Transport Analytics Training Series - Last Revision: October 2022
Transport Analytics Training Series - Last Revision: October 2022
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
import seaborn as sns; sns.set()
from sklearn.datasets import make_blobs
%matplotlib inline
plot_size = 14
plot_width = 5
plot_height = 5
params = {'legend.fontsize': 'large',
'figure.figsize': (plot_width,plot_height),
'axes.labelsize': plot_size,
'axes.titlesize': plot_size,
'xtick.labelsize': plot_size*0.75,
'ytick.labelsize': plot_size*0.75,
'axes.titlepad': 25}
plt.rcParams.update(params)
As before, we are importing the packages tht we are going to use, and prepare the properties of the plots.
num_customers = 40
center_box = (100, 200) # defines the box that cluster centres are allowed to be in
coord, clust_true = make_blobs(n_samples=num_customers,
centers=2,
cluster_std=20,
center_box=center_box,
random_state = 2)
weights = list(np.random.uniform(size=len(coord)))
for i in range(len(coord)):
plt.scatter(coord[i, 0], coord[i, 1], s=weights[i]*100, c='b');
We will use the make_blobs command again to generate a set of customers. What we do differently here, however, is to to define a centre_box vector, that forces the generator to position points around a different point (the default value is 0,0).
import csv
with open("flp_coords.csv","w+") as my_csv:
csvWriter = csv.writer(my_csv,delimiter=',')
csvWriter.writerows(coord)
Using the csv package, we are saving the coordinates to a csv file (flp_coords.csv) in the same directory.
To proceed further, we are going to import a new solver called CVXPY.
!pip install cvxpy
!conda install -y cvxopt
Requirement already satisfied: cvxpy in /Users/pa01/opt/anaconda3/lib/python3.9/site-packages (1.2.2) Requirement already satisfied: osqp>=0.4.1 in /Users/pa01/opt/anaconda3/lib/python3.9/site-packages (from cvxpy) (0.6.2.post5) Requirement already satisfied: numpy>=1.15 in /Users/pa01/opt/anaconda3/lib/python3.9/site-packages (from cvxpy) (1.21.5) Requirement already satisfied: scipy>=1.1.0 in /Users/pa01/opt/anaconda3/lib/python3.9/site-packages (from cvxpy) (1.7.3) Requirement already satisfied: ecos>=2 in /Users/pa01/opt/anaconda3/lib/python3.9/site-packages (from cvxpy) (2.0.10) Requirement already satisfied: scs>=1.1.6 in /Users/pa01/opt/anaconda3/lib/python3.9/site-packages (from cvxpy) (3.2.2) Requirement already satisfied: qdldl in /Users/pa01/opt/anaconda3/lib/python3.9/site-packages (from osqp>=0.4.1->cvxpy) (0.1.5.post2) Collecting package metadata (current_repodata.json): done Solving environment: done # All requested packages already installed. Retrieving notices: ...working... done
from cvxpy import Minimize, Problem, CVXOPT
from cvxpy.atoms.affine.sum import sum as csum
from cvxpy.expressions.variable import Variable
from cvxpy.atoms.norm import norm
from cvxpy.atoms.elementwise.sqrt import sqrt
from cvxpy.atoms.elementwise.square import square
We are using the cvxpy to solve the continuous facility location problem. Unfortunately, we cannot use the default solver provided by PuLP as they are not capable of handling the non-linearities that are present in the formulation.
As cvxpy is fairly complex and is not used elsewhere in this module, we are providing this formulation for your information only, and without comments.
You might, however, recognise some similarities in syntax between cvxpy and PuLP models.
x = list(coord[:,0])
y = list(coord[:,1])
K = len(x)
xvar = Variable()
yvar = Variable()
objective_function = Minimize(csum([weights[k]*(square(xvar-x[k])+square(yvar-y[k])) for k in range(K)]))
problem = Problem(objective_function)
problem.solve(solver=CVXOPT)
27502.935226709855
print('x: ',xvar.value)
print('y: ', yvar.value)
x: 143.11575487044237 y: 126.33052589224143
for i in range(len(coord)):
plt.scatter(coord[i, 0], coord[i, 1], s=weights[i]*100,c='b');
plt.scatter(xvar.value, yvar.value, s=100,c='r')
<matplotlib.collections.PathCollection at 0x151048400>
