Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
87 lines
3.0 KiB
MiniZinc
87 lines
3.0 KiB
MiniZinc
/* Linearized version
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* Uses a predicate which constructs a subcircuit which always includes an extra dummy vertex
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* Is worse than the just slightly adapted standard variant...
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*/
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include "alldifferent.mzn";
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/** @group globals
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Constrains the elements of \a x to define a subcircuit where \a x[\p i] = \p j
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means that \p j is the successor of \p i and \a x[\p i] = \p i means that \p i
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is not in the circuit.
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*/
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%% Linear version
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predicate subcircuit(array[int] of var int: x) =
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let { set of int: S = index_set(x),
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int: l = min(S),
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int: u = max(S),
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int: n = card(S),
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constraint forall(i in S)(x[i] in l..u),
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array[l..u+1] of var l..u+1: xx,
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constraint forall(i in S)(xx[i] in dom(x[i]) union {u+1}),
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} in
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alldifferent(x) /\
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subcircuit_wDummy(xx) /\
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forall( i in S, j in dom(x[i]) )( %% also when i==j?
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eq_encode(x[i])[j] >= 2*eq_encode(xx[i])[j]
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+ eq_encode(xx[i])[u+1] + eq_encode(xx[u+1])[j] - 1 %% -1
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/\
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eq_encode(x[i])[j] >= eq_encode(xx[i])[j]
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/\
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eq_encode(x[i])[j] <= eq_encode(xx[i])[j] + eq_encode(xx[i])[u+1]
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/\
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eq_encode(x[i])[j] <= eq_encode(xx[i])[j] + eq_encode(xx[u+1])[j]
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)
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/\
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forall( i in S )(
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eq_encode(x[i])[i] == eq_encode(xx[i])[i]
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)
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;
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%% Should include at least 2 nodes if >0?
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%% xx[n] is dummy
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predicate subcircuit_wDummy(array[int] of var int: x) =
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let { set of int: S = index_set(x),
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int: l = min(S),
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int: u = max(S),
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int: n = card(S),
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set of int: S__ = S diff {u}, %% the real nodes
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array[S__] of var 2..n: order,
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%% constraint order[n]==1, %% fix the dummy
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%% var bool: empty = (firstin == u+1), no, break 2-cycles with dummy
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} in
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alldifferent(x) /\
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% NO alldifferent(order) /\
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%%% MTZ model. Note that INTEGER order vars seem better!:
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forall( i in S__, j in dom(x[i]) where i!=j /\ j!=u )(
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order[i] - order[j] + (n-1)*eq_encode(x[i])[j]
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% + (n-3)*bool2int(x[j]==i) %% the Desrochers & Laporte '91 term
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% --- strangely enough it is much worse on vrp-s2-v2-c7_vrp-v2-c7_det_ADAPT_1_INVERSE.mzn!
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<= n-2 ) /\
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%% Break 2-cycles with dummy:
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forall( i in S__ )(
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eq_encode(x[i])[u] + eq_encode(x[u])[i] <= 1
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/\
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%% Ensure dummy is in:
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if i in dom(x[i]) then
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eq_encode(x[i])[i] >= eq_encode(x[u])[u]
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else
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true
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endif
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)
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/\
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% Symmetry? Each node that is not in is numbered after the lastin node.
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forall(i in S) (
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true
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% (not ins[i]) <-> (n == order[i])
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)
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;
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predicate subcircuit_reif(array[int] of var int: x, var bool: b) =
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abort("Reified subcircuit/1 is not supported.");
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%-----------------------------------------------------------------------------%
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%-----------------------------------------------------------------------------%
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