Is it possible to find all integer solutions? - linear-programming

Question

I wanna get all integer solutions in a limited time, is it possible?

Answer 1

This is a linear, integer constraint satisfaction problem, which can be solved efficiently by OR Tools' CP-SAT. I've modified their example to solve your problem in Python:
from ortools.sat.python import cp_model
class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):
"""Print intermediate solutions."""
def __init__(self, variables):
cp_model.CpSolverSolutionCallback.__init__(self)
self.__variables = variables
self.__solution_count = 0
def on_solution_callback(self):
self.__solution_count += 1
for v in self.__variables:
print('%s=%i' % (v, self.Value(v)), end=' ')
print()
def solution_count(self):
return self.__solution_count
def SearchForAllSolutionsSampleSat():
"""Showcases calling the solver to search for all solutions."""
# Creates the model.
model = cp_model.CpModel()
p = [1, 2, 3, 4]
ceq = 30
cgeq = 2
N = len(p)
# Creates the variables
x = [model.NewIntVar(0, 100, f'x{i}') for i in range(N)]
# Create the constraints.
model.Add(sum([xi*pi for xi, pi in zip(x, p)]) == ceq)
model.Add(sum(x) >= cgeq)
# Create a solver and solve.
solver = cp_model.CpSolver()
solution_printer = VarArraySolutionPrinter(x)
status = solver.SearchForAllSolutions(model, solution_printer)
print('Status = %s' % solver.StatusName(status))
print('Number of solutions found: %i' % solution_printer.solution_count())
SearchForAllSolutionsSampleSat()