def solve_sat(self, expression=None, callback=None,
return_processor=None, kwargs={}):
"""Runs a solve sat with a callback. This is similar to the
other SAT solving procedures in this test suite, with some
modifications to enable testing of the MIP callback
functionality.
expression is the expression argument, and defaults to the
expression declared in the MIPCallbackTest.
callback is the callback instance being tested.
return_processor is a function called with the retval from the
lp.integer call, and the lp, e.g., return_processor(retval,
lp), prior to any further processing of the results.
kwargs is a dictionary of other optional keyword arguments and
their values which is passed to the lp.integer solution
procedure."""
if expression is None:
expression = self.expression
if len(expression) == 0:
return []
numvars = max(max(abs(v) for v in clause) for clause in expression)
lp = LPX()
lp.cols.add(2*numvars)
for col in lp.cols:
col.bounds = 0.0, 1.0
def lit2col(lit):
if lit > 0:
return 2*lit-2
return 2*(-lit)-1
for i in range(1, numvars+1):
lp.cols[lit2col(i)].name = 'x_%d' % i
lp.cols[lit2col(-i)].name = '!x_%d' % i
lp.rows.add(1)
lp.rows[-1].matrix = [(lit2col(i), 1.0), (lit2col(-i), 1.0)]
lp.rows[-1].bounds = 1.0
for clause in expression:
lp.rows.add(1)
lp.rows[-1].matrix = [(lit2col(lit), 1.0) for lit in clause]
lp.rows[-1].bounds = 1, None
retval = lp.simplex()
if retval is not None:
return None
if lp.status != 'opt':
return None
for col in lp.cols:
col.kind = int
retval = lp.integer(callback=callback, **kwargs)
if return_processor:
return_processor(retval, lp)
if retval is not None:
return None
if lp.status != 'opt':
return None
return [col.value > 0.99 for col in lp.cols[::2]]
def testLpxRay(self):
lp = LPX()
self.assertTrue(lp.ray is None)
lp.cols.add(2)
x1, x2 = lp.cols[0:2]
lp.obj[:] = [-1.0, 1.0]
lp.rows.add(2)
r1, r2 = lp.rows[0:2]
r1.matrix = [1.0, -1.0]
r1.bounds = (-3, None)
r2.matrix = [-1.0, 2.0]
r2.bounds = (-2.0, None)
x1.bounds = None
x2.bounds = None
lp.simplex()
self.assertEqual(lp.status, 'unbnd')
self.assertTrue(lp.ray.iscol)
def solve_sat(self, expression):
"""Attempts to satisfy a formula of conjunction of disjunctions.
If there are n variables in the expression, this will return a
list of length n, all elements booleans. The truth of element i-1
corresponds to the truth of variable i.
If no satisfying assignment could be found, None is returned."""
if len(expression) == 0:
return []
numvars = max(max(abs(v) for v in clause) for clause in expression)
lp = LPX()
lp.cols.add(2*numvars)
for col in lp.cols:
col.bounds = 0.0, 1.0
def lit2col(lit):
if lit > 0:
return 2*lit-2
return 2*(-lit)-1
for i in range(1, numvars+1):
lp.cols[lit2col(i)].name = 'x_%d' % i
lp.cols[lit2col(-i)].name = '!x_%d' % i
lp.rows.add(1)
lp.rows[-1].matrix = [(lit2col(i), 1.0), (lit2col(-i), 1.0)]
lp.rows[-1].bounds = 1.0
for clause in expression:
lp.rows.add(1)
lp.rows[-1].matrix = [(lit2col(lit), 1.0) for lit in clause]
lp.rows[-1].bounds = 1, None
retval = lp.simplex()
if retval is not None:
return None
if lp.status != 'opt':
return None
for col in lp.cols:
col.kind = int
retval = lp.integer()
if retval is not None:
return None
if lp.status != 'opt':
return None
return [col.value > 0.99 for col in lp.cols[::2]]
lp.name = 'example'
lp.obj.maximize = True
# append 3 rows, named p, q, r
row_names = ["p", "q", "r"]
lp.rows.add(len(row_names))
for r in lp.rows:
r.name = row_names[r.index]
lp.rows[0].bounds = None, 100.0
lp.rows[1].bounds = None, 600.0
lp.rows[2].bounds = None, 150.0
# append 3 cols, named x0, x1, x2
lp.cols.add(3)
for c in lp.cols:
c.name = 'x%d' % c.index
c.bounds = 0.0, None
# set the objective coefficients and
# non-zero entries of the constraint matrix
lp.obj[:] = [ 5.0, 3.0, 2.0 ]
lp.matrix = [ 1.0, 1.0, 3.0, 10.0, 4.0, 5.0, 1.0, 1.0, 3.0 ]
# report the objective function value and structural variables
lp.simplex(msg_lev=LPX.MSG_ALL)
print 'Z = %g;' % lp.obj.value,
