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"""SCIP and SoPlex solver interface for LP and MILP"""
from random import randint
from scipy import sparse
from numpy import isnan, nan, inf, isinf, sum, nonzero
import pyscipopt as pso
from straindesign.names import *
from typing import Tuple, List
import time as t
import logging
[docs]class SCIP_MILP(pso.Model):
"""SCIP interface for MILP
This class is a wrapper for the SCIP-Python API to offer bindings and namings
for functions for the construction and manipulation of MILPs in an
vector-matrix-based manner that are consistent with those of the other solver
interfaces in the StrainDesign package. The purpose is to unify the instructions
for operating with MILPs and LPs throughout StrainDesign.
The SCIP interface provides support for indicator constraints as well as for
the populate function. The SCIP interface does not natively support the populate
function. A high level implementation emulates the behavior of populate.
Accepts a (mixed integer) linear problem in the form:
minimize(c),
subject to:
A_ineq * x <= b_ineq,
A_eq * x = b_eq,
lb <= x <= ub,
forall(i) type(x_i) = vtype(i) (continous, binary, integer),
indicator constraints:
x(j) = [0|1] -> a_indic * x [<=|=|>=] b_indic
Please ensure that the number of variables and (in)equalities is consistent
Example:
scip = SCIP_MILP(c, A_ineq, b_ineq, A_eq, b_eq, lb, ub, vtype, indic_constr)
Args:
c (list of float): (Default: None)
The objective vector (Objective sense: minimization).
A_ineq (sparse.csr_matrix): (Default: None)
A coefficient matrix of the static inequalities.
b_ineq (list of float): (Default: None)
The right hand side of the static inequalities.
A_eq (sparse.csr_matrix): (Default: None)
A coefficient matrix of the static equalities.
b_eq (list of float): (Default: None)
The right hand side of the static equalities.
lb (list of float): (Default: None)
The lower variable bounds.
ub (list of float): (Default: None)
The upper variable bounds.
vtype (str): (Default: None)
A character string that specifies the type of each variable:
'c'ontinous, 'b'inary or 'i'nteger
indic_constr (IndicatorConstraints): (Default: None)
A set of indicator constraints stored in an object of IndicatorConstraints
(see reference manual or docstring).
Returns:
(SCIP_MILP):
A SCIP MILP interface class.
"""
def __init__(self, c, A_ineq, b_ineq, A_eq, b_eq, lb, ub, vtype, indic_constr):
super().__init__()
# uncomment to forward SCIP output to python terminal
# self.redirectOutput()
try:
numvars = A_ineq.shape[1]
except:
numvars = A_eq.shape[1]
# prepare coefficient matrix
if isinstance(A_eq, list):
if not A_eq:
A_eq = sparse.csr_matrix((0, numvars))
if isinstance(A_ineq, list):
if not A_ineq:
A_ineq = sparse.csr_matrix((0, numvars))
ub = [u if not isinf(u) else None for u in ub]
lb = [l if not isinf(l) else None for l in lb]
# add variables and constraints
x = [self.addVar(lb=l, ub=u, obj=o, vtype=v) for l, u, o, v in zip(lb, ub, c, vtype)]
self.vars = x
self.binvars = [i for i in range(len(x)) if vtype[i] == 'B']
# generate "Terms" and "Expressions" for faster problem construction
self.trms = [list(x[i].terms.items())[0][0] for i in range(numvars)]
self.constr = []
# add inequality constraints
ineqs = [self.addCons(pso.Expr() <= b_i) for b_i in b_ineq]
for row, a_ineq in zip(ineqs, A_ineq):
X = [x[i] for i in a_ineq.indices]
for col, coeff in zip(X, a_ineq.data):
