Question about converting a matrix to indicator matrix in gurobi

Answered

LUYANG ZHANG

December 05, 2022 09:47

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Hi, suppose I have a matrix/vector containing decision variable x, such as v =  [x_1, 2*x_2, x_3+x_4,...], now I want to convert it into a binary matrix such as k_i = 0 if v_i = 0, k_i = 1 if v_i >0,... May I ask if there's any way to do it?

FYI, I use Python API, so may I ask if I can use numpy here like: https://stackoverflow.com/questions/26551825/converting-an-array-to-positive-indicator? If not, then how to write it in Gurobi? Thanks a lot!

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  Simon Bowly

  • Gurobi Staff

  December 08, 2022 22:53

  It's not possible to do this via numpy's type casting functions; you need to construct constraints to specify the relationship between v and k. I'm assuming here that k_i are binary variables in the model, as opposed to a post-processing step where the values of v_i are already known.

  You can express the necessary constraints using either a big-M formulation:

  model.addConstr(v[i] <= M*k[i])

  where M is an upper bound on the value of v_i, or using indicator constraints:

  model.addConstr((k[i] == 0) >> (v[i] == 0))

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