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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  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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