Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
710 lines
28 KiB
MiniZinc
710 lines
28 KiB
MiniZinc
/*
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% FlatZinc built-in redefinitions for linear solvers.
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%
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% AUTHORS
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% Sebastian Brand
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% Gleb Belov (2015-)
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% cf. Belov, Stuckey, Tack, Wallace. Improved Linearization of Constraint Programming Models. CP 2016.
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*/
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%----------------------------- BOOL2INT --------------------------------%
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function var bool: reverse_map(var int: x) = (x==1);
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function bool: reverse_map(int: x) = (x==1);
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predicate mzn_reverse_map_var(var bool: b) = let {
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var int: x = bool2int(b)
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} in true;
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function var int: bool2int(var bool: x) :: promise_total =
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let { var 0..1: b2i;
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constraint (x = reverse_map(b2i)) ::is_reverse_map ;
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} in
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b2i;
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predicate bool_eq(var bool: x, var bool: y) =
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%% trace(" bool_eq: \(x), \(y) \n") /\
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bool2int(x)==bool2int(y);
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predicate bool2int(var bool: x, var int: y) = y = bool2int(x);
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%---------------------------- BASIC (HALF)REIFS -----------------------------%
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include "options.mzn";
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include "redefs_bool_reifs.mzn";
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include "redefs_bool_imp.mzn";
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include "domain_encodings.mzn";
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include "redefs_lin_reifs.mzn";
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include "redefs_lin_imp.mzn";
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include "redefs_lin_halfreifs.mzn";
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include "nosets.mzn"; %% For set_le, set_lt ... Usind std/nosets
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%% as long as the linearization is good.
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%-----------------------------------------------------------------------------%
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% Strict inequality
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% Uncomment the following redefinition for FlatZinc MIP solver interfaces that
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% do not support strict inequality. Note that it does not preserve equivalence
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% (some solutions of the original problem may become invalid).
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predicate float_lt(var float: x, var float: y) =
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% (x - y) <= (-float_lt_EPS_coef__)*max(abs(ub(x - y)), abs(ub(y-x)));
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x <= y - float_lt_EPS;
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predicate float_lin_lt(array[int] of float: c, array[int] of var float: x,
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float: d) =
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float_lt(sum(i in index_set(x))( c[i]*x[i] ), d);
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%-----------------------------------------------------------------------------%
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% Minimum, maximum, absolute value
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% Use unary as well? TODO
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predicate int_abs(var int: x, var int: z) =
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%% The simplifications seem worse on league.mzn model90-18-20.dzn:
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%% but the .lp seem to differ just by order...?? TODO
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if lb(x)>=0 then z==x
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elseif ub(x)<=0 then z==-x
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else
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let { var bool: p }
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in
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z >= x /\
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z >= -x /\
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z >= 0 /\ % This is just for preprocessor
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z <= max([ub(x), -lb(x)]) /\ % And this
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% z <= x \/ z <= -x %% simple
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aux_int_le_if_1(z, x, p) /\ %% even simpler
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aux_int_le_if_0(z, -x, p) /\
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int_le_reif(0, x, p) % with reifs
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%int_eq_reif(z, x, p) /\
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%int_eq_reif(z, -x, not p)
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endif
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;
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predicate int_min(var int: x, var int: y, var int: z) =
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array_int_minimum(z, [x, y]);
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predicate int_max(var int: x, var int: y, var int: z) =
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array_int_maximum(z, [x, y]);
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predicate float_abs(var float: x, var float: z) =
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if lb(x)>=0.0 then z==x
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elseif ub(x)<=0.0 then z==-x
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else
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let { var bool: p }
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in
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z >= x /\
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z >= -x /\
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z >= 0.0 /\ % This is just for preprocessor
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z <= max([ub(x), -lb(x)]) /\ % And this
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% z <= x \/ z <= -x
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aux_float_le_if_1(z, x, (p)) /\
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aux_float_le_if_0(z, -x, (p))
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% /\
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% float_le_reif(0.0, x, p) % with reifs - no point for floats? TODO
