[HELP] Translation of Algebraic Mathematical Model to using python gurobi api

Answered

Evans Etrue Howard

• October 18, 2020 08:02
• Edited

I have a max flow problem for an emergency evacuation planning. The model is based on the Cell Transmission Model (CTM), basically the entire area to be evacuated is partitioned into cells using square grid, where cells=nodes and the passage/links between adjacent cells = arcs. G=(V,A). The whole idea is to find the maximum number of evacuated at each time slot. 

The model will be run for tau = 1, 2, ...until a solution for N is found.

 

NB: My degree/life literally depends on this and I have Tuesday to submit and present it on Thursday. 

I I have the mathematical formulation of the problem I am working on but I honestly cant do the python formulation for the problem to be solved by gurobi. I would be very grateful in the kind people here could help me out with the implementation because my whole life literally depends on it and I will be indebted to you guys forever. Thanks

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• Official comment

  

  Simranjit Kaur

  Gurobi Staff

  • December 06, 2024 00:40

  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 why not try our AI Gurobot?.
• 

  Richard Oberdieck

  Gurobi Staff

  • October 19, 2020 12:01

  Hi Evans,

   

  here is an implementation of your problem in Python using Gurobi:

  First, we define a few basics. Since I don't know anything about your problem‚ I just generated some random data.

  import gurobipy as gp
  import numpy as np
  
  # The nodes
  nodes = 10
  V = range(nodes)
  n = np.random.rand(nodes)         # max capacity of node i
  
  # The arcs
  A = [(i,j) for i in V for j in V] # The set of arcs. This may have to be adjusted for your problem
  c = np.random.rand(nodes, nodes)  # max capacity of arc ij
  
  

   

  Next, we formulate and solve the problem:

  solution_found = False
  tau = 2
  
  while not solution_found:
    T = range(tau)
    m = gp.Model()
  
    # Add the variables
    y = m.addVars(nodes,tau)
    x = m.addVars(A, tau, lb=-gp.GRB.INFINITY)
  
    # This picks the last element from y and maximizes that
    m.setObjective(y[nodes-1,tau-1], sense=gp.GRB.MAXIMIZE)
  
    # The constraints
    for t in T:
      for j in V:
        if t > 0:
          m.addConstr(y[j,t] - y[j,t-1] - x.sum('*',j,t-1) + x.sum(j,'*',t-1) == 0)
  
        m.addConstr(y[j,t] <= n[j])
  
      for i,j in A:
        m.addConstr(x[i,j,t] + x[j,i,t] >= 0)
        m.addConstr(x[i,j,t] + x[j,i,t] <= c[i,j])
  
    m.optimize()
  
    if m.Status == gp.GRB.OPTIMAL:
      solution_found = True
  
    tau += 1

  Note that Python indexes at 0, which leads to the "-1" in a few places. Also, note that I assume that the super sink is the last node for convenience.

   

  Good luck

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• 

  Evans Etrue Howard

  • October 19, 2020 12:34

  

  

  

  Thanks very much Richard for the solution. You are a life saver. 

  Honestly I have 5 more constraints. Please help me out if am not asking for too much.  Attached is a picture of the other constraints.

  

  

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• 

  Richard Oberdieck

  Gurobi Staff

  • October 19, 2020 13:26

  Hi Evans,

  I think you should give it shot yourself based on the code that I sent. You can see that the gurobipy interface is quite easy to use, so it should be possible for you to add the additional constraints.

  Best regards

  Richard

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• 

  Evans Etrue Howard

  • October 19, 2020 13:28

  

  

  

  Thanks. I have been able to implement it. Thanks very much. Your code was very intuitive and and straightforward. 

  You are need very helpful

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