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ilp.py
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ilp.py
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from gurobipy import GRB
import gurobipy as gp
import logging
import graph
import utils
logger = logging.getLogger(__name__)
TOLERANCE = 0.1 #tolerance allowed for Gurobi numerical values
def tail(grb_edge): return int(grb_edge.split("[")[1].split(",")[0])
def head(grb_edge): return int(grb_edge.split("[")[1].split(",")[1])
class Encode_LeastSquares:
def __init__(self,n,E,source,sink,F,edge_width,R,P2F,epsilon,timeout,threads):
self.n = n
self.m = len(E)
self.source = source
self.target = sink
self.E = E
self.F = F
self.R = R
self.vars2fix = P2F
self.epsilon = epsilon
self.k = edge_width #the largest edge antichain is a lower bound for the size of any flow decomposition
self.w_max = max(map(lambda edge : F[edge], self.E))
self.edge_vars = {}
self.pi_vars = {}
self.weights = {}
self.spc_vars = {}
self.timeout = timeout
self.threads = threads
self.model = self.create_solver()
self.final_k = None
def create_solver(self):
env = gp.Env(empty=True)
env.setParam('OutputFlag' , 0)
env.setParam('LogToConsole' , 0)
env.setParam('TimeLimit' , self.timeout)
env.setParam('Threads' , self.threads)
env.start()
model = gp.Model("MFD_LeastSquares", env=env)
if not model:
logger.error("FATAL, could not create Gurobi model")
exit(0)
return model
def clear(self):
self.model = self.create_solver()
self.edge_vars = {}
self.pi_vars = {}
self.weights = {}
self.spc_vars = {}
def solve(self):
self.model.optimize()
def encode(self):
# Create variables
edge_indexes = [ (u,v,i) for i in range(self.k) for (u, v) in self.E ]
path_indexes = [ ( i) for i in range(self.k) ]
subpath_indexes = [ (i,j ) for i in range(self.k) for j in range(len(self.R)) ]
self.edge_vars = self.model.addVars( edge_indexes, vtype=GRB.BINARY , name='e' )
self.pi_vars = self.model.addVars( edge_indexes, vtype=GRB.INTEGER, name='p', lb=0, ub=self.w_max)
self.weights = self.model.addVars( path_indexes, vtype=GRB.INTEGER, name='w', lb=1, ub=self.w_max)
self.spc_vars = self.model.addVars(subpath_indexes, vtype=GRB.BINARY , name='r' )
#The identifiers of the constraints come from https://arxiv.org/pdf/2201.10923 page 14-15
for i in range(self.k):
self.model.addConstr( self.edge_vars.sum(self.source,'*',i) == 1, "10a_i={}".format(i) )
self.model.addConstr( self.edge_vars.sum('*',self.target,i) == 1, "10b_i={}".format(i) )
for i in range(self.k):
for v in range(1,self.n-1): #find all wedges u->v->w for v in V\{s,t}
self.model.addConstr( self.edge_vars.sum('*',v,i) - self.edge_vars.sum(v,'*',i) == 0, "10c_v={}_i={}".format(v,i) )
for (u,v) in self.E:
for i in range(self.k):
self.model.addConstr( self.pi_vars[u,v,i] <= self.edge_vars[u,v,i] * self.w_max , "10e_u={}_v={}_i={}".format(u,v,i) )
self.model.addConstr( self.pi_vars[u,v,i] <= self.weights[i] , "10f_u={}_v={}_i={}".format(u,v,i) )
self.model.addConstr( self.pi_vars[u,v,i] >= self.weights[i] - (1 - self.edge_vars[u,v,i]) * self.w_max , "10g_u={}_v={}_i={}".format(u,v,i) )
#Example of a subpath constraint: R=[ [(1,3),(3,5)], [(0,1)] ], means that we have 2 paths to cover, the first one is 1-3-5. the second path is just a single edge 0-1
def EncodeSubpathConstraints():
for i in range(self.k):
for j in range(len(self.R)):
edgevars_on_subpath = list(map(lambda e: self.edge_vars[e[0],e[1],i], self.R[j]))
self.model.addConstr( sum(edgevars_on_subpath) >= len(self.R[j]) * self.spc_vars[i,j] )
for j in range(len(self.R)):
self.model.addConstr( self.spc_vars.sum('*',j) >= 1 )
def Fix_Variables():
for i in range(len(self.vars2fix)):
