length]['distance'],
ub=1,
lb=0)
def optimize(self):
counter = 1
while counter < self._num_iteration:
# Solve the relaxed version:
self.relax = self.master.relax()
self.relax.optimize()
lam_cons = np.array([ele.Pi for ele in self.relax.getConstrs()])
self.y = np.array([
self.slave.addVar(vtype="I", lb=0)
for _ in range(self.num_cons)
])
self.slave.update()
self.slave.addConstr(self.y @ np.array(self.length) <= b_stock)
self.slave.setObjective(-self.y @ lam_cons)
self.slave.optimize()
# get new columns from dual problem
new_cut_pattern = [int(ele.X) for ele in self.y]
# add new cuts with early termination
if new_cut_pattern not in self.all_cut_pattern.tolist():
self.all_cut_pattern = np.concatenate(
(self.all_cut_pattern,
np.array(new_cut_pattern).reshape(1, -1)))
else:
print(
"Early termination as the cutting method has existed: {}.".
format(new_cut_pattern))
print("Terminate at iteration {}. \n".format(counter))
break
# add new var to master:
new_col = gb.Column()
for i in range(self.num_cons):
new_col.addTerms(new_cut_pattern[i], self.cons[i])
self.x = np.append(self.x, None)
self.x[self.num_vars - 1] = self.master.addVar(vtype="I",
obj=1,
column=new_col)
self.master.update()
counter += 1
# if max no iteration or early termination is reached, optimize original problem
self.master.optimize()
self.res_x = np.array([int(self.x[i].X) for i in range(self.num_vars)])
def add_path(self, path, reduced_cost):
"""Add path to the master problem.
Arguments:
path: the path to be added
reduced_cost: the path reduced cost
"""
path_t = tuple(path)
if path_t in self.paths_set:
return
self.paths.append(path_t)
self.paths_set.add(path_t)
n_customers = len(self.customers)
path[-1] = n_customers
coeffs = np.zeros(n_customers + 1)
coeffs[path] = 1
cost = reduced_cost + sum(self.espprc.duals[path[:-1]])
self.model.addVar(obj=cost, name=f"v{len(self.paths)-1}",
column=gp.Column(coeffs, self.model.getConstrs()))
def column_generation(n, demands, capacity, distances, duals, MP_branch):
SP_branch = SubProblem(n, demands, capacity, distances, duals)
SP_branch.build_model()
SP_branch.optimize()
new_MP = None
newAssing = [SP_branch.y[i].x for i in SP_branch.y] # new route
obj = get_min_dist(newAssing, distances) # Cost of new route
if obj + SP_branch.modelo.ObjVal < 0.0:
newColumn = gp.Column(newAssing, MP_branch.modelo.getConstrs())
MP_branch.modelo.addVar(vtype=GRB.BINARY, obj=obj, column=newColumn)
MP_branch.modelo.update()
MP_branch.RelaxOptimize()
best_cost = MP_branch.getCosts()
routes = MP_branch.modelo.getA().toarray()
new_MP = copy_model(best_cost, routes, MP_branch)
return new_MP
def branch(branch_cost, branch_routes, n, demands, capacity, distances, duals,
solution_to_branch, MP_to_copy, queue, best_inc_obj):
frac_ixs = []
for ix, val in enumerate(solution_to_branch):
if val > 0.0 and val < 1.0:
frac_ixs.append(ix)
A_mp = MP_to_copy.modelo.getA().toarray()
locations_index = list(MP_to_copy.locations_index)
for comb in combinations(frac_ixs, 2):
SP_1 = SubProblem(n, demands, capacity, distances, duals)
SP_2 = SubProblem(n, demands, capacity, distances, duals)
SP_1.build_model()
SP_2.build_model()
s1_and_s2 = [
True if (A_mp[i - 1, comb[0]] == 1 and A_mp[i - 1, comb[1]] == 1)
else False for i in range(len(MP_to_copy.locations_index))
]
s1_not_s2 = [
True if (A_mp[i - 1, comb[0]] == 1 and A_mp[i - 1, comb[1]] == 0)
else False for i in range(len(MP_to_copy.locations_index))
]
for i in locations_index:
locations_prime = [x for x in locations_index if x != i]
for j in locations_prime:
if (s1_and_s2[i - 1] and s1_not_s2[j - 1]):
# SP_1.modelo.addConstr(SP_1.y[i - 1] + SP_1.y[j - 1] == 2)
# SP_2.modelo.addConstr(SP_2.y[i - 1] + SP_2.y[j - 1] == 1)
SP_1.modelo.addConstr(SP_1.y[i - 1] == 1)
SP_1.modelo.addConstr(SP_1.y[j - 1] == 1)
SP_2.modelo.addConstr(SP_2.y[i - 1] == 1)
SP_2.modelo.addConstr(SP_2.y[j - 1] == 0)
MP_1, MP_2 = copy_models(branch_cost, branch_routes, MP_to_copy)
SP_1.modelo.update()
SP_1.optimize()
if SP_1.modelo.Status == 2:
newAssing = [SP_1.y[i].x for i in SP_1.y] # new Assingment
obj = get_min_dist(newAssing, distances) # Cost of new route
if obj + SP_1.modelo.ObjVal < 0.0:
newColumn = gp.Column(newAssing, MP_1.modelo.getConstrs())
MP_1.modelo.addVar(vtype=GRB.BINARY, obj=obj, column=newColumn)
MP_1.modelo.update()
MP_1.RelaxOptimize()
mp1_cost = MP_1.getCosts()
mp1_routes = MP_1.modelo.getA().toarray()
if MP_1.relax_modelo.ObjVal <= best_inc_obj:
