Rolling Horizon Approach

Marco Sp

• September 21, 2022 09:01

Hi, 

I am trying to implement a rolling horizon approach and wonder how I can set my solution j to my inital start value of j+1 ? So I have basically 5 different contionus and 5 binary variables. and I each horizon step I want to set the old solutions as start values of the new optimization problem. Any idea how to do so ?

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• 

  Marika Karbstein

  Gurobi Staff

  • September 21, 2022 09:10

  You can use the variable attribute Start to do this.

  See also How do I use MIP starts? and/or MIP starts for explanations.

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  Marco Sp

  • September 21, 2022 11:04

  

  

  

  Hi Marika, 

  thanks for your fast response. Could you maybe give me an example how I do this in python for two dimensional variables ?

  I tried with one variable "energy_consumption" which is dependend on a Period "t" and a device "i"

  I tried different options:

  m.energy_consumption.Start = 0 

  energy_consumption[0, j].Start = 0

  energy_consumption.Start = 0

  but it was not working 

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• 

  Marika Karbstein

  Gurobi Staff

  • September 21, 2022 11:55
  • Edited

  Could you share a minimum reproducible example and the error you are facing?

  It might be that m.update() is missing. 

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• 

  Marco Sp

  • September 22, 2022 07:49
  • Edited

  

  

  

  I have a list of devices "j" and they have to supply energy in every period "i" depending on the energy demand

   

  for j in range(device_list):
    while (x2 <= 35040):  # number of Periods (15 min steps)
    m = gp.Model("milp1)
    m.modelSense = GRB.Minimize
  
    energy_consumption = m.addVars(Period, Number_devices , lb=0, vtype=GRB.CONTINUOUS, name = "Power_c")
    heat_production = m.addVars(Period, Number_devices , lb=0, vtype=GRB.CONTINUOUS, name = "Heat_p")
    dhw_temperature = m.addVars(Period, Number_devices , lb=43, ub = 50, vtype=GRB.CONTINUOUS, name = "dhw_temp")
    ...
    ...
    
    m.addConstrs((dhw_temperature[i,j] = dhw_temperature[i-1,j] - losses + factor * heat_production[i,j] ) for i in range(x1+1, x2) for j Number_devices) 
    m.optimize()
    solution_dhw = m.getAttr('X', dhw_temperature)
    solution_heat_production = m.getAttr('X', heat_production)
    ...
  
   #transfer solution to numpy array
    for i in Periode: 
       heat_production_solution[i][j] = solution_heat_production[i,j]
       ...
     
   x1 = x2 - 96
   if(x2 < (35040 -1500)):
       x2 = x2 +1500
   if (x2 == 35040):
       x2 = 35041
   elif(x2 >= (35040 -1500)):
       x2 = 35040
  
  
  

  with x1 and x2 I tell the programe how big my period steps are for each optimization round. I now would like to take the solutions after optimizing and set it to the variables of the next optimzation round. Hope that makes it more clear ? :)

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  Marika Karbstein

  Gurobi Staff

  • September 26, 2022 09:21

  Hi Marco,

  Your example is not reproducible, so I cannot see where exactly your problem is. 
  So far there are only continuous variables defined. But you mentioned binary variables in your first post as well. Setting the start attribute only affects MIP models. Do you only have continuous variables?
  Here is an example of defining in each round a MIP model that uses the solution computed in the last round

  import gurobipy as gp
  
  A = [2 ,4 ,5 ,8 ,9, 4]
  B = [3, 4, 3, 2 ,5, 5]
  
  # some start value for the first round
  xSol = [0]
  ySol = [0]
  
  for j in range(4):
      m = gp.Model("test1")
  
      x = m.addVars(j+1, lb=0, obj=1, vtype=gp.GRB.INTEGER, name = "x")
      y = m.addVars(j+1, lb=0, obj=1, vtype=gp.GRB.CONTINUOUS, name = "y")    
  
      m.addConstrs((x[i] + 2*y[i] >=  A[i]) for i in range(j+1))
      m.addConstrs((3*y[i] - x[i] <=  B[i]) for i in range(j+1))
  
      #set start values for first j variables
      for i in range(j):
         x[i].Start = xSol[i]
         y[i].Start = ySol[i]
  
      m.optimize()
  
      xSol = m.getAttr('X', x)
      ySol = m.getAttr('X', y)

  However, in this case, the model could also be built iteratively and then Gurobi automatically uses the MIP solution from the previous optimization:

  import gurobipy as gp
  
  A = [2 ,4 ,5 ,8 ,9, 4]
  B = [3, 4, 3, 2 ,5, 5]
  
  x = {}
  y = {}
  
  m = gp.Model("test2")
  
  x[0] = m.addVar(obj=1, vtype=gp.GRB.INTEGER, name='x0')
  y[0] = m.addVar(obj=1, vtype=gp.GRB.CONTINUOUS, name='y0')
  
  m.addConstr(x[0] + 2*y[0] >=  A[0])
  m.addConstr(3*y[0] - x[0] <=  B[0])
  
  m.optimize()
  
  for j in range(1,4):
      x[j] = m.addVar(obj=1, vtype=gp.GRB.INTEGER, name='x'+str(j))
      y[j] = m.addVar(obj=1, vtype=gp.GRB.CONTINUOUS, name='y'+str(j))
  
      m.addConstr(x[j] + 2*y[j] >=  A[j])
      m.addConstr(3*y[j] - x[j] <=  B[j])
  
      m.optimize()
      m.printAttr('X')

   

  Does this help? If not please be more specific in what problem you are facing.

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  Marco Sp

  • October 10, 2022 19:57

  

  

  

  Hi Marika, 

  thank you very much for your response. I am trying to modell heat devices. They should shift their power consumption to low price periods of the energy market. And when having energy devices you also have a hot water storage. When minimizing prices it leads always to a cooling down of the hot water storage at the end of the planned/modelled period. Therfore I want for example go back in the time periods (e.g. 96 periods a 15 min) and set the solution e.g. (x-96) as the new start solution. Is there a way to do so ? I hope it got more clear now :)

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