print '; '.join('%s = %g' % (c.name, c.primal) for c in lp.cols)
def _optimize_glpk(
cobra_model,
new_objective=None,
objective_sense='maximize',
min_norm=0,
the_problem=None,
tolerance_optimality=1e-6,
tolerance_feasibility=1e-6,
tolerance_integer=1e-9,
error_reporting=None,
print_solver_time=False,
lp_method=1,
quadratic_component=None,
reuse_basis=True,
#Not implemented
tolerance_barrier=None,
lp_parallel=None,
copy_problem=None,
relax_b=None,
update_problem_reaction_bounds=True):
"""Uses the GLPK (www.gnu.org/software/glpk/) optimizer via pyglpk
(http://www.tfinley.net/software/pyglpk/release.html) to perform an optimization
on cobra_model for the objective_coefficients in cobra_model._objective_coefficients
based on the objective sense.
cobra_model: A cobra.Model object
new_objective: Reaction, String, or Integer referring to a reaction in
cobra_model.reactions to set as the objective. Currently, only supports single
objective coeffients. Will expand to include mixed objectives.
objective_sense: 'maximize' or 'minimize'
min_norm: not implemented
the_problem: None or a problem object for the specific solver that can be used to hot
start the next solution.
tolerance_optimality: Solver tolerance for optimality.
tolerance_feasibility: Solver tolerance for feasibility.
error_reporting: None or True to disable or enable printing errors encountered
when trying to find the optimal solution.
print_solver_time: False or True. Indicates if the time to calculate the solution
should be displayed.
quadratic_component: None. GLPK cannot solve quadratic programs at the moment.
reuse_basis: Boolean. If True and the_problem is a model object for the solver,
attempt to hot start the solution. Currently, only True is available for GLPK
update_problem_reaction_bounds: Boolean. Set to True if you're providing the_problem
and you've modified reaction bounds on your cobra_model since creating the_problem. Only
necessary for CPLEX
lp.simplex() with Salmonella model:
cold start: 0.42 seconds
hot start: 0.0013 seconds
"""
from numpy import zeros, array, nan
#TODO: Speed up problem creation
if hasattr(quadratic_component, 'todok'):
raise Exception('GLPK cannot solve quadratic programs please '+\
'try using the gurobi or cplex solvers')
from glpk import LPX
from cobra.flux_analysis.objective import update_objective
from cobra.solvers.legacy import status_dict, variable_kind_dict
status_dict = eval(status_dict['glpk'])
variable_kind_dict = eval(variable_kind_dict['glpk'])
if new_objective and new_objective != 'update problem':
update_objective(cobra_model, new_objective)
#Faster to use these dicts than index lists
index_to_metabolite = dict(
zip(range(len(cobra_model.metabolites)), cobra_model.metabolites))
index_to_reaction = dict(
zip(range(len(cobra_model.reactions)), cobra_model.reactions))
reaction_to_index = dict(
zip(index_to_reaction.values(), index_to_reaction.keys()))
if the_problem == None or the_problem in ['return', 'setup'] or \
not isinstance(the_problem, LPX):
lp = LPX() # Create empty problem instance
lp.name = 'cobra' # Assign symbolic name to problem
lp.rows.add(len(cobra_model.metabolites))
lp.cols.add(len(cobra_model.reactions))
linear_constraints = []
for r in lp.rows:
the_metabolite = index_to_metabolite[r.index]
r.name = the_metabolite.id
b = float(the_metabolite._bound)
c = the_metabolite._constraint_sense
if c == 'E':
r.bounds = b, b # Set metabolite to steady state levels
elif c == 'L':
r.bounds = None, b
elif c == 'G':
r.bounds = b, None
#Add in the linear constraints
for the_reaction in the_metabolite._reaction:
reaction_index = reaction_to_index[the_reaction]
the_coefficient = the_reaction._metabolites[the_metabolite]
linear_constraints.append(
(r.index, reaction_index, the_coefficient))
#Need to assign lp.matrix after constructing the whole list
lp.matrix = linear_constraints
objective_coefficients = []
for c in lp.cols:
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
