How to Define a Constraint for Calculating the Maximum of Two Multi-Dimensional Variables in Gurobi

回答済み

Amir Fayaz Heidari

2023年10月27日 13:48

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Hi team,

 

The max_ function for the 1-dimension variable works. However, I need to add the constraint below:

model.addConstrs(X_3[m,r] == max_( X_1[m,r] , X_2[m,r] ) for m in range(M) for r in range(R))

Where X_1, X_2, and X_3 are multi-dimensional variables. When I run my code, I get the error below:

GurobiError: Invalid data in vars array

How can I consider this type of constraint? I do not want to use binary variables to linearize this constraint. I do not want to replace it with the two constraints below because there are some other challenges regarding my objective function and other constraints.

model.addConstrs(X_3[m,r] >= X_1[m,r] for m in range(M) for r in range(R))

model.addConstrs(X_3[m,r] >= X_2[m,r] for m in range(M) for r in range(R))

 

Also, I cannot write the constraints for each m and r individually because the input parameters M and R are big.

 

What about the constraint below which the variables have different dimensions?

model.addConstrs(X_6[m,r,y,d,h] == min_( X_4[m,r,y,d,h] , X_5[m,r] ) for m in range(M) for r in range(R) for y in range(Y) for d in range(D) for h in range(H))

 

Thanks for your time in advance

関連

• Python

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  Maliheh Aramon

  • Gurobi Staff

  2023年10月28日 01:16

  Hi Amir, 

  It is possible to use the max_() helper function regardless of the variables dimension and there is no need for the variables to have similar dimensions. See the code snippet below:

  import gurobipy as gp
  
  model = gp.Model()
  
  M, R = 5, 4
  x1 = model.addVars(M, R, name="x1")
  x2 = model.addVars(M, R, name="x2")
  x3 = model.addVars(M, R, name="x3")
  
  model.addConstrs((x3[m,r] == gp.max_(x1[m,r], x2[m,r]) for m in range(M) for r in range(R)), name="c_max")

  Could you please post a small working example so that we can reproduce the error you see?

  Best regards,

  Maliheh

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  Amir Fayaz Heidari

  2023年10月28日 02:03

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  Thanks for your response.
  
  Could you please check the code below? It works correctly without the constraint regarding the max function.
  
  " model.addConstrs((con_SCG[m,r] == gp.max_(x_SCG[m,r], min_con_SCG[m,r]) for m in range(M) for r in range(R)), name="c_max") "
  
  However, when I deactivate it (excluded from the optimization problem), I get the error "GurobiError: Invalid data in vars array"
  
  

  import gurobipy as gp
  from gurobipy import *
  import numpy as np

  # Create a new model
  model = Model()

  M = 2
  R = 2
  N = 2

  P_tot = np.zeros((M,R))
  P_tot[0,0] = 5000
  P_tot[0,1] = 2000
  P_tot[1,0] = 3000
  P_tot[1,1] = 1000

  min_con_SCG = np.zeros((M,R))
  min_con_SCG[0,0] = 200
  min_con_SCG[0,1] = 200
  min_con_SCG[1,0] = 300
  min_con_SCG[1,1] = 300

  
  # Define decision variables
  x_SCG = model.addVars(M,R, lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="x_SCG")
  x_ON_SCG = model.addVars(M,R, lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="x_ON_SCG")
  x_act_SCG = model.addVars(M,R, lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="x_act_SCG")
  con_SCG = model.addVars(M,R, lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="con_SCG")
  Total_con_SCG = model.addVars(R, lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="con_RES")

  x_SCG[0,0].ub = 1000
  x_SCG[1,0].ub = 800
  x_SCG[0,1].ub = 500
  x_SCG[1,1].ub = 600

   

  x_RES = model.addVars(N,R, lb=0.0, ub=400, vtype=GRB.CONTINUOUS, name="x_RES")
  con_RES = model.addVars(N,R, lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="con_RES")
  Total_con_RES = model.addVars(R, lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="con_RES")

  
  z = model.addVar(lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="z")

  
  delta_P = model.addVars(R, lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="delta_P")

  
  SSS_1 = model.addVar(lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="SSS_1")
  SSS_2 = model.addVar(lb=0.0, ub=GRB.INFINITY, vtype=GRB.CONTINUOUS, name="SSS_2")

  
  # objective_expr = 10 * x_SCG + 5 * x_act_SCG + 3 * x_RES + ( SSS_1 + SSS_2 )*1000 + con_SCG

  objective_expr = gp.quicksum( gp.quicksum( 10 * x_SCG[m,r] for r in range(R) ) for m in range(M) ) + gp.quicksum( gp.quicksum( 5 * x_act_SCG[m,r] for r in range(R) ) for m in range(M) ) + gp.quicksum( gp.quicksum( 3 * x_RES[n,r] for r in range(R) ) for n in range(N) ) 

  
  model.addConstr(gp.quicksum( x_SCG[m,0] for m in range(M) )  + gp.quicksum( x_RES[n,0] for n in range(N) )  == 2500 , name="Demand")
  model.addConstr(gp.quicksum( x_SCG[m,1] for m in range(M) )  + gp.quicksum( x_RES[n,1] for n in range(N) )  == 500 , name="Demand")

  
  model.addConstrs(x_SCG[m,r] <= x_ON_SCG[m,r] for m in range(M) for r in range(R))
  model.addConstrs(x_ON_SCG[m,r] <= x_act_SCG[m,r] for m in range(M) for r in range(R))
  model.addConstrs(x_act_SCG[m,r] <= P_tot[m,r] for m in range(M) for r in range(R))

