I am trying to get all solutions for a Mixed Integer program through ortools. I have two lists x and y of size 4. I want to get all solutions which satisfy sum(x) = 4 * sum(y). I created a function which takes list of past solutions as input and returns next solution. I am able to get only 2 solutions even though there are more. What am I doing wrong here?
I am expecting the following solutions
Solution 1: xs1 = [0,0,0,0], ys1 = [0,0,0,0]
Solution 2: xs2 = [4,0,0,0], ys2 = [1,0,0,0]
Solution 3: xs3 = [0,4,0,0], ys3 = [1,0,0,0]
Solution 4: xs4 = [0,0,4,0], ys4 = [0,0,1,0]
and soon on
from ortools.linear_solver import pywraplp
def opt(xs, ys):
solver = pywraplp.Solver.CreateSolver('SCIP')
infinity = solver.infinity()
# x and y are integer non-negative variables.
n = 4
M = 20
x = [0]* n
y = [0]* n
w = [[0]* n]*len(xs)
δ = [[0]* n]*len(xs)
for i in range(0,n):
x[i] = solver.IntVar(0, 20, 'x'+str(i))
y[i] = solver.IntVar(0, 20, 'y'+str(i))
for j in range(len(xs)):
w[j][i] = solver.IntVar(0, 20, 'zp'+str(j)+ '-' + str(i))
δ[j][i] = solver.IntVar(0, 1, 'δ'+str(j)+ '-' + str(i))
for j in (range(len(xs))):
for i in range(0,n):
solver.Add((w[j][i] - x[i] + xs[j][i]) >=0)
solver.Add((w[j][i] - x[i] + xs[j][i]) <= M*(1-δ[j][i]))
solver.Add((w[j][i] + x[i] - xs[j][i]) >=0)
solver.Add((w[j][i] + x[i] - xs[j][i]) <= M*δ[j][i])
for j in range(len(xs)):
solver.Add(solver.Sum([w[j][i] for i in range(0,n)]) >= 1)
solver.Add(solver.Sum([x[i] for i in range(0, n)]) - 4 * solver.Sum([y[i] for i in range(0, n)]) == 0)
solver.Minimize(solver.Sum([x[i] for i in range(0, n)]))
status = solver.Solve()
if status == pywraplp.Solver.OPTIMAL:
solver_x = [0]*n
solver_y = [0]*n
for i in range(0,n):
solver_x[i] = x[i].solution_value()
solver_y[i] = y[i].solution_value()
return ([solver_x, solver_y, solver.Objective().Value()])
else:
print('No Solution')
return ([[0], [0]], -1)
psx = [[0,0,0,0], [0,4,0,0]]
psy = [[0,0,0,0], [1,0,0,0]]
ns = opt(psx, psy)
print(ns)
Output:
No Solution
([[0], [0]], -1)
Reference:
