#!/usr/bin/env python3
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# Copyright 2022 Max Planck Insitute Magdeburg
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"""GLPK solver interface for LP and MILP"""
from scipy import sparse
from numpy import nan, isnan, inf, isinf, sum
from straindesign.names import *
from typing import Tuple, List
from swiglpk import *
import logging
[docs]class GLPK_MILP_LP():
"""GLPK interface for MILP and LP
This class is a wrapper for the GLPK-Python API to offer bindings and namings
for functions for the construction and manipulation of MILPs and 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.
The GLPK interface does not natively support indicator constraints. They are
hence translated to bigM-constraints when passed to the GLPK constructor
(see docstring of IndicatorConstraints). The GLPK 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:
glpk = GLPK_MILP_LP(c, A_ineq, b_ineq, A_eq, b_eq, lb, ub, vtype, indic_constr, M)
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.
To make GLPK compatible with indicator constraints, they are translated into
bigM-constraints (see reference manual or docstring of IndicatorConstraints).
M (int): (Default: None)
A large value that is used in the translation of indicator constraints to
bigM-constraints. If no value is provided, 1000 is used.
Returns:
(GLPK_MILP_LP):
A GLPK MILP/LP interface class.
"""
def __init__(self, c, A_ineq, b_ineq, A_eq, b_eq, lb, ub, vtype, indic_constr, M=None):
self.glpk = glp_create_prob()
# Careful with indexing! GLPK indexing starts with 1 and not with 0
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))
if all([v == 'C' for v in vtype]):
self.ismilp = False
else:
self.ismilp = True
# add and set variables, types and bounds
if numvars > 0:
glp_add_cols(self.glpk, numvars)
for i, v in enumerate(vtype):
if v == 'C':
glp_set_col_kind(self.glpk, i + 1, GLP_CV)
if v == 'I':
glp_set_col_kind(self.glpk, i + 1, GLP_IV)
if v == 'B':
glp_set_col_kind(self.glpk, i + 1, GLP_BV)
# set bounds
lb = [float(l) for l in lb]
ub = [float(u) for u in ub]
for i in range(numvars):
if isinf(lb[i]) and isinf(ub[i]):
glp_set_col_bnds(self.glpk, i + 1, GLP_FR, lb[i], ub[i])
elif not isinf(lb[i]) and isinf(ub[i]):
glp_set_col_bnds(self.glpk, i + 1, GLP_LO, lb[i], ub[i])
elif isinf(lb[i]) and not isinf(ub[i]):
glp_set_col_bnds(self.glpk, i + 1, GLP_UP, lb[i], ub[i])
elif not isinf(lb[i]) and not isinf(ub[i]) and lb[i] < ub[i]:
glp_set_col_bnds(self.glpk, i + 1, GLP_DB, lb[i], ub[i])
elif not isinf(lb[i]) and not isinf(ub[i]) and lb[i] == ub[i]:
glp_set_col_bnds(self.glpk, i + 1, GLP_FX, lb[i], ub[i])
# set objective
glp_set_obj_dir(self.glpk, GLP_MIN)
for i, c_i in enumerate(c):
glp_set_obj_coef(self.glpk, i + 1, float(c_i))
# add indicator constraints
A_indic = sparse.lil_matrix((0, numvars))
b_indic = []
if not indic_constr == None:
if not M:
M = 1e3
logging.warning('There is no native support of indicator constraints with GLPK.')
logging.warning('Indicator constraints are translated to big-M constraints with M=' + str(M) + '.')