for (u,v) in self.vars2fix[i]:
self.model.addConstr( self.edge_vars[u,v,i] == 1 )
if self.R!=[]:
EncodeSubpathConstraints()
if self.vars2fix!=[]:
Fix_Variables()
self.model.setObjective( sum( (self.F[(u,v)] - self.pi_vars.sum(u,v,'*') )**2 for (u,v) in self.E), GRB.MINIMIZE )
def print_solution(self,solution):
opt, dif, paths = solution
print("\n#####SOLUTION#####\n","> FD size :", opt,"\n> LeastSquares difference :", dif,"\n> Weight-Path decomposition:")
for p in paths:
print(*p)
def build_solution(self):
paths = []
for i in range(self.k):
path = []
u = self.source
while u != self.target:
edges = list(filter(lambda grb_var : grb_var.X>1-TOLERANCE , self.edge_vars.select(u,'*',i) ))
assert(len(edges)==1)
v = head(edges[0].VarName)
path.append(v)
u = v
paths.append( (self.weights[i].X, path[:-1]) )
return (self.k, self.model.ObjVal, paths)
def solve_once(self):
logger.info(">>> Solving once")
self.encode()
self.solve()
logger.info("Gurobi solver status " + str(self.model.status))
if self.model.status == GRB.TIME_LIMIT:
raise utils.GRB_TimeOut("ilp.LeastSquares.solve_once while finding feasible solution")
elif self.model.status == GRB.OPTIMAL:
_,_,p = self.build_solution()
weights,paths = list(map(lambda x : x[0], p)), list(map(lambda x : x[1], p))
return (paths,weights)
else:
logger.error("FATAL: solver finished with status " + str(self.model.status) + ", which is not OPT nor TIME_LIMIT.")
def optimize_linear(self):
#Assumption: the initial value of self.k is sufficiently high so that the ILP solver starts with a feasible solution
self.encode()
self.solve()
if self.model.status == GRB.TIME_LIMIT:
self.final_k = self.k
raise utils.GRB_TimeOut("ilp.LeastSquares.optimize_linear while optimizing")
prev_obj = self.model.ObjVal
if prev_obj == 0:
logger.info(">>> No optimization step required, found perfect solution in init solving with " + str(self.k))
self.final_k = self.k
return self.final_k
self.clear()
self.k += 1
logger.info(">>> Optimality, starting with " + str(self.k))
while True: #optimality criteria: find the k for which the ratio of slacks between two consecutive iterations becomes sufficiently small
self.encode()
self.solve()
logger.info("Gurobi solver status " + str(self.model.status))
if self.model.status == GRB.TIME_LIMIT:
self.final_k = self.k - 1
raise utils.GRB_TimeOut("ilp.LeastSquares.optimize_linear while optimizing")
#assert(self.model.ObjVal <= prev_obj) not necessarily true, as the lower bound of the weight variables is 1
if self.model.ObjVal >= prev_obj: #if we do not improve by allowing more paths we stop
self.final_k = self.k-1
break
if self.model.ObjVal==0: #if we found a perfect solution we stop
self.final_k = self.k
break
assert(prev_obj != 0)
if 1-self.model.ObjVal/prev_obj < self.epsilon: # if the relative improvement is small we also stop
self.final_k = self.k - 1
break
prev_obj = self.model.ObjVal
self.clear()
self.k += 1
return self.final_k
class Encode_Robust:
def __init__(self,n,E,source,sink,F,edge_width,R,P2F,epsilon,timeout,threads):
self.n = n
self.m = len(E)
self.source = source
self.target = sink
self.E = E
self.F = F
self.R = R
self.vars2fix = P2F
self.epsilon = epsilon
self.k = edge_width #the largest edge antichain is a lower bound for the size of any flow decomposition
self.w_max = max(map(lambda edge : F[edge], self.E))
self.edge_vars = {}
self.phi_vars = {}
self.gam_vars = {}
self.weights = {}
self.slacks = {}
self.spc_vars = {}
self.timeout = timeout
self.threads = threads
self.model = self.create_solver()
self.final_k = None
def create_solver(self):
env = gp.Env(empty=True)
env.setParam('OutputFlag' , 0)
env.setParam('LogToConsole' , 0)