queue.insert(MP_1.relax_modelo.ObjVal,
copy_model(mp1_cost, mp1_routes, MP_1))
SP_2.modelo.update()
SP_2.optimize()
if SP_2.modelo.Status == 2:
newAssing = [SP_2.y[i].x for i in SP_2.y] # new Assingment
obj = get_min_dist(newAssing, distances) # Cost of new route
if obj + SP_2.modelo.ObjVal < 0.0:
newColumn = gp.Column(newAssing, MP_2.modelo.getConstrs())
MP_2.modelo.addVar(vtype=GRB.BINARY, obj=obj, column=newColumn)
MP_2.modelo.update()
MP_2.RelaxOptimize()
mp2_cost = MP_2.getCosts()
mp2_routes = MP_2.modelo.getA().toarray()
if MP_2.relax_modelo.ObjVal <= best_inc_obj:
queue.insert(MP_2.relax_modelo.ObjVal,
copy_model(mp2_cost, mp2_routes, MP_2))
return queue
objective2 = grb.LinExpr(coef3, var3)
cgsp_model.setObjective(objective2, grb.GRB.MAXIMIZE)
cgsp_model.update()
ob = cgsp_model.getObjective()
#print(ob)
cgsp_model.write('cgsp.lp')
#Column generation
K = len(set_I) + 1
while True:
rmp_model.optimize()
print('RMP_Objective : ', rmp_model.ObjVal)
rmp_model.write('day2_rmp.mps')
dual = get_dual(rmp_model) #get dual from the 'rmp_model'
update_obj(dual)
cgsp_model.optimize()
x_values = cgsp_model.x
print('CGSP_Objective : ', cgsp_model.ObjVal)
if cgsp_model.ObjVal <=1.001:
break
else:
col = grb.Column()
for i in range(1,n):
col.addTerms(x_values[i-1], temp[i])
y_var[K] = rmp_model.addVar(obj=1, vtype=grb.GRB.CONTINUOUS, name="y_var[%d]"%K, column = col)
rmp_model.update()
rmp_model.write('updated.lp')
K += 1
# create a copy to use FeasRelax feature later
feasmodel1 = feasmodel.copy()
# clear objective
feasmodel.setObjective(0.0)
# add slack variables
for c in feasmodel.getConstrs():
sense = c.sense
if sense != '>':
feasmodel.addVar(obj=1.0,
name="ArtN_" + c.constrName,
column=gp.Column([-1], [c]))
if sense != '<':
feasmodel.addVar(obj=1.0,
name="ArtP_" + c.constrName,
column=gp.Column([1], [c]))
# optimize modified model
feasmodel.optimize()
feasmodel.write('feasopt.lp')
# use FeasRelax feature
feasmodel1.feasRelaxS(0, True, False, True)
def column_generation(benchmark, param, node, verbose_print):
model, x, A, sc, rj, dj = node['value']
S = A.shape[1]
n_iter = 1 # number of total iteration
verbose_print('Starting column generation')
cgtime = process_time() # start counting time
while True:
master = model.relax(
) # solve the continuous relaxation of current master
# write & solve master - RLP
# master.write(param['PATH']['model_path'] + 'master_model.rlp')
master.optimize()
# compute the dual variables lambda_j
lambda_j = np.array([const.Pi for const in master.getConstrs()])
# compute reduced cost
# rc = np.array([sc[s] - A[:, s] @ lambda_j for s in range(S)])
# if rc < 1e-9:
# break
# ** PRICING ALGORITHM **
# call the pricing subproblem in case there are negatives rc
new_schedules = pricing_algorithm(benchmark, rj, dj, lambda_j,
param['PARAMETERS']['nnc'])
if not len(new_schedules):
# exit because there isn't new schedule to add
verbose_print(
'No new schedule to add, already into the optimal solution')
node['value'][2], node['value'][3] = A.copy(), sc.copy()
return
# update A with the new schedules
# check column existence is counterproductive because the algorithm don't go on the next column in this way
A = np.concatenate((A, new_schedules), axis=1)
# simple check on the correspondence of the name with the index of the dictionary
# in order to avoid that in case of branch and bound the variables take the same name
last_var_name = x[len(x) - 1].getAttr(gp.GRB.Attr.VarName)
var_idx = int(re.search(r'(\d+)', last_var_name).group(0))
for i in range(A.shape[1] - S):
# for each new column
new_sched = A[:, S + i].copy()
# compute schedule cost and append it to sc variable
new_cost = sched_cost(
np.where(new_sched)[0], benchmark['p'], benchmark['w'], True)
sc = np.append(sc, new_cost)
# creates a new Column with the corresponding coefficients and constraints
new_col = gp.Column(
list(np.ones(len(np.where(new_sched)[0]) + 1)),
list(
np.array(model.getConstrs())[np.where(
np.insert(new_sched, 0, 1))[0]]))
# add a variable for the new column of the set-cover
x[S + i] = model.addVar(obj=new_cost,
vtype=gp.GRB.BINARY,
name=f'x_s[{var_idx+i+1}]',
column=new_col)
S = A.shape[1] # re-assign the number of schedule
# model.reset()
model.update() # update the set-cover model
n_iter += 1
# print partial time
part_time = int(process_time() - cgtime)
verbose_print(
f'Iteration: {n_iter}\n'
f'Partial time: {int(part_time / 60)} min {part_time % 60} s')
