How to define a hybrid variable or define two separate set?

回答済み

Lilly Yang

2021年03月31日 11:06 編集済み

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I would like to convert the mathematical formulation below to Python code.

 

Below is what I have for my code. I think the main issue is caused by the wrong use of delta_ij and delta_oj; however, I don't know how to create a hybrid decision variable instead or define the decision variable based on conditions.

m = gp.Model()

delta_0j = m.addVars(cartesian_0j, obj=cost,lb = 0, ub=2, vtype=GRB.INTEGER, name='delta_0j')

delta_ij = m.addVars(cartesian_ij, obj=cost, vtype=GRB.BINARY, name='delta_ij')

delta_ji = m.addVars(cartesian_ji, obj=cost, vtype=GRB.BINARY, name='delta_ji')

#1.2

for i in Vcomp_index:

m.addConstr((gp.quicksum(delta_ij[(i, j)] for j in V_index if i<j)

+ (gp.quicksum(delta_ij[(j, i)] for j in V_index if i>j))==2),

name = 'degree constraint')

#1.3

for S in Gamma:

m.addConstr((gp.quicksum(delta_ij[(i, j)] for i in S for j in S_comp(S, V_index) if i<j)

+ (gp.quicksum(delta_ij[(i, j)] for i in S_comp(S, V_index) for j in S if i<j)) >= 2*r[S]), name='capacity constraint')

 

#1.4

for S in Gamma:

m.addConstr((gp.quicksum(delta_ij[i, j] for i in S for j in S if i<j)<=len(S) - r[S]), name='combined constraint')

#1.5

m.addConstr(((gp.quicksum(delta_0j[(0, j)]) for j in Vcomp_index) == 2*M), name='depot flow')

# objective function

m.setObjective(delta_ij.prod(cost, GRB.MINIMIZE))

m.update()

m.optimize()

0

• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 02:57 編集済み

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
• 

  Eli Towle

  • Gurobi Staff

  2021年03月31日 21:16 編集済み

  It would be easier to define the variables with a single call to Model.addVars(), then modify the upper bounds afterwards. You can modify the upper bounds by individually setting the UB attribute of each Var object, or by using Model.setAttr() to modify multiple variable bounds at once. E.g., with this code:

  import gurobipy as gp
  from gurobipy import GRB
  
  # Dummy data
  V = list(range(4))
  E = [(i, j) for i in V for j in V if i != j]
  
  m = gp.Model()
  
  # Create all variables as integer with domain [0, 1]
  delta = m.addVars(E, vtype=GRB.INTEGER, ub=1, name='delta')
  
  # Modify upper bounds of variables for edges emanating from node 0
  m.setAttr('UB', delta.select(0, '*'), 2)
  
  # Display bounds
  m.update()
  for v in delta.values():
      print(f'{v.VarName}.UB = {v.UB}')

  we only increase the upper bounds of variables corresponding to edges emanating from node 0:

  delta[0,1].UB = 2.0
  delta[0,2].UB = 2.0
  delta[0,3].UB = 2.0
  delta[1,0].UB = 1.0
  delta[1,2].UB = 1.0
  delta[1,3].UB = 1.0
  delta[2,0].UB = 1.0
  delta[2,1].UB = 1.0
  delta[2,3].UB = 1.0
  delta[3,0].UB = 1.0
  delta[3,1].UB = 1.0
  delta[3,2].UB = 1.0

  0

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