env.setParam('TimeLimit' , self.timeout)
env.setParam('Threads' , self.threads)
env.start()
model = gp.Model("MFD_Robust", env=env)
if not model:
logger.error("FATAL, could not create Gurobi model")
exit(0)
return model
def clear(self):
self.model = self.create_solver()
self.edge_vars = {}
self.phi_vars = {}
self.gam_vars = {}
self.weights = {}
self.slacks = {}
self.spc_vars = {}
def solve(self):
self.model.optimize()
def encode(self):
# Create variables
edge_indexes = [ (u,v,i) for i in range(self.k) for (u, v) in self.E ]
path_indexes = [ ( i) for i in range(self.k) ]
subpath_indexes = [ (i,j ) for i in range(self.k) for j in range(len(self.R)) ]
self.edge_vars = self.model.addVars( edge_indexes, vtype=GRB.BINARY , name='e' )
self.spc_vars = self.model.addVars(subpath_indexes, vtype=GRB.BINARY , name='r' )
self.phi_vars = self.model.addVars( edge_indexes, vtype=GRB.INTEGER, name='p', lb=0, ub=self.w_max)
self.gam_vars = self.model.addVars( edge_indexes, vtype=GRB.INTEGER, name='g', lb=0, ub=self.w_max)
self.weights = self.model.addVars( path_indexes, vtype=GRB.INTEGER, name='w', lb=1, ub=self.w_max)
self.slacks = self.model.addVars( path_indexes, vtype=GRB.INTEGER, name='s', lb=0, ub=self.w_max)
#The identifiers of the constraints come from https://www.biorxiv.org/content/10.1101/2023.03.20.533019v1.full.pdf page 13
for i in range(self.k):
self.model.addConstr( self.edge_vars.sum(self.source,'*',i) == 1, "14a_i={}".format(i) )
self.model.addConstr( self.edge_vars.sum('*',self.target,i) == 1, "14b_i={}".format(i) )
for i in range(self.k):
for v in range(1,self.n-1): #find all wedges u->v->w for v in V\{s,t}
self.model.addConstr( self.edge_vars.sum('*',v,i) - self.edge_vars.sum(v,'*',i) == 0, "14c_v={}_i={}".format(v,i) )
for (u,v) in self.E:
f_uv = self.F[(u,v)]
phi_sum = self.phi_vars.sum(u,v,'*')
gam_sum = self.gam_vars.sum(u,v,'*')
self.model.addConstr( f_uv - phi_sum <= gam_sum, "14d_u={}_v={}".format(u,v) )
self.model.addConstr( f_uv - phi_sum >= -gam_sum, "14e_u={}_v={}".format(u,v) )
for i in range(self.k):
self.model.addConstr( self.phi_vars[u,v,i] <= self.w_max * self.edge_vars[u,v,i] , "14f_u={}_v={}_i={}".format(u,v,i) )
self.model.addConstr( self.gam_vars[u,v,i] <= self.w_max * self.edge_vars[u,v,i] , "14i_u={}_v={}_i={}".format(u,v,i) )
self.model.addConstr( self.phi_vars[u,v,i] <= self.weights[i] , "14g_u={}_v={}_i={}".format(u,v,i) )
self.model.addConstr( self.gam_vars[u,v,i] <= self.slacks [i] , "14j_u={}_v={}_i={}".format(u,v,i) )
self.model.addConstr( self.phi_vars[u,v,i] >= self.weights[i] - (1 - self.edge_vars[u,v,i]) * self.w_max, "14h_u={}_v={}_i={}".format(u,v,i) )
self.model.addConstr( self.gam_vars[u,v,i] >= self.slacks [i] - (1 - self.edge_vars[u,v,i]) * self.w_max, "14k_u={}_v={}_i={}".format(u,v,i) )
#Example of a subpath constraint: R=[ [(1,3),(3,5)], [(0,1)] ], means that we have 2 paths to cover, the first one is 1-3-5. the second path is just a single edge 0-1
def EncodeSubpathConstraints():
for i in range(self.k):
for j in range(len(self.R)):
edgevars_on_subpath = list(map(lambda e: self.edge_vars[e[0],e[1],i], self.R[j]))
self.model.addConstr( sum(edgevars_on_subpath) >= len(self.R[j]) * self.spc_vars[i,j] )
for j in range(len(self.R)):
self.model.addConstr( self.spc_vars.sum('*',j) >= 1 )
def Fix_Variables():
for i in range(len(self.vars2fix)):
for (u,v) in self.vars2fix[i]:
self.model.addConstr( self.edge_vars[u,v,i] == 1 )
if self.R!=[]:
EncodeSubpathConstraints()
if self.vars2fix!=[]:
Fix_Variables()
self.model.setObjective( self.slacks.sum(), GRB.MINIMIZE )
def print_solution(self,solution):
opt, slack, paths = solution