self.addConsCoeff(row, col, coeff)
self.constr += ineqs
# add equality constraints
eqs = [self.addCons(pso.Expr() == b_i) for b_i in b_eq]
for row, a_eq in zip(eqs, A_eq):
X = [x[i] for i in a_eq.indices]
for col, coeff in zip(X, a_eq.data):
self.addConsCoeff(row, col, coeff)
self.constr += eqs
self.setMinimize()
# add indicator constraints
if indic_constr is not None:
for i in range(len(indic_constr.sense)):
if indic_constr.indicval[i] == 0: # if the constraints activity is indicated by 0, an auxiliary variable needs to be added
z = self.addVar(lb=0, ub=1, obj=0, vtype='B')
xor = self.addCons(pso.Expr() == 1)
self.addConsCoeff(xor, x[indic_constr.binv[i]], 1)
self.addConsCoeff(xor, z, 1)
else:
z = x[indic_constr.binv[i]]
if indic_constr.sense[i] == 'E':
A = sparse.vstack((indic_constr.A[i], -indic_constr.A[i]))
b = [indic_constr.b[i], -indic_constr.b[i]]
else:
A = indic_constr.A[i]
b = [indic_constr.b[i]]
for k in range(A.shape[0]):
for a in A[k]:
e = pso.scip.Expr({self.trms[j]: d for j, d in zip(a.indices, a.data)})
f = pso.scip.ExprCons(e, lhs=None, rhs=b[k])
self.constr += [self.addConsIndicator(f, binvar=z, initial=False)]
# set parameters
self.max_tlim = self.getParam('limits/time')
self.setParam('display/verblevel', 0)
if 'B' in vtype or 'I' in vtype:
seed = seed = randint(0, 2**31 - 1)
# logging.info(' MILP Seed: '+str(seed))
self.setParam('randomization/randomseedshift', seed)
# self.enableReoptimization()
# self.setParam('display/lpinfo',False)
# self.setParam('reoptimization/enable',True)
[docs] def solve(self) -> Tuple[List, float, float]:
"""Solve the MILP
Example:
sol_x, optim, status = scip.solve()
Returns:
(Tuple[List, float, float])
solution_vector, optimal_value, optimization_status
"""
try:
self.optimize()
status = self.getStatus()
if status in ['optimal']: # solution
min_cx = self.getObjVal()
status = OPTIMAL
elif status == 'timelimit' and self.getSols() == []: # timeout without solution
x = [nan] * len(self.vars)
min_cx = nan
status = TIME_LIMIT
return x, min_cx, status
elif status == 'infeasible': # infeasible
x = [nan] * len(self.vars)
min_cx = nan
status = INFEASIBLE
return x, min_cx, status
elif status == 'timelimit' and not self.getSols() == []: # timeout with solution
min_cx = self.getObjVal()
status = TIME_LIMIT_W_SOL
elif status in ['inforunbd', 'unbounded']: # solution unbounded
x = [nan] * len(self.vars)
min_cx = -inf
status = UNBOUNDED
return x, min_cx, status
else:
raise Exception('Status code ' + str(status) + " not yet handeld.")
x = self.getSolution()
return x, min_cx, status
except:
logging.error('Error while running SCIP.')
min_cx = nan
x = [nan] * len(self.vars)
return x, min_cx, ERROR
[docs] def slim_solve(self) -> float:
"""Solve the MILP, but return only the optimal value
Example:
optim = scip.slim_solve()
Returns:
(float)
Optimum value of the objective function.
"""
try:
self.optimize()
status = self.getStatus()
if status == 'optimal': # solution
opt = self.getObjVal()
elif status in ['infeasible', 'timelimit']:
opt = nan
elif status in ['inforunbd', 'unbounded']:
opt = -inf
else:
raise Exception('Status code ' + str(status) + " not yet handeld.")
return opt
except:
logging.error('Error while running SCIP.')
return nan
def populate(self, pool_limit) -> Tuple[List, float, float]:
numrows = len(self.constr)
"""Generate a solution pool for MILPs
This is only a high-level implementation of the populate function.