num_ic = len(indic_constr.binv)
eq_type_indic = [] # [GLP_UP]*len(b_ineq)+[GLP_FX]*len(b_eq)
for i in range(num_ic):
binv = indic_constr.binv[i]
indicval = indic_constr.indicval[i]
A = indic_constr.A[i]
b = float(indic_constr.b[i])
sense = indic_constr.sense[i]
if sense == 'E':
A = sparse.vstack((A, -A)).tolil()
b = [b, -b]
else:
A = A.tolil()
b = [b]
if indicval:
A[:, binv] = M
b = [v + M for v in b]
else:
A[:, binv] = -M
A_indic = sparse.vstack((A_indic, A))
b_indic = b_indic + b
# stack all problem rows and add constraints
if A_ineq.shape[0] + A_eq.shape[0] + A_indic.shape[0] > 0:
glp_add_rows(self.glpk, A_ineq.shape[0] + A_eq.shape[0] + A_indic.shape[0])
eq_type = [GLP_UP] * len(b_ineq) + [GLP_FX] * len(b_eq) + [GLP_UP] * len(b_indic)
for i, t, b in zip(range(len(b_ineq + b_eq + b_indic)), eq_type, b_ineq + b_eq + b_indic):
glp_set_row_bnds(self.glpk, i + 1, t, float(b), float(b))
A = sparse.vstack((A_ineq, A_eq, A_indic), 'coo')
ia = intArray(A.nnz + 1)
ja = intArray(A.nnz + 1)
ar = doubleArray(A.nnz + 1)
for i, row, col, data in zip(range(A.nnz), A.row, A.col, A.data):
ia[i + 1] = int(row) + 1
ja[i + 1] = int(col) + 1
ar[i + 1] = float(data)
if A.nnz:
glp_load_matrix(self.glpk, A.nnz, ia, ja, ar)
# not sure if the parameter setup is okay
# LP simplex parameters
self.lp_params = glp_smcp()
glp_init_smcp(self.lp_params)
self.max_tlim = self.lp_params.tm_lim
self.lp_params.tol_bnd = 1e-9
self.lp_params.msg_lev = 0
# MILP parameters
if self.ismilp:
self.milp_params = glp_iocp()
glp_init_iocp(self.milp_params)
self.milp_params.presolve = 1
self.milp_params.tol_int = 1e-12
self.milp_params.tol_obj = 1e-9
self.milp_params.msg_lev = 0
# ideally, one would generate random seeds here, but glpk does not seem to
# offer this function
[docs] def solve(self) -> Tuple[List, float, float]:
"""Solve the MILP or LP
Example:
sol_x, optim, status = glpk.solve()
Returns:
(Tuple[List, float, float])
solution_vector, optimal_value, optimization_status
"""
try:
min_cx, status, bool_tlim = self.solve_MILP_LP()
if status in [GLP_OPT, GLP_FEAS]: # solution
status = OPTIMAL
elif bool_tlim and status == GLP_UNDEF: # timeout without solution
x = [nan] * glp_get_num_cols(self.glpk)
min_cx = nan
status = TIME_LIMIT
return x, min_cx, status
elif status in [GLP_INFEAS, GLP_NOFEAS]: # infeasible
x = [nan] * glp_get_num_cols(self.glpk)
min_cx = nan
status = INFEASIBLE
return x, min_cx, status
elif bool_tlim and status == GLP_FEAS: # timeout with solution
min_cx = self.ObjVal
status = TIME_LIMIT_W_SOL
elif status in [GLP_UNBND, GLP_UNDEF]: # solution unbounded
x = [nan] * glp_get_num_cols(self.glpk)
min_cx = -inf
status = UNBOUNDED
return x, min_cx, status
else:
raise Exception('Status code ' + str(status) + " not yet handeld.")
x = self.getSolution(status)
x = [round(y, 12) for y in x] # workaround, round to 12 decimals
min_cx = round(min_cx, 12)
return x, min_cx, status
except:
logging.error('Error while running GLPK.')
min_cx = nan
x = [nan] * glp_get_num_cols(self.glpk)
return x, min_cx, -1
[docs] def slim_solve(self) -> float:
"""Solve the MILP or LP, but return only the optimal value
Example:
optim = glpk.slim_solve()
Returns:
(float)
Optimum value of the objective function.
"""
try:
opt, status, bool_tlim = self.solve_MILP_LP()
if status in [GLP_OPT, GLP_FEAS]: # solution integer optimal (tolerance)
pass
elif status in [GLP_UNBND, GLP_UNDEF]: # solution unbounded (or inf or unbdd)
opt = -inf
elif bool_tlim or status in [GLP_INFEAS, GLP_NOFEAS]: # infeasible or timeout
opt = nan
else:
raise Exception('Status code ' + str(status) + " not yet handeld.")
opt = round(opt, 12) # workaround, round to 12 decimals
return opt
except:
logging.error('Error while running GLPK.')
return nan
[docs] def populate(self, pool_limit) -> Tuple[List, float, float]:
"""Generate a solution pool for MILPs
This is only a high-level implementation of the populate function.