print("\n#####SOLUTION#####\n","> FD size :", opt,"\n> Slack sum :", slack,"\n> Weight-Slack-Path decomposition:")
for p in paths:
print(*p)
def build_solution(self):
paths = []
for i in range(self.k):
path = []
u = self.source
while u != self.target:
edges = list(filter(lambda grb_var : grb_var.X>1-TOLERANCE , self.edge_vars.select(u,'*',i) ))
assert(len(edges)==1)
v = head(edges[0].VarName)
path.append(v)
u = v
paths.append( (self.weights[i].X, self.slacks[i].X, path[:-1]) )
return (self.k, self.model.ObjVal, paths)
def solve_once(self):
logger.info(">>> Solving once")
self.encode()
self.solve()
logger.info("Gurobi solver status " + str(self.model.status))
if self.model.status == GRB.TIME_LIMIT:
raise utils.GRB_TimeOut("ilp.Robust.solve_once while finding feasible solution")
elif self.model.status == GRB.OPTIMAL:
_,_,p = self.build_solution()
weights,paths = list(map(lambda x : x[0], p)), list(map(lambda x : x[2], p))
return (paths,weights)
else:
logger.error("FATAL: solver finished with status " + str(self.model.status) + ", which is not OPT nor TIME_LIMIT.")
def optimize_linear(self):
#Assumption: the initial value of self.k is sufficiently high so that the ILP solver starts with a feasible solution
self.encode()
self.solve()
if self.model.status == GRB.TIME_LIMIT:
self.final_k = self.k
raise utils.GRB_TimeOut("ilp.Robust.optimize_linear while optimizing")
previous_slack = self.model.ObjVal
if previous_slack == 0:
logger.info(">>> No optimization step required, found perfect solution in init solving with " + str(self.k))
self.final_k = self.k
return self.final_k
self.clear()
self.k += 1
logger.info(">>> Optimality, starting with " + str(self.k))
while True: #optimality criteria: find the k for which the ratio of slacks between two consecutive iterations becomes sufficiently small
self.encode()
self.solve()
logger.info("Gurobi solver status " + str(self.model.status))
if self.model.status == GRB.TIME_LIMIT:
self.final_k = self.k-1
raise utils.GRB_TimeOut("ilp.Robust.optimize_linear while optimizing")
#assert(self.model.ObjVal <= previous_slack) not necessarily true, as the lower bound of the weight variables is 1
if self.model.ObjVal >= previous_slack: #if we do not improve by allowing more paths we stop
self.final_k = self.k-1
break
if self.model.ObjVal==0: #if we found a perfect solution we stop
self.final_k = self.k
break
assert(previous_slack != 0)
if 1-self.model.ObjVal/previous_slack < self.epsilon: # if the relative improvement is small we also stop
self.final_k = self.k-1
break
previous_slack = self.model.ObjVal
self.clear()
self.k += 1
return self.final_k
def robust(G : graph.st_DAG, epsilon=0.25, timeout=300, threads=4, path_constraints=[], vars_to_fix=[], optimize=False):
logger.info("Robust BEGIN on graph %s", G.id)
if len(G.edge_list)==0:
logger.warning("Empty edge list in graph %s. Returning empty list of paths.", G.id)
return []
encoder = Encode_Robust(G.n, G.edge_list, G.source, G.sink, G.flow, G.w, path_constraints, vars_to_fix, epsilon, timeout, threads)
if optimize:
return encoder.optimize_linear()
else:
status,paths = encoder.solve_once()
return (status,paths)
def leastsquares(G : graph.st_DAG, epsilon=0.25, timeout=300, threads=4, path_constraints=[], vars_to_fix=[], optimize=False):
logger.info("LeastSquares BEGIN on graph %s", G.id)
if len(G.edge_list)==0:
logger.warning("Empty edge list in graph %s. Returning empty list of paths.", G.id)
return []
encoder = Encode_LeastSquares(G.n, G.edge_list, G.source, G.sink, G.flow, G.w, path_constraints, vars_to_fix, epsilon, timeout, threads)
if optimize:
return encoder.optimize_linear()
else:
status,paths = encoder.solve_once()
return (status,paths)