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from StringIO import StringIO
from collections import defaultdict
try:
import cplex
from itertools import izip
from tempfile import NamedTemporaryFile as TmpFile
cplex_available = True
except ImportError:
cplex_available = False
# Constraint format: tuple of ( vector, value),
# where vector is a list of (coefficient, variable_name) pairs.
def write_cplex_terms(file, vector):
for (c, v) in vector:
if c < 0:
file.write("- %s %s " % (-c, v))
else:
file.write("+ %s %s " % (c, v))
def write_cplex_sum(file, sum, per_line=None):
if len(sum) == 0:
file.write("0")
return
file.write("%s %s " % sum[0])
if per_line is None:
write_cplex_terms(file, sum[1:])
else:
write_cplex_terms(file, sum[1:per_line])
for i in xrange(per_line, len(sum), per_line):
file.write('\n ')
write_cplex_terms(file, sum[i:i+per_line])
def filter_vars(removed, sum):
return [(c, v) for (c, v) in sum if not v in removed]
def apply_prefix(vector, prefix):
"Prepend prefix to each variable name in vector."
return [(coeff, prefix + '_' + var) for (coeff, var) in vector]
class Solution(defaultdict):
def __init__(self):
super(Solution, self).__init__(int)
def evaluate(self, vector):
value = 0
for (coeff, variable) in vector:
if variable in self:
value += coeff * self[variable]
return value
def __call__(self, vector):
return self.evaluate(vector)
class LinearProgram(object):
def __init__(self):
self.equalities = []
self.inequalities = []
self.objective_function = None
self.goal = 'Maximize'
self.name = 'OPT'
## Data model
def add_inequality(self, vector, upper_bound):
self.inequalities.append((vector, upper_bound))
def add_equality(self, vector, value):
self.equalities.append((vector, value))
def set_objective(self, objective_function):
self.objective_function = objective_function
def apply_variable_prefix(self, prefix):
self.inequalities = [(apply_prefix(vector, prefix), upper_bound)
for (vector, upper_bound) in self.inequalities]
self.equalities = [(apply_prefix(vector, prefix), bound)
for (vector, bound) in self.equalities]
self.objective_function = apply_prefix(self.objective_function, prefix)
def merge(self, other_LP):
assert(other_LP.goal == self.goal)
for ineq in other_LP.inequalities:
self.inequalities.append(ineq)
for eq in other_LP.equalities:
self.equalities.append(eq)
if self.objective_function == None:
self.objective_function = []
for term in other_LP.objective_function:
self.objective_function.append(term)
## Convenience constraint DSL
def equality(self, *args, **kargs):
"""Specify equality constraint as:
equality(coeff1, var1, coeff2, var2, ..., equal_to=value)
"""
assert len(args) % 2 == 0 # num coefficients == num variables?
assert len(kargs) == 1 and 'equal_to' in kargs # constraint?
vector = zip(args[0::2], args[1::2])
self.add_equality(vector, kargs['equal_to'])
def inequality(self, *args, **kargs):
"""Specify inequality constraint as:
inequality(coeff1, var1, coeff2, var2, ..., at_most=value)
"""
assert len(args) % 2 == 0 # num coefficients == num variables?
assert len(kargs) == 1 and 'at_most' in kargs # constraint?
vector = zip(args[0::2], args[1::2])
self.add_inequality(vector, kargs['at_most'])
def objective(self, *args):
"""Specify objective function as:
objective(coeff1, var1, coeff2, var2, ...)
"""
assert len(args) % 2 == 0 # num coefficients == num variables?
vector = zip(args[0::2], args[1::2])
self.set_objective(vector)
## Helper for model conversion
def write_cplex_lp_format(self, file):
file.write('%s\n' % self.goal)
write_cplex_sum(file, self.objective_function, per_line=7)
file.write('\nSubject To\n')
for vector, value in self.equalities:
write_cplex_sum(file, vector, per_line=7)
file.write(' = %f\n' % value)
for vector, value in self.inequalities:
write_cplex_sum(file, vector, per_line=7)
file.write(' <= %f\n' % value)
file.write('End\n')
file.flush()
def kill_non_positive_vars(self):
"""Removes all variables that are forced to <= 0.
Assumes that all coefficients are positive.
"""
# find pointless variables
killed = set()
for vector, value in self.equalities:
if value <= 0:
for coeff, var in vector:
killed.add(var)
for vector, value in self.inequalities:
if value <= 0:
for coeff, var in vector:
killed.add(var)
# remove pointless variables
self.objective_function = filter_vars(killed, self.objective_function)
if 'local_objective' in self.__dict__:
self.local_objective = filter_vars(killed, self.local_objective)
self.equalities = [(filter_vars(killed, vect), bound) for
(vect, bound) in self.equalities if bound > 0]
self.equalities = [(vect, bound) for (vect, bound) in self.equalities if vect]
self.inequalities = [(filter_vars(killed, vect), bound) for
(vect, bound) in self.inequalities if bound > 0]
self.inequalities = [(vect, bound) for (vect, bound) in self.inequalities if vect]
def __str__(self):
f = StringIO()
self.write_cplex_lp_format(f)
return f.getvalue()
## Conditional solver integration.
if cplex_available:
def get_cplex_model(self, model=None):
if model is None:
model = cplex.Cplex()
# load problem via file to avoid API overheads
tmp = TmpFile()
self.write_cplex_lp_format(tmp)
model.read(tmp.name)
model.set_results_stream(None)
del tmp
return model
def solve_with_cplex(self):
solution = Solution()
# If the objective is empty (e.g., after killing
# all zero-constrained variables), then we automatically have
# a trivial solution.
if len(self.objective_function) == 0:
return solution
# Let CPLEX do the job.
model = self.get_cplex_model()
model.solve()
# Extract the variables that we care about.
variables = [var for (coeff, var) in self.objective_function]
values = model.solution.get_values(variables)
for (var, val) in izip(variables, values):
solution[var] = val
return solution
def solve(self):
if cplex_available:
return self.solve_with_cplex()
# Add additional solvers here...
else:
assert False # No solver available!
def example():
# simple example of the convenience API
x = LinearProgram()
x.objective(-3, 'x2', 99, 'x1')
x.inequality(10, 'x1', at_most=100)
x.inequality(-9, 'x1', 10, 'x2', at_most=99)
x.equality(10, 'x2', equal_to=0)
print x
x.inequality(0, 'x3', at_most=1)
x.equality(0, 'x10', equal_to=0)
if __name__ == '__main__':
example()
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