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yap-6.3/packages/gecode/clp_examples/3jugs.yap

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2013-11-03 14:12:38 +00:00
% Example with matrices,based on:
%
% Three jugs problem in Minzinc modelled as a shortest path problem.
%
% Problem from Taha "Introduction to Operations Research", page 245
%
% Model created by Hakan Kjellerstrand, hakank@bonetmail.com
% See also my MiniZinc page: http://www.hakank.org/minizinc
%
% VSC: had to transpose the matrix, and change the constraints....
%
:- style_check( all ).
:- use_module(library(gecode/clpfd)).
:- use_module(library(maplist)).
:- use_module(library(lists)).
main :-
problem(Z, X, InFlow, OutFlow, N),
out(Z, X, InFlow, OutFlow, N),
fail.
main.
problem(Z, X, InFlow, OutFlow, N) :-
N = 15,
Start = 1,
End = 15,
M = 999,
d( M, DD ),
D = array[1..N,1..N] of DD, % distance
RHS = array[1..N] of _, % requirements (right hand statement)
X = array[1..N, 1..N] of 0..1, % the resulting matrix, 1 if connected, 0 else
OutFlow = array[1..N] of 0..1,
InFlow = array[1..N] of 0..1,
% objective to minimize
Z in 0..M,
Z #= sum( [I in 1..N, J in 1..N] where D[I,J]<M,
D[I,J]*X[I,J]),
% solve minimize z;
% alternative solve statements which may give faster solution
%solve :: int_search([ x[i,j] | i,j in 1..n], first_fail, indomain_min, complete) minimize z;
% solve minimize z;
minimize(Z),
% constraint
foreach(I in 1..N,
( I == Start ->
RHS[I] <== 1 ;
I == End ->
RHS[I] <== -1 ;
RHS[I] <== 0 )
),
% must be larger than 0??
foreach( [I in 1..N, J in 1..N],
( D[J,I] = M ->
X[J,I] #= 0 ;
true )
),
% outflow constraint
foreach(I in 1..N,
OutFlow[I] #= sum(J in 1..N where D[J,I]<M, X[J,I])
),
% inflow constraint
foreach(J in 1..N,
InFlow[J] #= sum(I in 1..N where D[J,I]<M, X[J,I])
),
% inflow = outflow
foreach(I in 1..N, OutFlow[I]-InFlow[I]#=RHS[I]),
% labeling
labeling( [], X).
% data
d(M, [
M, 1, M, M, M, M, M, M, 1, M, M, M, M, M, M,
M, M, 1, M, M, M, M, M, M, M, M, M, M, M, M,
M, M, M, 1, M, M, M, M, 1, M, M, M, M, M, M,
M, M, M, M, 1, M, M, M, M, M, M, M, M, M, M,
M, M, M, M, M, 1, M, M, 1, M, M, M, M, M, M,
M, M, M, M, M, M, 1, M, M, M, M, M, M, M, M,
M, M, M, M, M, M, M, 1, 1, M, M, M, M, M, M,
M, M, M, M, M, M, M, M, M, M, M, M, M, M, 1,
M, M, M, M, M, M, M, M, M, 1, M, M, M, M, M,
M, 1, M, M, M, M, M, M, M, M, 1, M, M, M, M,
M, M, M, M, M, M, M, M, M, M, M, 1, M, M, M,
M, 1, M, M, M, M, M, M, M, M, M, M, 1, M, M,
M, M, M, M, M, M, M, M, M, M, M, M, M, 1, M,
M, 1, M, M, M, M, M, M, M, M, M, M, M, M, 1,
M, M, M, M, M, M, M, M, M, M, M, M, M, M, M
]).
/*
% shows the result matrix
output [
if i = 1 /\ j = 1 then
"z: " ++ show(z) ++ "\n" ++
"inFlow: " ++ show(inFlow) ++ "\n" ++ "outFlow: " ++ show(outFlow) ++ "\n" ++
" 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5\n"
else "" endif ++
if j = 1 then show(i) ++ " : " else "" endif ++
show(x[i,j]) ++ if j = n then "\n" else " " endif
| i in 1..n, j in 1..n
];
*/
out(Cost, Ts, Ins, Out, N) :-
format('cost = ~d~n', [Cost]),
InsL <== list(Ins),
OutL <== list(Out),
format('Inputs =', []), maplist(out, InsL), nl,
format('Outputs =', []), maplist(out, OutL), nl,
format('transitions =~n', []),
foreach(I in 1..N, outl(Ts[_,I]) ).
outl( X ) :-
L <== X, % evaluate matrix notation to Prolog lists.
format(' ', []),
maplist(out, L), nl.
out(0) :- format(' .', []).
out(1) :- format(' 1', []).