the_reaction = index_to_reaction[c.index]
c.kind = variable_kind_dict[the_reaction.variable_kind]
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(
float(the_reaction.objective_coefficient))
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
else:
lp = the_problem
#BUG with changing / unchanging the basis
if new_objective is not None:
objective_coefficients = []
for c in lp.cols: # Iterate over all rows
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(
float(the_reaction.objective_coefficient))
c.kind = variable_kind_dict[the_reaction.variable_kind]
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
else:
for c in lp.cols: # Iterate over all rows
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
c.kind = variable_kind_dict[the_reaction.variable_kind]
if objective_sense.lower() == 'maximize':
lp.obj.maximize = True # Set this as a maximization problem
else:
lp.obj.maximize = False
if the_problem == 'setup':
return lp
if print_solver_time:
start_time = time()
the_methods = [1, 2, 3]
if lp_method in the_methods:
the_methods.remove(lp_method)
else:
lp_method = 1
if not isinstance(the_problem, LPX):
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method)
# Solve this LP or MIP with the simplex (depending on if integer variables exist). Takes about 0.35 s without hot start
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
for lp_method in the_methods:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method)
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
break
else:
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method,
tm_lim=100) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method,
tm_lim=100)
#If the solver takes more than 0.1 s with a hot start it is likely stuck
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
for lp_method in the_methods:
lp.simplex(tol_bnd=tolerance_optimality,
tol_dj=tolerance_optimality,
meth=lp_method)
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
break
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp = optimize_glpk(
cobra_model,
new_objective=new_objective,
objective_sense=objective_sense,
min_norm=min_norm,
the_problem=None,
print_solver_time=print_solver_time,
tolerance_optimality=tolerance_optimality,
tolerance_feasibility=tolerance_feasibility)['the_problem']
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp.simplex(tol_bnd=tolerance_optimality,
presolve=True,
tm_lim=5000)
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
if print_solver_time:
print 'simplex time: %f' % (time() - start_time)
x = []
y = []
x_dict = {}
y_dict = {}
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status == 'optimal':
objective_value = lp.obj.value
[(x.append(float(c.primal)), x_dict.update({c.name: c.primal}))
for c in lp.cols]
if lp.kind == float:
#return the duals as well as the primals for LPs
[(y.append(float(c.dual)), y_dict.update({c.name: c.dual}))
for c in lp.rows]
else:
#MIPs don't have duals
y = y_dict = None
x = array(x)
else:
x = y = x_dict = y_dict = objective_value = None
if error_reporting:
print 'glpk failed: %s' % lp.status
cobra_model.solution = the_solution = Solution(objective_value,
x=x,
x_dict=x_dict,
y=y,
y_dict=y_dict,
status=status)
solution = {'the_problem': lp, 'the_solution': the_solution}
return solution
def _optimize_glpk(cobra_model, new_objective=None, objective_sense='maximize',
min_norm=0, the_problem=None,
tolerance_optimality=1e-6, tolerance_feasibility=1e-6, tolerance_integer=1e-9,
error_reporting=None, print_solver_time=False,
lp_method=1, quadratic_component=None,
reuse_basis=True,
#Not implemented
tolerance_barrier=None, lp_parallel=None,
copy_problem=None, relax_b=None,update_problem_reaction_bounds=True):
"""Uses the GLPK (www.gnu.org/software/glpk/) optimizer via pyglpk
(http://www.tfinley.net/software/pyglpk/release.html) to perform an optimization
on cobra_model for the objective_coefficients in cobra_model._objective_coefficients
based on the objective sense.