There is no native support in GLPK.
Example:
sols_x, optim, status = glpk.populate()
Returns:
(Tuple[List of lists, float, float])
solution_vectors, optimal_value, optimization_status
"""
numvars = glp_get_num_cols(self.glpk)
numrows = glp_get_num_rows(self.glpk)
try:
if pool_limit > 0:
sols = []
stoptime = glp_time() + self.milp_params.tm_lim * 1000
# 1. find optimal solution
self.set_time_limit(glp_difftime(stoptime, glp_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
c = [glp_get_obj_coef(self.glpk, i + 1) for i in range(numvars)]
self.add_ineq_constraints(sparse.csr_matrix(c), [min_cx])
# 3. exclude first solution pool
self.addExclusionConstraintsIneq(x)
# 4. loop solve and exclude until problem becomes infeasible
while status in [OPTIMAL,UNBOUNDED] and not isnan(x[0]) \
and glp_difftime(stoptime,glp_time()) > 0 and pool_limit > len(sols):
self.set_time_limit(glp_difftime(stoptime, glp_time()))
x, _, status = self.solve()
if status in [OPTIMAL, UNBOUNDED]:
self.addExclusionConstraintsIneq(x)
sols += [x]
if glp_difftime(stoptime, glp_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 = glp_get_num_rows(self.glpk)
for j in range(numrows, totrows):
self.set_ineq_constraint(j, [0] * numvars, inf)
# Alternatively rows may be deleted, but this seems to be very unstable
# delrows = intArray(totrows-numrows)
# for i,j in range(numrows,totrows):
# delrows[i+1] = j+1
# glp_del_rows(self.glpk,totrows-numrows,delrows)
return sols, min_cx, status
except:
logging.error('Error while running GLPK.')
x = []
min_cx = nan
return x, min_cx, ERROR
[docs] def set_objective(self, c):
"""Set the objective function with a vector"""
for i, c_i in enumerate(c):
glp_set_obj_coef(self.glpk, i + 1, float(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 c in C:
glp_set_obj_coef(self.glpk, c[0] + 1, float(c[1]))
[docs] def set_ub(self, ub):
"""Set the upper bounds to a given vector"""
setvars = [ub[i][0] for i in range(len(ub))]
lb = [glp_get_col_lb(self.glpk, i + 1) for i in setvars]
ub = [ub[i][1] for i in range(len(ub))]
type = [glp_get_col_type(self.glpk, i + 1) for i in setvars]
for i, l, u, t in zip(setvars, lb, ub, type):
if t in [GLP_FR, GLP_LO] and isinf(u):
glp_set_col_bnds(self.glpk, i + 1, t, float(l), float(u))
elif t == GLP_UP and isinf(u):
glp_set_col_bnds(self.glpk, i + 1, GLP_FR, float(l), float(u))
elif t in [GLP_LO, GLP_DB, GLP_FX] and not isinf(u) and l < u:
glp_set_col_bnds(self.glpk, i + 1, GLP_DB, float(l), float(u))
elif t in [GLP_LO, GLP_DB, GLP_FX] and not isinf(u) and l == u:
glp_set_col_bnds(self.glpk, i + 1, GLP_FX, float(l), float(u))
[docs] def set_time_limit(self, t):
"""Set the computation time limit (in seconds)"""
if t * 1000 > self.max_tlim:
if self.ismilp:
self.milp_params.tm_lim = self.max_tlim
self.lp_params.tm_lim = self.max_tlim
else:
if self.ismilp:
self.milp_params.tm_lim = int(t * 1000)
self.lp_params.tm_lim = int(t * 1000)
[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
"""
numvars = glp_get_num_cols(self.glpk)
numrows = glp_get_num_rows(self.glpk)
num_newrows = A_ineq.shape[0]
col = intArray(numvars + 1)
val = doubleArray(numvars + 1)
glp_add_rows(self.glpk, num_newrows)
for j in range(num_newrows):
for i, v in enumerate(A_ineq[j].toarray()[0]):
col[i + 1] = i + 1
val[i + 1] = float(v)
glp_set_mat_row(self.glpk, numrows + j + 1, numvars, col, val)