There is no native support in SCIP.
Example:
sols_x, optim, status = scip.populate()
Returns:
(Tuple[List of lists, float, float])
solution_vectors, optimal_value, optimization_status
"""
try:
if pool_limit > 0:
sols = []
stoptime = t.time() + self.getParam('limits/time')
# 1. find optimal solution
self.set_time_limit(stoptime - t.time())
x, min_cx, status = self.solve()
if status not in [OPTIMAL, UNBOUNDED]:
return sols, min_cx, status
sols = [x]
# 2. constrain problem to optimality
objTerms = self.getObjective().terms
c = [objTerms[x] if x in objTerms.keys() else 0.0 for x in self.trms]
self.add_ineq_constraints(sparse.csr_matrix(c), [min_cx])
# 3. exclude first solution pool
self.addExclusionConstraintIneq(x)
# 4. loop solve and exclude until problem becomes infeasible
while status in [OPTIMAL,UNBOUNDED] and not isnan(x[0]) \
and stoptime-t.time() > 0 and pool_limit > len(sols):
self.set_time_limit(stoptime - t.time())
x, _, status = self.solve()
if status in [OPTIMAL, UNBOUNDED]:
self.addExclusionConstraintIneq(x)
sols += [x]
if stoptime - t.time() < 0:
status = TIME_LIMIT_W_SOL
elif status == INFEASIBLE:
status = OPTIMAL
# 5. remove auxiliary constraints
# Here, we only free the upper bound of the constraints
totrows = len(self.constr)
self.freeTransform()
for j in range(numrows, totrows):
self.chgRhs(self.constr[j], None)
return sols, min_cx, status
except:
logging.error('Error while running SCIP.')
min_cx = nan
x = []
return x, min_cx, ERROR
[docs] def set_objective(self, c):
"""Set the objective function with a vector"""
if self.getParam('reoptimization/enable'):
self.freeReoptSolve()
self.chgReoptObjective(pso.Expr({self.trms[i]: c[i] for i in nonzero(c)[0]}))
else:
self.freeTransform()
self.setObjective(pso.Expr({self.trms[i]: c[i] for i in nonzero(c)[0]}))
[docs] def set_objective_idx(self, C):
"""Set the objective function with index-value pairs
e.g.: C=[[1, 1.0], [4,-0.2]]"""
if self.getParam('reoptimization/enable'):
self.freeReoptSolve()
self.chgReoptObjective(pso.Expr({self.trms[c[0]]: c[1] for c in C}))
else:
self.freeTransform()
self.setObjective(pso.Expr({self.trms[c[0]]: c[1] for c in C}))
[docs] def set_ub(self, ub):
"""Set the upper bounds to a given vector"""
self.freeTransform()
for i in range(len(ub)):
if not isinf(ub[i][1]):
self.chgVarUb(self.vars[ub[i][0]], float(ub[i][1]))
else:
self.chgVarUb(self.vars[ub[i][0]], None)
[docs] def set_time_limit(self, t):
"""Set the computation time limit (in seconds)"""
if t >= self.max_tlim:
self.setParam('limits/time', self.max_tlim)
else:
self.setParam('limits/time', t)
[docs] def add_ineq_constraints(self, A_ineq, b_ineq):
"""Add inequality constraints to the model
Additional inequality constraints have the form A_ineq * x <= b_ineq.
The number of columns in A_ineq must match with the number of variables x
in the problem.
Args:
A_ineq (sparse.csr_matrix):
The coefficient matrix
b_ineq (list of float):
The right hand side vector
"""
self.freeTransform()
ineqs = [self.addCons(pso.Expr() <= b_i) for b_i in b_ineq]
for row, a_ineq in zip(ineqs, A_ineq):
X = [self.vars[i] for i in a_ineq.indices]
for col, coeff in zip(X, a_ineq.data):
self.addConsCoeff(row, col, float(coeff))
self.constr += ineqs
[docs] def add_eq_constraints(self, A_eq, b_eq):
"""Add equality constraints to the model
Additional equality constraints have the form A_eq * x = b_eq.
