Mixed Integer Programming

Answered

Ehab Issa

• July 28, 2021 22:04

I want to solve this problem by using mixed integer programming ,i know if there is a quadratic term in the objective function, the problem is termed a Mixed Integer Quadratic Program (MIQP). Can you help me with more detial detail about MIQP such as mathmatical formulation ,Flowchart of algorithm and methods of impementation . if i want to impement this problem using GUROBI solver  ,i start with

m.addVar()

m.setobjective (obj)

m.addConstr()

m.optimize()

thanks for your help

##objective function
ft=fa+fb 
fa = ai + bi * X1 + ci * X1^2
fb = ai + bi * X2 + ci * X2^2

#bound constraints l ≤ X1 ≤ u l ≤ X2 ≤ u A X1+B X2 = b (linear constraints)

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• 

  Alison Cozad

  Gurobi Staff

  • August 02, 2021 13:48
  • Edited

  To give you a feel for how you could implement your example in Gurobi, I adapted our qcp.py example to your post:

  # This is adapted from the example in https://www.gurobi.com/documentation/9.1/examples/qcp_py.html#subsubsection:qcp.py
  
  import gurobipy as gp
  from gurobipy import GRB
  
  # Create a new model
  m = gp.Model("Ehab's MIQP")
  
  # Create variables
  # From your post:
  #    l ≤ X1 ≤ u 
  #    l ≤ X2 ≤ u
  # For illustrative purposes, I made X1 continuous and X2 integer
  l = 0
  u = 5
  X1 = m.addVar(name="X1", vtype=GRB.CONTINUOUS, lb=l, ub=u) 
  X2 = m.addVar(name="X2", vtype=GRB.INTEGER, lb=l, ub=u)
  
  # Set objective:
  # From your post:
  #    ft=fa+fb 
  #    fa = ai + bi * X1 + ci * X1^2
  #    fb = ai + bi * X2 + ci * X2^2
  ai = 1
  bi = 2
  ci = 3
  fa = ai + bi * X1 + ci * X1**2 # This creates a gurobipy.QuadExpr object
  fb = ai + bi * X2 + ci * X2**2 # This creates a gurobipy.QuadExpr object
  ft = fa + fb
  m.setObjective(ft, GRB.MINIMIZE)
  
  # Add constraints
  # From your post:
  #    A X1+B X2 = b (linear constraints)
  A = 2
  B = 4
  b = 10
  m.addConstr(A*X1 + B*X2 == b , "c0")
  
  
  m.optimize()
  
  for v in m.getVars():
      print('%s %g' % (v.varName, v.x))
  
  print('Obj: %g' % ft.getValue())

  For more information, I recommend you check out the Gurobi Example page and the Python API Details.

   

   

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• 

  Ehab Issa

  • August 02, 2021 21:15

  

  

  

  Dear Alison Cozad

  Thanks a lot for the great explanation

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• 

  Ehab Issa

  • August 05, 2021 12:36

  

  

  

  Dear Alison Cozad ,

  i adapted my problem with code but after running get this error

  Can you help me to solve it ?

  #A=int1
  #B=int2
  #X1 = Diesel
  #X2 = bat
  l1 = 0
  l2 = 0 
  u1 = maxDiesel
  u2 = bat_ub
  
  m = gp.Model("Ehab's MIQP")
  
  
  for i in range(0, len0):
  	if netload[i] <= 0:  # not happen in this case
  		pass
  
  	else:  # solar + wind < load, diesel and battery supply
  		if bat_now > bat_min:
  			bat_gap = bat_now - bat_min
  			bat_ub = min(maxBat, bat_gap)  # update bat bound every step
  
  			# create variables
  			diesel = m.addVar(name="diesel", vtype=GRB.CONTINUOUS, lb=l1, ub=u1) 
  			bat = m.addVar(name="bat", vtype=GRB.INTEGER, lb=l2, ub=u2)
  			int1 = m.addVar(vtype=GRB.BINARY, name='int1')
  			int2 = m.addVar(vtype=GRB.BINARY, name='int2')
  
  			m.update()
  
  			# objective function
  			fa = 2.6975 + 1.1153 * diesel + 0.05 * diesel**2 # This creates a gurobipy.QuadExpr object
  			fb = 0.1154 + 0.7975 * bat + 0.1409 * bat**2 # This creates a gurobipy.QuadExpr object
  			ft = fa + fb
  			m.setObjective(ft, GRB.MINIMIZE)
  
  			# add constraints
  			m.addConstr(diesel * int1 + bat * int2, GRB.EQUAL, netload[i], "c0")
  			m.addConstr(diesel <= maxDiesel * int1, "c1")
  			m.addConstr(bat <= bat_ub * int2, "c2")
  
  			m.optimize()
  			set_diesel[i] = diesel.x
  			set_bat[i] = bat.x
  			set_int1[i] = int1.x
  			set_int2[i] = int2.x
  			bat_now = bat_now - set_bat[i]
  		else:  # battery at lowest energy, cannot discharge, diesel supplied solely
  			set_diesel[i] = min(maxDiesel, netload[i])
  for v in m.getVars():
      print('%s %g' % (v.varName, v.x))
  
  print('Obj: %g' % ft.getValue())

  

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• 

  Ehab Issa

  • August 05, 2021 14:22

  

  

  

  Alison Cozad ,

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• 

  Alison Cozad

  Gurobi Staff

  • August 05, 2021 15:29

  Hi Ehab,

  It looks like you are unable to retrieve the solution value for your variables (\(\texttt{variable.X}\)) because the solution is infeasible.  You are smart to add a check of the \(\texttt{m.status}\) value before trying to retrieve this attribute.

  If you want some advice on dealing with infeasibility, I recommend checking this out: How do I determine why my model is infeasible? 

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• 

  Ehab Issa

  • August 05, 2021 17:16

  

  

  

  Dear Alison Cozad  thank you for your interest and help

  I actually read the article, but I couldn't find the steps to solve the problem

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• 

  Alison Cozad

  Gurobi Staff

  • August 05, 2021 19:17

  Hi Ehab,

  You are unable to retrieve solution values because the model is infeasible.  You can see this in the log file:

  ...
  Model is infeasible
  - Best objective, -, best bound -, gap

  In order to get solution values, you will need to address why your model is infeasible.  I simply included the article to help you determine why your model is infeasible.

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