Indexing over specific sets depending on index of variable

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Johanna Skåntorp

June 13, 2023 07:48

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Hi,
I have a set of indices (U[v]) tied to the index of my decision-variable b[v,t] but I can't seem to make it work. A small version of the problem reads as follows:

T = [7,8,9] 
V = [0,1,2,3] 
U = [[0,1,2], [1,2], [2,3,4] [3,4]] #set of indices

b[t,v] is a set of tuples: [(t,i) for t in T_idx for i in Vp_idx]

The constraints will depend on the set of indices, for example v=0:
(b[t,0] <= sum(b[t+1, j] for j in U[0]) ) for all t  in T[0:-1]
i.e. since U[0] = [0,1,2] i want:
b[7,0] <= b[8, 0] + b[8,1] + b[8,2], and
b[8,0] <= b[9,0] + b[9,1] + b[9,2],

for all v in V of course.

***

I've tried a couple different ways:

1:

for v in V:
    m.addConstrs((gp.quicksum(b[t+1,j] for j in U[v]) >= b[t,v] for t in T[0:-1]), "test")

 2:

for v in V:
    for t in T:
        m.addConstr(help_U[t,v] == sum(b[t,j] for j in U[v]))
m.addConstrs((help_U[t+1,v] >= b[t,v] for v in V for t in T[0:-1]), "test")   

3.

m.addConstrs((gp.quicksum(b[t+1,j] for j in U[v]) >= b[t,v] for t in T[0:-1] for v in V, "test")

(With reservation that I might have made some typos when trying to generalize this somewhat)

Invariably I get KeyError: (1,107)

Any help would be appreciated!

 

 

0

• 

  Jaromił Najman

  • Gurobi Staff

  June 13, 2023 11:36

  Hi Johanna,

  I think something like the following should work

  import gurobipy as gp
  
  m = gp.Model()
  
  T = [7,8,9] 
  V = [0,1,2,3] 
  U = [[0,1,2], [1,2], [2,3,4], [3,4]] #set of indices
  
  b = m.addVars(T,5,name="b") # here 5 is set as second dimension because the indices in U go up to 4
  
  for v in V:
      L = U[v] # get index list U[v]
      for t in T[:-1]: # don't use last index in T to avoid key errors
          m.addConstr(b[t,v] <= gp.quicksum(b[t+1, l] for l in L), name="con_v%d_t%d"%(v,t))
  
  m.write("myLP.lp") # write human readable LP file to analyze

  Is this what you were looking for? You can have a look at the generated \(\texttt{myLP.lp}\) file to check whether the constraints look as they should.

  Best regards, 
  Jaromił

  0

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