The number of columns in A_eq must match with the number of variables x
in the problem.
Args:
A_eq (sparse.csr_matrix):
The coefficient matrix
b_eq (list of float):
The right hand side vector
"""
self.freeTransform()
eqs = [self.addCons(pso.Expr() == b_i) for b_i in b_eq]
for row, a_eq in zip(eqs, A_eq):
X = [self.vars[i] for i in a_eq.indices]
for col, coeff in zip(X, a_eq.data):
self.addConsCoeff(row, col, float(coeff))
self.constr += eqs
[docs] def set_ineq_constraint(self, idx, a_ineq, b_ineq):
"""Replace a specific inequality constraint
Replace the constraint with the index idx with the constraint a_ineq*x ~ b_ineq
Args:
idx (int):
Index of the constraint
a_ineq (list of float):
The coefficient vector
b_ineq (float):
The right hand side value
"""
self.freeTransform()
# Make previous constraint non binding. removing or
# changing old constraints would be better but doesn't work
self.chgRhs(self.constr[idx], None)
# add new constraint and replace constraint pointer in list
self.constr[idx] = self.addCons(pso.Expr() <= 0)
for i, a in enumerate(a_ineq):
self.addConsCoeff(self.constr[idx], self.vars[i], a)
if isinf(b_ineq):
self.chgRhs(self.constr[idx], None)
else:
self.chgRhs(self.constr[idx], b_ineq)
pass
[docs] def getSolution(self) -> list:
"""Retrieve solution from SCIP backend"""
return [self.getVal(x) for x in self.vars]
[docs] def addExclusionConstraintIneq(self, x):
"""Function to add exclusion constraint (SCIP compatibility function)"""
data = [1.0 if x[i] else -1.0 for i in self.binvars]
row = [0] * len(self.binvars)
A_ineq = sparse.csr_matrix((data, (row, self.binvars)), (1, len(self.vars)))
b_ineq = sum([x[i] for i in self.binvars]) - 1
self.add_ineq_constraints(A_ineq, [b_ineq])
[docs]class SCIP_LP(pso.LP):
"""SoPlex interface for LP
This class is a wrapper for the SoPlex-Python API to offer bindings and namings
for functions for the construction and manipulation of LPs in an
vector-matrix-based manner that are consistent with those of the other solver
interfaces in the StrainDesign package. The purpose is to unify the instructions
for operating with MILPs and LPs throughout StrainDesign.
"""
def __init__(self, c, A_ineq, b_ineq, A_eq, b_eq, lb, ub):
"""Constructor of the SCIP (SoPlex) LP interface class
Accepts a (mixed integer) linear problem in the form:
minimize(c)
subject to: A_ineq * x <= b_ineq
A_eq * x = b_eq
lb <= x <= ub
forall(i) type(x_i) = vtype(i) (continous, binary, integer)
indicator constraints:
x(j) = [0|1] -> a_indic * x [<=|=|>=] b_indic
Please ensure that the number of variables and (in)equalities is consistent
Example:
scip = SCIP_LP(c, A_ineq, b_ineq, A_eq, b_eq, lb, ub)
Args:
c (list of float): (Default: None)
The objective vector (Objective sense: minimization).
A_ineq (sparse.csr_matrix): (Default: None)
A coefficient matrix of the static inequalities.
b_ineq (list of float): (Default: None)
The right hand side of the static inequalities.
A_eq (sparse.csr_matrix): (Default: None)
A coefficient matrix of the static equalities.
b_eq (list of float): (Default: None)
The right hand side of the static equalities.
lb (list of float): (Default: None)
The lower variable bounds.
ub (list of float): (Default: None)
The upper variable bounds.
Returns:
(SCIP_LP):
A SCIP LP interface class.
