Convert a LP in a form of matrix

I try to convert a LP in a form of matrix, i.e., Ax <=b. The code is shown below. However, the optimal solution value is different. What dis I miss?

import gurobipy as gp
from gurobipy import GRB
import numpy as np

m=gp.read('expPP.mps')

m.optimize()

with result

Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)

CPU model: Intel(R) Core(TM) i7-10750H CPU @ 2.60GHz, instruction set [SSE2|AVX|AVX2]
Thread count: 6 physical cores, 6 logical processors, using up to 6 threads

Optimize a model with 2992 rows, 2992 columns and 7976 nonzeros
Model fingerprint: 0x364e7d38
Coefficient statistics:
  Matrix range     [1e+00, 1e+02]
  Objective range  [1e+00, 2e+01]
  Bounds range     [1e+00, 5e+03]
  RHS range        [1e+00, 9e+01]
Presolve removed 1995 rows and 1001 columns
Presolve time: 0.01s
Presolved: 997 rows, 1992 columns, 2988 nonzeros

Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0    5.6468667e+02   7.066250e+02   0.000000e+00      0s
    1215   -2.8126036e+04   0.000000e+00   0.000000e+00      0s

Solved in 1215 iterations and 0.01 seconds (0.01 work units)
Optimal objective -2.812603633e+04

I extract the A, b, and c

A = m.getA()
rhs = m.getAttr("RHS",m.getConstrs())
obj = m.getAttr("Obj",m.getVars())

define a new model with these coefficients

mA = gp.Model()
x = mA.addMVar(shape=A.shape[1], lb=0, vtype=GRB.CONTINUOUS)
mA.addConstr(A @ x <= np.array(rhs))
mA.setObjective(np.array(obj) @ x, GRB.MAXIMIZE)
mA.optimize()

but the result is different

Gurobi Optimizer version 10.0.1 build v10.0.1rc0 (linux64)

CPU model: Intel(R) Core(TM) i7-10750H CPU @ 2.60GHz, instruction set [SSE2|AVX|AVX2]
Thread count: 6 physical cores, 6 logical processors, using up to 6 threads

Optimize a model with 2992 rows, 2992 columns and 7976 nonzeros
Model fingerprint: 0xa6385b94
Coefficient statistics:
  Matrix range     [1e+00, 1e+02]
  Objective range  [1e+00, 2e+01]
  Bounds range     [0e+00, 0e+00]
  RHS range        [1e+00, 9e+01]
Presolve removed 2992 rows and 2992 columns
Presolve time: 0.01s
Presolve: All rows and columns removed
Iteration    Objective       Primal Inf.    Dual Inf.      Time
       0   -5.3220000e+03   0.000000e+00   0.000000e+00      0s

Solved in 0 iterations and 0.01 seconds (0.00 work units)
Optimal objective -5.322000000e+03

Jaromił Najman

Gurobi Staff

November 06, 2023 09:09

From the coefficient statistics you can see

Coefficient statistics:
  Matrix range     [1e+00, 1e+02]
  Objective range  [1e+00, 2e+01]
  Bounds range     [1e+00, 5e+03]
  RHS range        [1e+00, 9e+01]

Coefficient statistics:
  Matrix range     [1e+00, 1e+02]
  Objective range  [1e+00, 2e+01]
  Bounds range     [0e+00, 0e+00]
  RHS range        [1e+00, 9e+01]

It looks like you need to set variable bounds.

Best regards,
Jaromił

Sen Xue

November 07, 2023 02:54

Thanks a lot. beside, I found that not only the variable bounds is not set, but some row of matrix A and b must be reset according to the corresponding constr sense, the code is

for i in range(len(m.getConstrs())):
    if m.getConstrs()[i].sense == '>':
        A[i,:]=A[i,:]*(-1)
        rhs[i]=rhs[i]*(-1)

I thought that gurobi can automatically give the corresponding matrix Ax<=b, but it is not. By the way, it seems that for constr sense of '=', that part of matrix Ax<=b given by gurobi is correct.

November 07, 2023 07:34

You can make it better by using the addMConstr method. To use it, you have to also extract constraint senses as you did with RHS.

Convert a LP in a form of matrix

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