cobra_model: A cobra.Model object
new_objective: Reaction, String, or Integer referring to a reaction in
cobra_model.reactions to set as the objective. Currently, only supports single
objective coeffients. Will expand to include mixed objectives.
objective_sense: 'maximize' or 'minimize'
min_norm: not implemented
the_problem: None or a problem object for the specific solver that can be used to hot
start the next solution.
tolerance_optimality: Solver tolerance for optimality.
tolerance_feasibility: Solver tolerance for feasibility.
error_reporting: None or True to disable or enable printing errors encountered
when trying to find the optimal solution.
print_solver_time: False or True. Indicates if the time to calculate the solution
should be displayed.
quadratic_component: None. GLPK cannot solve quadratic programs at the moment.
reuse_basis: Boolean. If True and the_problem is a model object for the solver,
attempt to hot start the solution. Currently, only True is available for GLPK
update_problem_reaction_bounds: Boolean. Set to True if you're providing the_problem
and you've modified reaction bounds on your cobra_model since creating the_problem. Only
necessary for CPLEX
lp.simplex() with Salmonella model:
cold start: 0.42 seconds
hot start: 0.0013 seconds
"""
from numpy import zeros, array, nan
#TODO: Speed up problem creation
if hasattr(quadratic_component, 'todok'):
raise Exception('GLPK cannot solve quadratic programs please '+\
'try using the gurobi or cplex solvers')
from glpk import LPX
from cobra.flux_analysis.objective import update_objective
from cobra.solvers.legacy import status_dict, variable_kind_dict
status_dict = eval(status_dict['glpk'])
variable_kind_dict = eval(variable_kind_dict['glpk'])
if new_objective and new_objective != 'update problem':
update_objective(cobra_model, new_objective)
#Faster to use these dicts than index lists
index_to_metabolite = dict(zip(range(len(cobra_model.metabolites)),
cobra_model.metabolites))
index_to_reaction = dict(zip(range(len(cobra_model.reactions)),
cobra_model.reactions))
reaction_to_index = dict(zip(index_to_reaction.values(),
index_to_reaction.keys()))
if the_problem == None or the_problem in ['return', 'setup'] or \
not isinstance(the_problem, LPX):
lp = LPX() # Create empty problem instance
lp.name = 'cobra' # Assign symbolic name to problem
lp.rows.add(len(cobra_model.metabolites))
lp.cols.add(len(cobra_model.reactions))
linear_constraints = []
for r in lp.rows:
the_metabolite = index_to_metabolite[r.index]
r.name = the_metabolite.id
b = float(the_metabolite._bound)
c = the_metabolite._constraint_sense
if c == 'E':
r.bounds = b, b # Set metabolite to steady state levels
elif c == 'L':
r.bounds = None, b
elif c == 'G':
r.bounds = b, None
#Add in the linear constraints
for the_reaction in the_metabolite._reaction:
reaction_index = reaction_to_index[the_reaction]
the_coefficient = the_reaction._metabolites[the_metabolite]
linear_constraints.append((r.index, reaction_index,
the_coefficient))
#Need to assign lp.matrix after constructing the whole list
lp.matrix = linear_constraints
objective_coefficients = []
for c in lp.cols:
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
the_reaction = index_to_reaction[c.index]
c.kind = variable_kind_dict[the_reaction.variable_kind]
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(float(the_reaction.objective_coefficient))
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
else:
lp = the_problem
#BUG with changing / unchanging the basis
if new_objective is not None:
objective_coefficients = []
for c in lp.cols: # Iterate over all rows
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
objective_coefficients.append(float(the_reaction.objective_coefficient))
c.kind = variable_kind_dict[the_reaction.variable_kind]
