tsp.py
#!/usr/bin/python
# Copyright 2018, Gurobi Optimization, LLC
# Solve a traveling salesman problem on a randomly generated set of
# points using lazy constraints. The base MIP model only includes
# 'degree-2' constraints, requiring each node to have exactly
# two incident edges. Solutions to this model may contain subtours -
# tours that don't visit every city. The lazy constraint callback
# adds new constraints to cut them off.
import sys
import math
import random
import itertools
from gurobipy import *
# Callback - use lazy constraints to eliminate sub-tours
def subtourelim(model, where):
if where == GRB.Callback.MIPSOL:
# make a list of edges selected in the solution
vals = model.cbGetSolution(model._vars)
selected = tuplelist((i,j) for i,j in model._vars.keys() if vals[i,j] > 0.5)
# find the shortest cycle in the selected edge list
tour = subtour(selected)
if len(tour) < n:
# add subtour elimination constraint for every pair of cities in tour
model.cbLazy(quicksum(model._vars[i,j]
for i,j in itertools.combinations(tour, 2))
<= len(tour)-1)
# Given a tuplelist of edges, find the shortest subtour
def subtour(edges):
unvisited = list(range(n))
cycle = range(n+1) # initial length has 1 more city
while unvisited: # true if list is non-empty
thiscycle = []
neighbors = unvisited
while neighbors:
current = neighbors[0]
thiscycle.append(current)
unvisited.remove(current)
neighbors = [j for i,j in edges.select(current,'*') if j in unvisited]
if len(cycle) > len(thiscycle):
cycle = thiscycle
return cycle
# Parse argument
if len(sys.argv) < 2:
print('Usage: tsp.py npoints')
exit(1)
n = int(sys.argv[1])
# Create n random points
random.seed(1)
points = [(random.randint(0,100),random.randint(0,100)) for i in range(n)]
# Dictionary of Euclidean distance between each pair of points
dist = {(i,j) :
math.sqrt(sum((points[i][k]-points[j][k])**2 for k in range(2)))
for i in range(n) for j in range(i)}
m = Model()
# Create variables
vars = m.addVars(dist.keys(), obj=dist, vtype=GRB.BINARY, name='e')
for i,j in vars.keys():
vars[j,i] = vars[i,j] # edge in opposite direction
# You could use Python looping constructs and m.addVar() to create
# these decision variables instead. The following would be equivalent
# to the preceding m.addVars() call...
#
# vars = tupledict()
# for i,j in dist.keys():
# vars[i,j] = m.addVar(obj=dist[i,j], vtype=GRB.BINARY,
# name='e[%d,%d]'%(i,j))
# Add degree-2 constraint
m.addConstrs(vars.sum(i,'*') == 2 for i in range(n))
# Using Python looping constructs, the preceding would be...
#
# for i in range(n):
# m.addConstr(sum(vars[i,j] for j in range(n)) == 2)
# Optimize model
m._vars = vars
m.Params.lazyConstraints = 1
m.optimize(subtourelim)
vals = m.getAttr('x', vars)
selected = tuplelist((i,j) for i,j in vals.keys() if vals[i,j] > 0.5)
tour = subtour(selected)
assert len(tour) == n
print('')
print('Optimal tour: %s' % str(tour))
print('Optimal cost: %g' % m.objVal)
print('')
