C1P/TU check in Gurobi

回答済み

Carl Baier

• 2025年01月28日 09:23

Hello, I wanted to ask if there is a possibility with Gurobi to check if the constraint matrix A has Total Unimodular (TU) or the Consecutive ones property (C1P). Thank you!

0

• 

  Bot Marley (with AI contributions)

  • 2025年01月29日 06:12

  

  

  Hi Carl,

  In Gurobi, there isn't a built-in function specifically designed to check if a constraint matrix A has Total Unimodularity (TU) or the Consecutive Ones Property (C1P). However, you can write custom code to verify these properties based on their definitions.

  Total Unimodularity (TU)

  A matrix is said to be Total Unimodular (TU) if every square submatrix of the matrix has a determinant of 0, +1, or -1. For checking TU, you would need to examine all square submatrices of A, calculate their determinants, and verify if they are within this set.

  You can approach this problem by:

  1. Extracting all square submatrices.
  2. Calculating the determinant of each submatrix.
  3. Checking if all determinants are 0, +1, or -1.

  This can be done using Python libraries like numpy or scipy to extract submatrices and compute their determinants.

  Consecutive Ones Property (C1P)

  A binary matrix has the Consecutive Ones Property (C1P) if, for each row, the 1’s in the row appear consecutively. To check this property, you can loop through each row of the matrix and verify that the 1’s are consecutive (i.e., there are no isolated 1's in the row).

  Here’s a high-level outline of how to implement both checks:

  Checking for Total Unimodularity:

  import numpy as np
  from itertools import combinations
  
  def is_unimodular(matrix):
      rows, cols = matrix.shape
      for r in range(1, min(rows, cols) + 1):  # Checking submatrices of size r
          for rows_comb in combinations(range(rows), r):
              for cols_comb in combinations(range(cols), r):
                  submatrix = matrix[np.array(rows_comb), np.array(cols_comb)]
                  if np.linalg.det(submatrix) not in [0, 1, -1]:
                      return False
      return True
  

  Checking for Consecutive Ones Property:

  def has_consecutive_ones(matrix):
      for row in matrix:
          ones_indices = np.where(row == 1)[0]
          if len(ones_indices) > 1 and not np.all(np.diff(ones_indices) == 1):
              return False
      return True
  

  You can get your constraint matrix in gurobipy using model.getA() then use these functions on your matrix to check if it has the TU property or C1P.

  - Bot
  Give Gurobot a try!

  0

サインインしてコメントを残してください。