--- 1 Mathematical Modeling linear programming assignment problem python

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Introduction: In recent prepare for digital to analog and see the assignment problem, with interest, on Baidu to find a lot about the solution assignment problem, it is clear that use the Hungarian algorithm, by hand calculation, all kinds of various blog very detailed, probably you are aware of the specific principles (people can not understand their own Baidu), but the basic algorithm can not be found, it is difficult to verify with the right. Possible in order to save time it (do not want to re-create the wheel, lazy), wanted to look for python Is there any library function can be achieved, to find a lot blog or something, still can not find. 0-1 assignment problem is thinking about programming, linear programming is also used scipy.optimize library functions, angrily, direct look through scipy.optimize official website. Or the official website invincible ah. Ado, overhead matrix look at a sample:

Then the naked eye, then it is simple, the first line [413] to a selected second row, a second row [205] on the selected first row 2, a third row [322] to selected third column 2, and then the cost is 5. Then the solution with a python, then use scipy.optimize.linear_sum_assignment (cost_matrix) function of. Directly attached to the code:

  
  
from scipy.optimize import linear_sum_assignment

cost =np.array([[ 4, 1, 3],[ 2, 0, 5],[ 3, 2, 2]])
row_ind,col_ind=linear_sum_assignment(cost)
Print (row_ind) # row index corresponding to the cost matrix
print (col_ind) OptimalAssignment column index # corresponding to the row index
Print (cost [row_ind, col_ind]) # elements of optimal assignment extraction column index where the index of each row, the array is formed
Print (cost [row_ind, col_ind] .sum ()) # summing array
  
  

Then the output results:

  
  
[0 1 2]
[1 0 2]
[1 2 2]
5
  
  

Indexes start at zero is not to say, or speak out of turn one, the official website is invincible! Officer posted at the cafe then this function https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.linear_sum_assignment.html#scipy.optimize.linear_sum_assignment

the above.

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