automatically get values of auxiliary variables

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ANH TU VU

2022年07月15日 07:06

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I have main variables (V) and auxiliary variables (U) with the below formula example

U1 = 0.5 V1 + 0.7 V2 + 0.1 V3

After Gurobi solves the optimization problems, I get an array of V, like V1=5, V2=7, V3=9. However, I do not have a value for each Ui. It still returns the above formula.

Is there any way to automatically get the value of each U after having V? Following the example, U1 should be 0.5 * 5 + 0.7 * 7 + 0.1 * 9 = 8.3

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• 正式なコメント

  

  Simranjit Kaur

  • Gurobi Staff

  2025年11月16日 23:32

  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 try Gurobot, our chatbot interface offering instant, expert-level support.
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  Marika Karbstein

  • Gurobi Staff

  2022年07月15日 09:38 編集済み

  Did you add your U-variables with addVar(s) to the model? And also the constraint (U1= 0.5 V1 + 0.7 V2 + 0.1 V3) with addConstr?

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  ANH TU VU

  2022年07月15日 16:42

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  yes, I do. Here is an example. U-variables[0] = {0: <gurobi.LinExpr: 0.0 state_value_variable[1] + 0.0 state_value_variable[33] + 0.0 state_value_variable[153] + 0.26963645536163366 state_value_variable[8] + 0.2964055079203106 state_value_variable[18]}

  Gurobi solved for specific values of state_value_variable, but not for U-variables

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  ANH TU VU

  2022年07月15日 19:10 編集済み

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  Here are all my codes. It's scarcely long because I haven't known how to optimize code with Gurobi's variables. There are two problems I need your support

  1) As you can see, the variable CV_value_variable is calculated by a formula. Thus, when Gurobi completed, that variable did not have specific values. Therefore, I must manually recalculate the values for CV_value_variable

  2) I am trying to do multi-processing on my computer, but it hasn't worked with the variable, state_value_variable. Do you suggest any solutions

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  ANH TU VU

  2022年07月15日 19:11

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  for _ in range(5):

  state_value_table_new = state_value_table_gu.copy()

  invest_policy_table_gu = invest_policy_table.copy()

  exit_policy_table_gu = exit_policy_table.copy()

  entry_policy_table_gu = entry_policy_table.copy()

  
  

  # create a new model

  m = gp.Model('naive_LP_model')

  
  

  # create variables

  state_value_variable = m.addVars(num_state, lb=0, ub=float('inf'),

  vtype='C', name='state_value_variable')

  
  

  aux_variable = m.addVars(num_state * n, lb=0, ub=float('inf'),

  vtype='C', name='aux_variable')

  
  

  CV_value_variable = m.addVars(num_state * len(invArr), lb=0, ub=float('inf'),

  vtype='C', name='aux_variable')

  
  

  # set objective

  m.setObjective(state_value_variable.sum(), GRB.MINIMIZE)

  
  

  # add constraints

  for state_idx in range(num_state):

  
  

  state = all_states_10[state_idx]

  industry_state = list(state[1])

  lst_firm_states = extract_firm_states_operator(state)

  
  

  lst_profit = get_profit(industry_state, profit_params, industry_params)

  
  

  for kappa_idx in range(n):

  
  

  m.addConstr(aux_variable[state_idx * n + kappa_idx] >= lst_kappa[kappa_idx])

  
  

  for inv in range(len(invArr)):

  # firms' actions

  firm_0 = {'inv': None, 'rho': None, 'lam': None}

  firm_1 = firm_action(lst_firm_states[1], tuple([lst_firm_states[1], state[1]]),

  invest_policy_table, exit_policy_table, entry_policy_table)

  firm_2 = firm_action(lst_firm_states[2], tuple([lst_firm_states[2], state[1]]),

  invest_policy_table, exit_policy_table, entry_policy_table)

  lst_firm_actions = [firm_0, firm_1, firm_2]

