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lp.py
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lp.py
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from cvxopt import matrix, spmatrix, solvers, log, spdiag
import numpy
import math
import csv
recordParam = False
class ODFilter(object):
def __init__(self, matrix = None, lmatrix = None, origins = None, destinations = None):
solvers.options['maxiters'] = 200
self.tours = []
self.validTours = []
self.invalidTours = []
self.k = 1
self.o = origins
self.d = destinations
self.cost = None
self.linkCost = None
self.diffusion = None
if (matrix):
self.original = matrix
self.tours.append(matrix)
self.validTours.append(matrix)
if (lmatrix):
self.linkCost = lmatrix
self.wlmatrix = None
def new(self, matrix, lmatrix, wlmatrix, origins, destinations):
self.o = origins
self.d = destinations
self.tours = []
self.original = matrix
self.linkCost = lmatrix
self.wlmatrix = wlmatrix
self.cost = None
self.validTours = []
self.invalidTours = []
self.k = 1
self.tours.append(matrix)
self.validTours.append(matrix)
self.diffusion = None
if (recordParam):
self.record(self.original, 'Original', '', self.o, self.d)
# Remakes original matrix so that it is distance optimized
#uses a weighted matrix based on zone
#for pure distance, switch cost matrix from self.wlmatrix to self.lmatrix
def optimizeLinkCost(self):
costMat = matrix(self.wlmatrix, (len(self.original), 1))
variableConstraints = matrix(-1.*numpy.eye(len(costMat)))
equalityConstraints = matrix(0., (self.o + self.d, len(costMat)))
variableSolutions = matrix(numpy.zeros(len(costMat)), (len(costMat), 1))
equalitySolutions = matrix(0., (self.o + self.d, 1))
#sets the equailty constraints to the correct sum in row / column
for i in range(self.d):
temp = self.original[:, i]
for index in range(self.o):
equalityConstraints[i,index + self.o*i] = 1
equalitySolutions[i] = sum(temp)
for i in range(self.o):
temp = self.original[i, :]
for index in range(self.d):
equalityConstraints[i + self.d, self.o*index + i] = 1
equalitySolutions[self.d + i] = sum(temp)
self.original = matrix(solvers.lp(costMat, variableConstraints, variableSolutions,
equalityConstraints, equalitySolutions, solver='glpk')['x'], (self.o, self.d))
print(self.original)
#sp1 - generate new tours
def generateTours(self, max):
while self.k < max:
costMat = matrix(0., (len(self.original), 1))
#cost matrix aggregating in U and K everystep
for mat in self.tours:
for index, value in enumerate(mat):
costMat[index] += value
self.cost = costMat
if (recordParam):
self.record(self.cost, 'Cost', self.k, self.o, self.d)
variableConstraints = matrix(-1.*numpy.eye(len(costMat)))
equalityConstraints = matrix(0., (self.o + self.d, len(costMat)))
variableSolutions = matrix(numpy.zeros(len(costMat)), (len(costMat), 1))
equalitySolutions = matrix(0., (self.o + self.d, 1))
#sets the equailty constraints to the correct sum in row / columm
for i in range(self.d):
temp = self.original[:, i]
for index in range(self.o):
equalityConstraints[i,index + self.o*i] = 1
equalitySolutions[i] = sum(temp)
for i in range(self.o):
temp = self.original[i, :]
for index in range(self.d):
equalityConstraints[i + self.d, self.o*index + i] = 1
equalitySolutions[self.d + i] = sum(temp)
#glpk solver to get new od matrix. cvxopt for documentation
newMat = solvers.lp(costMat, variableConstraints, variableSolutions,
equalityConstraints, equalitySolutions, solver='glpk')
if (recordParam):
self.record(newMat['x'], 'generated_OD', self.k, self.o, self.d)
self.validTours.append(newMat['x'])
