Implementing uncertainty in dynamic optimization problem

I have a question about implementing uncertainty terms into the Gekko optimization problem. I am a beginner in coding and starting by adding parts from the "fish management" example. I have two main questions.

1. I would like to add an uncertainty term in the model (e.g. fluctuating future prices) but it seems like I am not understanding how the module works. I am trying to draw a random value from a certain distribution and put it into m.Var, 'ss', hoping the module will take each value at each time as t moves on. But it seems like the module does not work that way. I am wondering if there is any way I can implement uncertainty terms into the process.

2. Assuming the optimization problem to allocate initial land, A(0), between use A and E, is solved for a single agent by controlling land to convert, e, I am planning to expand this to a multiple agents problem. For example, if land quality, h, and land quantity A differ among agents, n, I am planning to solve multiple optimization problems using for algorithm by calling the initial m.Var value and some parameters from a loaded dataframe. If possible, may I have a brief comment on this plan?

# -*- coding: utf-8 -*-    from gekko import GEKKO  from scipy.stats import norm  from scipy.stats import truncnorm  import pandas as pd  import numpy as np  import matplotlib.pyplot as plt  import operator  import math  import random    # create GEKKO model  m = GEKKO()      # Below, an agent is given initial land A(0) and makes a decision to convert this land to E  # Objective of an agent is to get maximum present utility(=log(income)) from both land use, income each period=(A+E(1-y))*Pa-C*u+E*Pe  # Uncertainty in future price lies for Pe, which I want to include with ss below  # After solving for a single agent, I want to solve this for all agents with different land quality h, risk aversion, mu, and land size A  # Then lastly collect data for total land use over time      # time points  n=51  year=10  k=50  m.time = np.linspace(0,year,n)  t=m.time  tt=t*(n-1)/year  tt = tt.astype(int)  ttt = np.exp(-t/(n-1))    # constants  Pa = 1  Pe = 1  C = 0.1  r = 0.05  y = 0.1    # distribution  # I am trying to generate a distribution, and use it as uncertainty term later in objective function  mu, sigma = 1, 0.1 # mean and standard deviation  #mu, sigman = df.loc[tt][2]  sn = np.random.normal(mu, sigma, n)  s= pd.DataFrame(sn)  ss=s.loc[tt][0]    # Control  # What is the difference between MV and CV? They give completely different solution  # MV seems to give correct answer  u = m.MV(value=0,lb=0,ub=10)  u.STATUS = 1  u.DCOST = 0  #u = m.CV(value=0,lb=0,ub=10)    # Variables  # m.Var and m.SV does not seem to lead to different results  # Can I call initial value from a dataset? for example, df.loc[tt][0] instead of 10 below?   # A = m.Var(value=df.loc[tt][0])  # h = m.Var(value=df.loc[tt][1])    A = m.SV(value=10)  E = m.SV(value=0)  #A = m.Var(value=10)  #E = m.Var(value=0)  t = m.Param(value=m.time)  Pe = m.Var(value=Pe)  d = m.Var(value=1)    # Equation  # It seems necessary to include restriction on u  m.Equation(A.dt()==-u)  m.Equation(E.dt()==u)  m.Equation(Pe.dt()==-1/k*Pe)  m.Equation(d==m.exp(-t*r))  m.Equation(A>=0)      # Objective (Utility)  J = m.Var(value=0)    # Final objective  # I want to include ss, uncertainty term in objective function  Jf = m.FV()  Jf.STATUS = 1  m.Connection(Jf,J,pos2='end')  #m.Equation(J.dt() == m.log(A*Pa-C*u+E*Pe))  m.Equation(J.dt() == m.log((A+E*(1-y))*Pa-C*u+E*Pe)*d)  #m.Equation(J.dt() == m.log(A*Pa-C*u+E*Pe*ss)*d)    # maximize profit  m.Maximize(Jf)  #m.Obj(-Jf)    # options  m.options.IMODE = 6  # optimal control  m.options.NODES = 3  # collocation nodes  m.options.SOLVER = 3 # solver (IPOPT)    # solve optimization problem  m.solve()    # print profit  print('Optimal Profit: ' + str(Jf.value[0]))      # collect data  # et=u.value  # print(et)  # At=A.value  # print(At)  # index = range(1, 2)  # columns = range(1, n+1)  # Ato=pd.DataFrame(index=index,columns=columns)  # Ato=At    # plot results  plt.figure(1)  plt.subplot(4,1,1)  plt.plot(m.time,J.value,'r--',label='profit')  plt.plot(m.time[-1],Jf.value[0],'ro',markersize=10,\           label='final profit = '+str(Jf.value[0]))  plt.plot(m.time,A.value,'b-',label='Agricultural Land')  plt.ylabel('Value')  plt.legend()  plt.subplot(4,1,2)  plt.plot(m.time,u.value,'k.-',label='adoption')  plt.ylabel('conversion')  plt.xlabel('Time (yr)')  plt.legend()  plt.subplot(4,1,3)  plt.plot(m.time,Pe.value,'k.-',label='Pe')  plt.ylabel('price')  plt.xlabel('Time (yr)')  plt.legend()  plt.subplot(4,1,4)  plt.plot(m.time,d.value,'k.-',label='d')  plt.ylabel('Discount factor')  plt.xlabel('Time (yr)')  plt.legend()  plt.show()      

https://stackoverflow.com/questions/66433978/implementing-uncertainty-in-dynamic-optimization-problem March 02, 2021 at 01:49PM