# Copyright 2010 Hakan Kjellerstrand hakank@bonetmail.com
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
"""
Traffic lights problem in Google CP Solver.
CSPLib problem 16
http://www.cs.st-andrews.ac.uk/~ianm/CSPLib/prob/prob016/index.html
'''
Specification:
Consider a four way traffic junction with eight traffic lights. Four of the
traffic
lights are for the vehicles and can be represented by the variables V1 to V4
with domains
{r,ry,g,y} (for red, red-yellow, green and yellow). The other four traffic
lights are
for the pedestrians and can be represented by the variables P1 to P4 with
domains {r,g}.
The constraints on these variables can be modelled by quaternary constraints
on
(Vi, Pi, Vj, Pj ) for 1<=i<=4, j=(1+i)mod 4 which allow just the tuples
{(r,r,g,g), (ry,r,y,r), (g,g,r,r), (y,r,ry,r)}.
It would be interesting to consider other types of junction (e.g. five roads
intersecting) as well as modelling the evolution over time of the traffic
light sequence.
...
Results
Only 2^2 out of the 2^12 possible assignments are solutions.
(V1,P1,V2,P2,V3,P3,V4,P4) =
{(r,r,g,g,r,r,g,g), (ry,r,y,r,ry,r,y,r), (g,g,r,r,g,g,r,r),
(y,r,ry,r,y,r,ry,r)}
[(1,1,3,3,1,1,3,3), ( 2,1,4,1, 2,1,4,1), (3,3,1,1,3,3,1,1), (4,1, 2,1,4,1,
2,1)}
The problem has relative few constraints, but each is very tight. Local
propagation
appears to be rather ineffective on this problem.
'''
Note: In this model we use only the constraint solver.AllowedAssignments().
Compare with these models:
* MiniZinc: http://www.hakank.org/minizinc/traffic_lights.mzn
* Comet : http://www.hakank.org/comet/traffic_lights.co
* ECLiPSe : http://www.hakank.org/eclipse/traffic_lights.ecl
* Gecode : http://hakank.org/gecode/traffic_lights.cpp
* SICStus : http://hakank.org/sicstus/traffic_lights.pl
This model was created by Hakan Kjellerstrand (hakank@bonetmail.com)
Also see my other Google CP Solver models:
http://www.hakank.org/google_or_tools/
"""
import string
import sys
from ortools.constraint_solver import pywrapcp
def main(base=10, start=1, len1=1, len2=4):
# Create the solver.
solver = pywrapcp.Solver("Traffic lights")
#
# data
#
n = 4
r, ry, g, y = range(n)
lights = ["r", "ry", "g", "y"]
# The allowed combinations
allowed = []
allowed.extend([(r, r, g, g),
(ry, r, y, r),
(g, g, r, r),
(y, r, ry, r)])
#
# declare variables
#
V = [solver.IntVar(0, n - 1, "V[%i]" % i) for i in range(n)]
P = [solver.IntVar(0, n - 1, "P[%i]" % i) for i in range(n)]
#
# constraints
#
for i in range(n):
for j in range(n):
if j == (1 + i) % n:
solver.Add(solver.AllowedAssignments((V[i], P[i], V[j], P[j]), allowed))
#
# Search and result
#
db = solver.Phase(V + P,
solver.INT_VAR_SIMPLE,
solver.INT_VALUE_DEFAULT)
solver.NewSearch(db)
num_solutions = 0
while solver.NextSolution():
for i in range(n):
print "%+2s %+2s" % (lights[V[i].Value()], lights[P[i].Value()]),
print
num_solutions += 1
solver.EndSearch()
print
print "num_solutions:", num_solutions
print "failures:", solver.Failures()
print "branches:", solver.Branches()
print "WallTime:", solver.WallTime()
print
if __name__ == "__main__":
main()