"""
super().__init__(sense='minimize')
# uncomment to forward SCIP output to python terminal
try:
numvars = A_ineq.shape[1]
except:
numvars = A_eq.shape[1]
# prepare coefficient matrix
if isinstance(A_eq, list):
if not A_eq:
A_eq = sparse.csr_matrix((0, numvars))
if isinstance(A_ineq, list):
if not A_ineq:
A_ineq = sparse.csr_matrix((0, numvars))
ub = [u if not isinf(u) else self.infinity() for u in ub]
lb = [l if not isinf(l) else -self.infinity() for l in lb]
# add variables and constraints
self.addCols([()] * len(c), objs=c, lbs=lb, ubs=ub)
# add inequality constraints
self.addRows([[(i,v) for i,v in zip(rows.indices,rows.data)] for rows in A_ineq], \
lhss = [-self.infinity()]*A_ineq.shape[0],\
rhss = b_ineq)
# add equality constraints
self.addRows([[(i,v) for i,v in zip(rows.indices,rows.data)] for rows in A_eq], \
lhss = b_eq,\
rhss = b_eq)
self.optimize = super().solve
[docs] def solve(self) -> Tuple[List, float, float]:
"""Solve the LP
Example:
sol_x, optim, status = scip.solve()
Returns:
(Tuple[List, float, float])
solution_vector, optimal_value, optimization_status
"""
try:
min_cx = self.optimize() # this function was inherited from super().solve() during initialization
if self.isInfinity(-min_cx): # solution
min_cx = -inf
status = UNBOUNDED
elif self.isInfinity(min_cx):
min_cx = nan
status = INFEASIBLE
if not isnan(min_cx) and not isinf(min_cx):
x = self.getPrimal()
status = OPTIMAL
else:
x = [nan] * len(self.getPrimal())
return x, min_cx, status
except:
logging.error('Error while running SCIP.')
min_cx = nan
x = [nan] * len(self.getPrimal())
return x, min_cx, ERROR
[docs] def slim_solve(self) -> float:
"""Solve the LP, but return only the optimal value
Example:
optim = scip.slim_solve()
Returns:
(float)
Optimum value of the objective function.
"""
try:
opt = self.optimize() # this function was inherited from super().solve() during initialization
if self.isInfinity(-opt): # solution
opt = -inf
elif self.isInfinity(opt):
opt = nan
return opt
except:
logging.error('Error while running SCIP.')
return nan
[docs] def set_objective(self, c):
"""Set the objective function with a vector"""
for i in range(len(c)):
self.chgObj(i, c[i])
[docs] def set_objective_idx(self, C):
"""Set the objective function with index-value pairs
e.g.: C=[[1, 1.0], [4,-0.2]]"""
for i_v in C:
self.chgObj(i_v[0], i_v[1])
[docs] def add_ineq_constraints(self, A_ineq, b_ineq):
"""Add inequality constraints to the model
Additional inequality constraints have the form A_ineq * x <= b_ineq.
The number of columns in A_ineq must match with the number of variables x
in the problem.
Args:
A_ineq (sparse.csr_matrix):
The coefficient matrix
b_ineq (list of float):
The right hand side vector
"""
self.addRows([[(i,v) for i,v in zip(rows.indices,rows.data)] for rows in A_ineq], \
lhss = [-self.infinity()]*A_ineq.shape[0],\
rhss = b_ineq)
[docs] def add_eq_constraints(self, A_eq, b_eq):
"""Add equality constraints to the model
Additional equality constraints have the form A_eq * x = b_eq.
The number of columns in A_eq must match with the number of variables x
in the problem.
Args:
A_eq (sparse.csr_matrix):
The coefficient matrix
b_eq (list of float):
The right hand side vector
"""
self.addRows([[(i,v) for i,v in zip(rows.indices,rows.data)] for rows in A_eq], \
lhss = b_eq,\
rhss = b_eq)