% % Traffic lights problem in MiniZinc. % % CSPLib problem 16 % http://www.csplib.org/Problems/prob016 % """ % 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: This is the same as http://www.hakank.org/minizinc/taffic_lights.mzn % except that it use the global constraint table. % % This MiniZinc model was created by Hakan Kjellerstrand, hakank@gmail.com % See also my MiniZinc page: http://www.hakank.org/minizinc % % Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/ include "globals.mzn"; int: n = 4; int: r = 1; % red int: ry = 2; % red-yellow int: g = 3; % green int: y = 4; % yellow set of int: Cars = {r,ry,g,y}; set of int: Pedestrians = {r,g}; array[1..4, 1..4] of Cars: allowed; array[1..n] of var Cars: V; array[1..n] of var Pedestrians: P; solve satisfy; constraint forall(i in 1..n, j in 1..n where j = (1+i) mod 4) ( table([V[i], P[i], V[j], P[j]], allowed) ) ; allowed = array2d(1..4, 1..4, [ r,r,g,g, ry,r,y,r, g,g,r,r, y,r,ry,r ]); % output [ % "V: ", show(V), "\nP: ", show(P), "\n" % ]; output [ show(V[i]) ++ " " ++ show(P[i]) ++ " " | i in 1..n ] ++ ["\n"];