   

  model.addConstrs((con_SCG[m,r] == gp.max_(x_SCG[m,r], min_con_SCG[m,r]) for m in range(M) for r in range(R)), name="c_max")

   

  model.addConstrs(Total_con_SCG[r] == max_( con_SCG[0,r] , con_SCG[1,r]) for r in range(R))

  # model.addConstr(con_SCG <= x_SCG , name="Constraint555")
  # model.addConstr(con_SCG <= 200 , name="Constraint555")

  # model.addConstr(con_SCG >= x_SCG - SSS_1 - SSS_2 , name="Constraint3")
  # model.addConstr(con_SCG >= 200 - SSS_1 - SSS_2 , name="Constraint4")
  # model.addConstr(SSS_1 >= x_SCG - 200, name="Constraint5")
  # model.addConstr(SSS_2 >= 200 - x_SCG , name="Constraint6")

  
  model.addConstrs(con_RES[n,r] == 0.25 * x_RES[n,r] for n in range(N) for r in range(R))
  model.addConstrs(Total_con_RES[r] == max_( con_RES[0,r] , con_RES[1,r]) for r in range(R))

  
  model.addConstrs(delta_P[r] == max_( Total_con_SCG[r] , Total_con_RES[r]) for r in range(R))

  
  # model.addConstr(delta_P >= con_SCG , name="Constraint555")
  # model.addConstr(delta_P[r] >= con_RES[n,r] for n in range(N) for r in range(R) )
  model.addConstrs(3 * gp.quicksum( x_act_SCG[m,r] for m in range(M) ) >= 50 * delta_P[r] for r in range(R))

  
  model.setObjective(objective_expr, GRB.MINIMIZE)
  model.optimize()

  # Access the values of decision variables
  x_SCG_values = model.getAttr('X', x_SCG)
  x_ON_SCG_values = model.getAttr('X', x_ON_SCG)
  x_act_SCG_values = model.getAttr('X', x_act_SCG)
  con_SCG_values = model.getAttr('X', con_SCG)

  
  x_RES_values = model.getAttr('X', x_RES)
  con_RES_values = model.getAttr('X', con_RES)
  Total_con_RES_values = model.getAttr('X', Total_con_RES)
  Total_con_SCG_values = model.getAttr('X', Total_con_SCG)

  
  z_value = z.X
  delta_P_values = model.getAttr('X', delta_P)

  
  SSS_1_value = SSS_1.X
  SSS_2_value = SSS_2.X

  # You can access the values of variables, one by one, like the examples above.

  # For example, to print the values of x_SCG for all indices:
  for m in range(M):
      for r in range(R):
          print(f'x_SCG[{m}, {r}] = {x_SCG_values[m, r]}')
          print(f'x_ON_SCG[{m}, {r}] = {x_ON_SCG_values[m, r]}')
          print(f'x_act_SCG[{m}, {r}] = {x_act_SCG_values[m, r]}')
          print(f'con_SCG[{m}, {r}] = {con_SCG_values[m, r]}')
          print()

  for n in range(N):
      for r in range(R):
          print(f'x_RES[{n}, {r}] = {x_RES_values[n, r]}')
          print(f'con_RES[{n}, {r}] = {con_RES_values[n, r]}')
          print()

  
  for r in range(R):
      print(f'Total_con_SCG[{r}] = {Total_con_SCG_values[r]}')
      print(f'Total_con_RES[{r}] = {Total_con_RES_values[r]}')
      print(f'delta_P[{r}] = {delta_P_values[r]}')
      print()
         

  
  # Close the model
  model.close()
  
  In my main code, I want to add these constraints:
  
  
  SCG_type_con[m,r,y,d,h] == min ( SCG_dis[m,r,y,d,h] , x_1[m,r] ) ∀ m, r, y, d, h

  
  SCG_con[r,y,d,h] == max ( SCG_type_con[m,r,y,d,h] ) over all m and ∀ r, y, d, h
  ## For example: SCG_con[r,y,d,h] == max ( SCG_type_con[0,r,y,d,h] , SCG_type_con[1,r,y,d,h] , SCG_type_con[2,r,y,d,h] )
  ## However, I want to define generally not manually like the above example

  
  RES_con[r,y,d,h] == max ( RES_type_con[n,r,y,d,h] ) over all n and ∀ r, y, d, h

  
  delta_P[r,y,d,h] == max ( SCG_con[r,y,d,h] , RES_con[r,y,d,h] ) ∀ r, y, d, h

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  Maliheh Aramon

  • Gurobi Staff

  2023年10月30日 18:26

  Hi, 

  In the constraint below:

  model.addConstrs(
       (
           con_SCG[m,r] == gp.max_(x_SCG[m,r], min_con_SCG[m,r]) 
           for m in range(M) 
           for r in range(R)
       ), 
       name="c_max",
  )

  The \(\texttt{min_con_SCG[m,r]}\) is a constant and not a Gurobi variable. According to the Gurobi documentation, the signature of the max_() function is: 

  max_(*args, constant=None )

  Therefore, your constraint needs to change to:

  model.addConstrs(
       (
           con_SCG[m, r] ==gp.max_(x_SCG[m, r], constant=min_con_SCG[m, r])
           for m in range(M)
           for r in range(R)
       ),
       name="c_max",
  )

  Best regards,
  Maliheh

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  Amir Fayaz Heidari

  2023年10月30日 19:25

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  Thanks Maliheh.

  0

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