为什么我的MIP求解器不采用“ NA”值？

Question

I have the below solver and it works perfectly if I replace the 'NA' values with integers in the cost array and take out the if statement checking if the value is 'NA' but throws a key error otherwise.

I have been stuck on this for hours and I know it is very simple but just can't get it!

I am also new to Google OR-Tools and Optimization so would love to know if I am using the right tool/solver or is there a better/ more efficient tool.

def main():
  solver = pywraplp.Solver('SolveAssignmentProblemMIP',
                           pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)

  cost = [[15.25, 18.50, 'NA', 17.25],
          [18.50, 19.50, 26.50, 21.00],
          [12.50, 'NA', 'NA', 'NA'],
          ['NA', 'NA', 23.50, 'NA'],
          ['NA', 'NA', 'NA', 16.50]
         ]


  num_workers = len(cost)
  num_tasks = len(cost[1])

  x = {}

  for i in range(0, num_workers):
    for j in range(0, num_tasks):
      if cost[i][j] != 'NA':
        x[i, j] = solver.BoolVar('x[%i,%i]' % (i, j))

  # Objective
  solver.Minimize(solver.Sum([cost[i][j] *  x[i,j] for i in range(num_workers)
                                                  for j in range(num_tasks)]))

  # Constraints

  # Each worker is assigned to at most 1 task.

  for i in range(num_workers):
    solver.Add(solver.Sum([x[i, j] for j in range(num_tasks)]) <= 1)

  # Each task is assigned to exactly one worker.

  for j in range(num_tasks):
    solver.Add(solver.Sum([x[i, j] for i in range(num_workers)]) == 1)

  sol = solver.Solve()

  print('Total cost = ', solver.Objective().Value())
  print()
  for i in range(num_workers):
    for j in range(num_tasks):
      if x[i, j].solution_value() > 0:
        print('Vessel %d assigned to Voyage %d.  Cost = %d' % (
              i,
              j,
              cost[i][j]))

  print()
  print("Time = ", solver.WallTime(), " milliseconds")
if __name__ == '__main__':
  main()

KeyError                                  Traceback (most recent call last)
<ipython-input-52-2f567281d1e6> in <module>()
     56   print("Time = ", solver.WallTime(), " milliseconds")
     57 if __name__ == '__main__':
---> 58   main()

1 frames
<ipython-input-52-2f567281d1e6> in main()
     26 
     27   # Objective
---> 28   solver.Minimize(solver.Sum([cost[i][j] *  x[i,j] for i in range(num_workers)
     29                                                   for j in range(num_tasks)]))
     30 

<ipython-input-52-2f567281d1e6> in <listcomp>(.0)
     27   # Objective
     28   solver.Minimize(solver.Sum([cost[i][j] *  x[i,j] for i in range(num_workers)
---> 29                                                   for j in range(num_tasks)]))
     30 
     31   # Constraints

KeyError: (0, 2)

Answer 1

You only generate variables x[i,j] where cost[i][j] is not NA. So you need to add protection everywhere. In your objective:

solver.Minimize(solver.Sum([cost[i][j] *  x[i,j] for i in range(num_workers)
                                              for j in range(num_tasks)]))

you run over all i,j. Instead you should run only over i,j where cost[i][j] is not NA. Eg

solver.Minimize(solver.Sum([cost[i][j] *  x[i,j] for i in range(num_workers)
                                              for j in range(num_tasks) 
                                              if cost[i][j] != 'NA']))