% % 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. % % """ % % Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/ % % This MiniZinc model was created by Hakan Kjellerstrand, hakank@gmail.com % See also my MiniZinc page: http://www.hakank.org/minizinc % 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; %; predicate cp1d(array[int] of var int: x, array[int] of var int: y) = assert(index_set(x) = index_set(y), "cp1d: x and y have different sizes", forall(i in index_set(x)) ( x[i] = y[i] )) ; % solve satisfy; solve :: int_search(V ++ P, first_fail, indomain_min, complete) satisfy; constraint forall(i in 1..n, j in 1..n where j = (1+i) mod 4) ( exists(a in 1..4) ( cp1d([V[i], P[i], V[j], P[j]], [allowed[a,k] | k in 1..4]) ) ) ; allowed = array2d(1..4, 1..4, [ r,r,g,g, ry,r,y,r, g,g,r,r, y,r,ry,r ]); output [ show(V[i]) ++ " " ++ show(P[i]) ++ " " | i in 1..n ] ++ ["\n"];