self.tours.append(newMat['x'])
self.k += 1
#not implemented
def inverseOptimization(self):
objectiveVariables = matrix(1.0, (2, len(self.original)))
inequalityConstraints = matrix()
#sp2 - assigns diffusion based on principle of maximum entropy
def checkEntropy(self, delta):
const = 0
for index in range(len(self.cost)):
const += self.linkCost[index]*self.original[index]
inequalityConstraints = matrix(-1., (2 + self.k, self.k))
inequalitySolutions = matrix(0., (2 + self.k, 1))
for i, mat in enumerate(self.validTours):
c = 0
for index in range(len(self.cost)):
c += mat[index] * self.linkCost[index]
inequalityConstraints[0, i] = -c
inequalityConstraints[1, i] = c
inequalitySolutions[0, 0] = delta - const
inequalitySolutions[1, 0] = delta + const
equalityConstraints = matrix(1., (1, self.k))
equalitySolutions = matrix(1., (1,1))
#uses a nonlinear convex problem solver. see cvxopt for documentation
sol = solvers.cp(self.F, G=inequalityConstraints, h=inequalitySolutions,
A=equalityConstraints, b=equalitySolutions)
if(recordParam):
self.record(sol['x'], 'Diffusion', '', sol['x'].size[0], sol['x'].size[1])
total = 0.
for i in range(self.k):
total += sol['x'][i]*inequalityConstraints[1,i]
#max iterations of 200 does not always find optimal solution.
#Unsure if I should increase the cap or just use unoptimal solution.
print(sol['x'])
print(self.linkCost)
return sol['x']
#objective function used for diffusion
#f is the function (x ln x)
#df is the first derivative
#H is the second derivative
def F(self, x = None, z = None):
if(x is None):
return 0, matrix(1., (len(self.validTours), 1))
if (min(x) < 0.0):
return None
f = (x.T * log(x))
Df = (1. + log(x)).T
if (z is None):
return f, Df
H = spdiag(z * x**(-1))
return f, Df, H
#running the filter
def run(self, maxK, delta):
#set original matrix
self.optimizeLinkCost()
maxIter = 10
iterations = 0
while (iterations < maxIter):
print("ITERATION " + str(iterations))
iterations += 1
#generate set of k tours
self.generateTours(maxK)
#assign diffuction
sol = self.checkEntropy(delta)
#if all are greater than zero, accept the solution
if (min(sol) > 0):
self.diffusion = sol
return
removal = []
#else continue to generate tours
for i in range(sol.size):
if (sol[i] == 0.):
self.invalidTours.append(self.validTours[i])
removal.append(self.validTours[i])
for t in removal:
self.validTours.remove(t)
k = len(self.validTours)
for mat in self.invalidTours:
if mat in self.tours:
continue
else:
self.tours.append(mat)
#returns (stop ids, locations, and probability) in format:
# ((originid, destinationid), (origin latlng, destination latlng), probability)
def getResults(self, ori, dest, oLoc, dLoc):
if (self.diffusion):
results = []
for index in range(len(self.validTours)):
mat = matrix(self.validTours[index], (self.o, self.d))
k = 0
locations = {}
ids = {}
for i, x in enumerate(ori):
for j, y in enumerate(dest):
if(mat[i, j] > 0.):
try:
locations[k] = (oLoc[ori[x]], dLoc[dest[y]])
ids[k] = (x, y)
k += 1
except:
import pdb; pdb.set_trace()
results.append((ids, locations, self.diffusion[index]))
return results
return None
#records results for testing
def record(self, matrix, type, iteration, o, d):
with open(str(type)+str(iteration)+'.csv', 'w', newline = '') as file:
writer = csv.writer(file, delimiter=',')
for i in range(o):
row = []
for j in range(d):
row.append(matrix[i*d + j])
writer.writerow(row)
file.close()
"""
start = matrix([[50,0,0],[0,0,200],[50, 150,0]])
link = matrix([[4,18,13],[17,7,13],[11,6,21]])
test = ODFilter(start, link, 3, 3)
test.run(4,900)
"""