Copyright 2025 Google LLC.

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

First, you must install ortools package in this colab.

%pip install ortools

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 ([email protected]) Also see my other Google CP Solver models: http://www.hakank.org/google_or_tools/

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 = list(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()]), end=" ")
    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()


main()