#Add the new objective coefficients to the problem
lp.obj[:] = objective_coefficients
else:
for c in lp.cols: # Iterate over all rows
the_reaction = index_to_reaction[c.index]
c.name = the_reaction.id
c.bounds = the_reaction.lower_bound, the_reaction.upper_bound
c.kind = variable_kind_dict[the_reaction.variable_kind]
if objective_sense.lower() == 'maximize':
lp.obj.maximize = True # Set this as a maximization problem
else:
lp.obj.maximize = False
if the_problem == 'setup':
return lp
if print_solver_time:
start_time = time()
the_methods = [1, 2, 3]
if lp_method in the_methods:
the_methods.remove(lp_method)
else:
lp_method = 1
if not isinstance(the_problem, LPX):
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method)
# Solve this LP or MIP with the simplex (depending on if integer variables exist). Takes about 0.35 s without hot start
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
for lp_method in the_methods:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method)
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
break
else:
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method, tm_lim=100) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method, tm_lim=100)
#If the solver takes more than 0.1 s with a hot start it is likely stuck
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
if lp.kind == int:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method) # we first have to solve the LP?
lp.integer(tol_int=tolerance_integer)
else:
for lp_method in the_methods:
lp.simplex(tol_bnd=tolerance_optimality, tol_dj=tolerance_optimality, meth=lp_method)
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
break
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp = optimize_glpk(cobra_model, new_objective=new_objective,
objective_sense=objective_sense,
min_norm=min_norm, the_problem=None,
print_solver_time=print_solver_time,
tolerance_optimality=tolerance_optimality,
tolerance_feasibility=tolerance_feasibility)['the_problem']
if lp.status == 'opt':
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status != 'optimal':
lp.simplex(tol_bnd=tolerance_optimality, presolve=True, tm_lim=5000)
if lp.kind == int:
lp.integer(tol_int=tolerance_integer)
if print_solver_time:
print 'simplex time: %f'%(time() - start_time)
x = []
y = []
x_dict = {}
y_dict = {}
if lp.status in status_dict:
status = status_dict[lp.status]
else:
status = 'failed'
if status == 'optimal':
objective_value = lp.obj.value
[(x.append(float(c.primal)),
x_dict.update({c.name:c.primal}))
for c in lp.cols]
if lp.kind == float:
#return the duals as well as the primals for LPs
[(y.append(float(c.dual)),
y_dict.update({c.name:c.dual}))
for c in lp.rows]
else:
#MIPs don't have duals
y = y_dict = None
x = array(x)
else:
x = y = x_dict = y_dict = objective_value = None
if error_reporting:
print 'glpk failed: %s'%lp.status
the_solution = Solution(objective_value, x=x, x_dict=x_dict,
y=y, y_dict=y_dict,
status=status)
solution = {'the_problem': lp, 'the_solution': the_solution}
return solution
lp.name = 'foobartendr'
lp.obj.maximize = True
# append 3 rows
row_names = ["ingrednt", "bartendr", "delivery"]
lp.rows.add(len(row_names))
for r in lp.rows:
r.name = row_names[r.index]
lp.rows[0].bounds = None, 100.0
lp.rows[1].bounds = None, 600.0
lp.rows[2].bounds = None, 150.0
# append 3 cols, named x0, x1, x2
lp.cols.add(3)
for c in lp.cols:
c.name = 'x%d' % c.index
c.bounds = 0.0, None
# set the objective coefficients and
# non-zero entries of the constraint matrix
lp.obj[:] = [ 5.0, 3.0, 2.0 ]
lp.matrix = [ 1.0, 1.0, 3.0, 10.0, 4.0, 5.0, 1.0, 1.0, 3.0 ]
# report the objective function value and structural variables
lp.simplex(msg_lev=LPX.MSG_ALL)
print 'Z = %g;' % lp.obj.value,
print '; '.join('%s = %g' % (c.name, c.primal) for c in lp.cols)