if isinf(b_ineq[j]):
glp_set_row_bnds(self.glpk, numrows + j + 1, GLP_FR, -inf, float(b_ineq[j]))
else:
glp_set_row_bnds(self.glpk, numrows + j + 1, GLP_UP, -inf, float(b_ineq[j]))
[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
"""
numvars = glp_get_num_cols(self.glpk)
numrows = glp_get_num_rows(self.glpk)
num_newrows = A_eq.shape[0]
col = intArray(numvars + 1)
val = doubleArray(numvars + 1)
glp_add_rows(self.glpk, num_newrows)
for j in range(num_newrows):
for i, v in enumerate(A_eq[j].toarray()[0]):
col[i + 1] = i + 1
val[i + 1] = float(v)
glp_set_mat_row(self.glpk, numrows + j + 1, numvars, col, val)
glp_set_row_bnds(self.glpk, numrows + j + 1, GLP_FX, float(b_eq[j]), float(b_eq[j]))
[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
"""
numvars = glp_get_num_cols(self.glpk)
col = intArray(numvars + 1)
val = doubleArray(numvars + 1)
for i, v in enumerate(a_ineq):
col[i + 1] = i + 1
val[i + 1] = float(v)
glp_set_mat_row(self.glpk, idx + 1, numvars, col, val)
if isinf(b_ineq):
glp_set_row_bnds(self.glpk, idx + 1, GLP_FR, -inf, float(b_ineq))
else:
glp_set_row_bnds(self.glpk, idx + 1, GLP_UP, -inf, float(b_ineq))
[docs] def getSolution(self, status) -> list:
"""Retrieve solution from GLPK backend"""
if self.ismilp and status in [OPTIMAL, UNBOUNDED, TIME_LIMIT_W_SOL]:
x = [glp_mip_col_val(self.glpk, i + 1) for i in range(glp_get_num_cols(self.glpk))]
else:
x = [glp_get_col_prim(self.glpk, i + 1) for i in range(glp_get_num_cols(self.glpk))]
return x
[docs] def solve_MILP_LP(self) -> Tuple[float, int, bool]:
"""Trigger GLPK solution through backend"""
starttime = glp_time()
# MILP solving needs prior solution of the LP-relaxed problem, because occasionally
# the MILP solver interface crashes when a problem is infesible, which, in turn,
# crashes the python program. This connection-loss to the solver can not be captured.
prelim_status = glp_simplex(self.glpk, self.lp_params)
# There is a GLPK bug where feasible LPs fail initialy but can complete when presolved
# in these cases, glp_simplex returns GLP_EFAIL. We capture these cases and solve again
# with prior resolve.
if prelim_status == GLP_EFAIL:
self.lp_params.presolve = 1
self.lp_params.meth = 3
prelim_status = glp_simplex(self.glpk, self.lp_params)
self.lp_params.presolve = 0
self.lp_params.meth = 1
status = glp_get_status(self.glpk)
if self.ismilp and status not in [GLP_INFEAS, GLP_NOFEAS]:
glp_intopt(self.glpk, self.milp_params)
status = glp_mip_status(self.glpk)
opt = glp_mip_obj_val(self.glpk)
else:
opt = glp_get_obj_val(self.glpk)
timelim_reached = glp_difftime(glp_time(), starttime) >= self.lp_params.tm_lim
return opt, status, timelim_reached
[docs] def addExclusionConstraintsIneq(self, x):
"""Function to add exclusion constraint (GLPK compatibility function)"""
numvars = glp_get_num_cols(self.glpk)
# Here, we also need to take integer variables into account, because GLPK changes
# variable type to integer when you lock a binary variable to zero
binvars = [i for i in range(numvars) if glp_get_col_kind(self.glpk, i + 1) in [GLP_BV, GLP_IV]]
data = [1.0 if x[i] else -1.0 for i in binvars]
row = [0] * len(binvars)
A_ineq = sparse.csr_matrix((data, (row, binvars)), (1, numvars))
b_ineq = sum([x[i] for i in binvars]) - 1
self.add_ineq_constraints(A_ineq, [b_ineq])