initialization

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Param Patel

• April 30, 2024 13:40

Hello, 

How can I assign a constant value to a variable at a particular timestep?

i have a set {8,16,24,32}. I tried formulating it as a linear expression, (8b1+16b2+..), enforcing sum value as 1, thereby it can select any one value out of the set and append it to the variable r[i,j] at time-step j. 

If I take model.addVar(8,64,GRB.INTEGER) ---> This also does not work.

Later I want to retrieve the values of the variable and plot them.

Thank you.

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• 

  Bot Marley (with AI contributions)

  • May 03, 2024 00:42

  

  

  Hi Param,

  To model a scenario where a variable can take only one value from a specified set at a particular time-step, and later use this variable for plotting or other purposes, you can utilize the capabilities of the Gurobi Optimizer in a more targeted manner. Here's a step-by-step explanation and a Python code snippet using the Gurobi Python API to achieve this:

  ### Defining the Problem
  You have a set \( \{8, 16, 24, 32\} \), and you want to assign exactly one of these values to a variable \( r[i, j] \) at time-step \( j \). This seems like a classic use-case for binary variables to select the value from the set.

  ### Step-by-Step Implementation
  1. **Variable Definitions**:
     - Define a binary variable for each value in the set for each timestep. For instance, \( b_8, b_{16}, b_{24}, b_{32} \) could be binary variables where \( b_k = 1 \) if \( r[i,j] = k \) and \( 0 \) otherwise.
     - Define \( r[i, j] \) as an integer or continuous variable depending on your specific requirements (e.g., sum of the products of set elements and corresponding binary variables).

  2. **Constraints**:
     - Ensure only one binary variable can take the value 1 at any time-step. This enforces that \( r[i, j] \) can only take one value from the set.
     - The value of \( r[i, j] \) should be equal to the sum of the products of each element in the set and its corresponding binary variable.

  3. **Objective (if any)**:
     - Depending on the broader problem, define an objective function.

  4. **Retrieving and Plotting Data**:
     - After solving the model, retrieve the value of \( r[i, j] \) for each timestep and use it for plotting or further analysis.

  This approach should solve your issue by setting up a decision variable linked with a set of binary variables to enforce the exclusive choice of values from your set.

   

  - Bot

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• 

  Param Patel

  • May 06, 2024 10:21
  • Edited

  

  

  Thank you for your reply. I tried that approach but it did not work 

  def model_variables_and_constraints(model, tk, v1_t, v2_t, e1, e2, v, T_full_charge, T_top_up, delta_t):

      r1t = {}

      e1t = {}

      # current_set = [8, 16, 24, 32, 48, 64]

  
  

      b1 = model.addVar(vtype=gb.GRB.BINARY, name='binary_var_current_8a')

      b2 = model.addVar(vtype=gb.GRB.BINARY, name='binary_var_current_16a')

      b3 = model.addVar(vtype=gb.GRB.BINARY, name='binary_var_current_24a')

      b4 = model.addVar(vtype=gb.GRB.BINARY, name='binary_var_current_32a')

      b5 = model.addVar(vtype=gb.GRB.BINARY, name='binary_var_current_48a')

      b6 = model.addVar(vtype=gb.GRB.BINARY, name='binary_var_current_64a')

  
  

      model.addConstr(gb.quicksum([b1,b2,b3,b4,b5,b6])==1)

      # Add the charging variables r and e for full charge and top-up EV

      for i in range(len(v1_t)):

          for j in range(len(tk)):

              r1t[i, j] = model.addVar(lb=0, ub=64, vtype=gb.GRB.INTEGER, name=f'EV_{i}_current_{j}')

              model.addConstr(r1t[i,j] == gb.quicksum([8*b1,16*b2,24*b3,32*b4,48*b5,64*b6]))

              e1t[i, j] = model.addVar(lb=0, ub=e1[i], vtype=gb.GRB.INTEGER, name=f'ChargingVariable_e1_{i}_{j}')

              if tk[i] <= tk[j] <= T_full_charge[i]:

                  model.addConstr(r1t[i, j] == 0)

  
  

      # Define constraints

      for i in range(len(v1_t)):

          for j in range(len(tk)):

              res = model.addVar(lb=0, ub=50000, vtype=gb.GRB.INTEGER, name=f'volts*current_{i}_{j}')

              final_res = model.addVar(lb=0, ub=50, vtype=gb.GRB.INTEGER, name=f'round_result_{i}_{j}')

              model.addConstr(res == r1t[i, j] * v * delta_t)

              model.addConstr(final_res == res / 1000)

              # Constraint to update pending energy based on cumulative charging completed till that step

              if tk[i]<=tk[j]<=T_full_charge[i]:

                  if j > 0:

                      model.addConstr(e1t[i, j] == e1[j-1] - final_res)

                  else:

                      model.addConstr(e1t[i, j] == e1[i] - final_res)

              else:

                  model.addConstr(e1t[i,j]==0)

   

  
  

      return r1t, e1t

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• 

  Riley Clement

  Gurobi Staff

  • May 06, 2024 13:53

  Hi Param,

  How can I assign a constant value to a variable at a particular timestep?

  What is meant here by timestep?

  - Riley

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