  
  

  # firms' action probabilities

  firm_0['inv'] = invArr[inv]

  lst_act_prob_0 = action_probability(lst_firm_states[0], firm_0, transition_params,

  industry_params, target_firm=True)

  lst_act_prob_1 = action_probability(lst_firm_states[1], firm_1, transition_params,

  industry_params, target_firm=False)

  lst_act_prob_2 = action_probability(lst_firm_states[2], firm_2, transition_params,

  industry_params, target_firm=False)

  all_act_prob = [lst_act_prob_0, lst_act_prob_1, lst_act_prob_2]

  
  

  # transition matrix

  trans_mat = Transition_table(industry_state, lst_firm_states, all_act_prob)

  
  

  # CV value

  expected_value = 0

  for next_state in list(trans_mat.keys()):

  expected_value += trans_mat[next_state] * state_value_variable[all_states_10.index(next_state)]

  CV_value = -economic_params['invCost'] * firm_0['inv'] + \

  economic_params['beta'] * expected_value

  CV_value_variable[state_idx * len(invArr) + inv] = CV_value

  
  

  m.addConstr(aux_variable[state_idx * n + kappa_idx] >= CV_value)

  
  

  m.addConstr(state_value_variable[state_idx] >= lst_profit[state[0]] +\

  sum([aux_variable[state_idx * n + i] for i in range(n)])/n)

  
  

  # Run LP model

  m.optimize()

  
  

  for i in range(num_state):

  state_value_table_gu[all_states_10[i]] = state_value_variable[i].X

  
  

  for i in range(num_state):

  state = all_states_10[i]

  industry_state = list(state[1])

  lst_firm_states = extract_firm_states_operator(state)

  firm_0 = {'inv': None, 'rho': None, 'lam': None}

  firm_1 = firm_action(lst_firm_states[1], tuple([lst_firm_states[1], state[1]]),

  invest_policy_table, exit_policy_table, entry_policy_table)

  firm_2 = firm_action(lst_firm_states[2], tuple([lst_firm_states[2], state[1]]),

  invest_policy_table, exit_policy_table, entry_policy_table)

  lst_firm_actions = [firm_0, firm_1, firm_2]

  
  

  CV_value_opt, inv_opt = CV_operator(lst_firm_actions, state, invArr, economic_params,

  transition_params, industry_params, state_value_table_gu)

  
  

  invest_policy_table[all_states_10[i]] = inv_opt

  exit_policy_table[all_states_10[i]] = CV_value_opt

  
  

  for industry_state in lst_industry_state_2:

  entry_policy_table[industry_state] = cal_entry_value_opt(industry_state, state_value_table_new, economic_params,

  invest_policy_table_gu, exit_policy_table_gu, entry_policy_table_gu)

  
  

  delta_inv = max(abs(np.array(list(invest_policy_table.values())) - np.array(list(invest_policy_table_gu.values()))))

  delta_exit = max(abs(np.array(list(exit_policy_table.values())) - np.array(list(exit_policy_table_gu.values()))))

  delta_entry = max(abs(np.array(list(entry_policy_table.values())) - np.array(list(entry_policy_table_gu.values()))))

  delta_policy = max(delta_inv, delta_exit, delta_entry)

  
  

  print(delta_policy)

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  Marika Karbstein

  • Gurobi Staff

  2022年07月18日 12:42

  I am not sure whether I understand your problem. The code you added is not executable (no indentation, undefined objects...). 

  I see that CV_value_variable is added to the model but there is no (model)constraint related to this variable?
  It seems to be dependent on state_value_variable. But then you need to add this relation as constraints to the model, for example (simplified):

  m.addConstr(CV_value_variable[0] == gp.quicksum(state_value_variable[i] for i in range(num_state)))

  Then if m.optimize() results in a solution, print(CV_value_variable[0].x) gives you the value for this variable (which is the sum of the other variables here).

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