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% float_eq_reif(z, x, p) /\
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% float_eq_reif(z, -x, not p)
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endif;
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predicate float_min(var float: x, var float: y, var float: z) =
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array_float_minimum(z, [x, y]);
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predicate float_max(var float: x, var float: y, var float: z) =
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array_float_maximum(z, [x, y]);
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predicate array_int_minimum_I(var int: m, array[int] of var int: x) =
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let { int: n = length(x),
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constraint assert(1 == min(index_set(x)), " array_int_minimum_I: argument indexed not from 1??"),
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int: iMinUB = arg_min([ub(x[i]) | i in 1..n]),
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int: MinUB = ub(x[iMinUB]),
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set of int: sLBLess = { i | i in 1..n where lb(x[i])<MinUB },
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set of int: sUBEqual = { i | i in 1..n where ub(x[i])==MinUB },
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set of int: sActive = if card(sLBLess intersect sUBEqual)>0 then sLBLess
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else sLBLess union { iMinUB } endif,
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} in
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if 1==card(sActive) then
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m == x[min(sActive)]
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elseif MZN__MinMaxGeneral then
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fzn_array_float_minimum(m, x) %% Send to backend
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else
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let {
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array[1..n] of var int: p = [
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if i in sActive then let { var 0..1: pi } in pi else 0 endif | i in 1..n ],
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constraint 1==sum(p),
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constraint m >= lb_array(x),
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constraint m <= MinUB,
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} in
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forall (i in index_set(x))
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(
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if i in sActive %% for at least 1 element
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then
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m<=x[i] /\ aux_int_ge_if_1(m, x[i], p[i])
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endif ) %% -- exclude too big x[i]
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endif;
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predicate array_float_minimum_I(var float: m, array[int] of var float: x) =
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let { int: n = length(x),
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constraint assert(1 == min(index_set(x)), " array_float_minimum_I: argument indexed not from 1??"),
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int: iMinUB = arg_min([ub(x[i]) | i in 1..n]),
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float: MinUB = ub(x[iMinUB]),
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set of int: sLBLess = { i | i in 1..n where lb(x[i])<MinUB },
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set of int: sUBEqual = { i | i in 1..n where ub(x[i])==MinUB },
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set of int: sActive = if card(sLBLess intersect sUBEqual)>0 then sLBLess
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else sLBLess union { iMinUB } endif,
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} in
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if 1==card(sActive) then
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m == x[min(sActive)]
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elseif MZN__MinMaxGeneral then
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fzn_array_float_minimum(m, x) %% Send to backend
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else
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let {
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array[1..n] of var int: p = [
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if i in sActive then let { var 0..1: pi } in pi else 0 endif | i in 1..n ],
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constraint 1==sum(p),
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constraint m >= lb_array(x),
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constraint m <= MinUB,
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} in
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forall (i in index_set(x))
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(
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if i in sActive %% for at least 1 element
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then
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m<=x[i] /\ aux_float_ge_if_1(m, x[i], p[i])
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endif ) %% -- exclude too big x[i]
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/\
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if card(sActive)>1 /\ fMinimumCutsXZ then
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let {
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array[int] of float: AL = [ lb(x[i]) | i in 1..n],
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array[int] of int: srt = sort_by([i | i in 1..n], AL),
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%indices of lb in sorted order
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array[int] of float: AL_srt = [AL[srt[i]] | i in 1..n],
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array[int] of float: AU_srt = [ub(x[srt[i]]) | i in 1..n],
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array[int] of float: AM_srt = AL_srt ++ [MinUB]
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%% -- these are z-levels of extreme points
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} in
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forall (i in 2..n+1 where
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AM_srt[i]<=MinUB /\ %% this is a new "start level"
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AM_srt[i]!=AM_srt[i-1] )( %% and would produce a new cut
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m >= AM_srt[i]
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- sum(j in 1..i-1 where AL_srt[j]<AM_srt[i] /\ AL_srt[j]<AU_srt[j])
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( (AU_srt[j]-x[srt[j]]) * (AM_srt[i]-AL_srt[j]) / (AU_srt[j]-AL_srt[j]) ) :: MIP_cut
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)
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else true endif
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/\
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if card(sActive)>1 /\ fMinimumCutsXZB then
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array_var_float_element__XBZ_lb([ -x[i] | i in sActive ], [ p[i] | i in sActive ], -m) :: MIP_cut
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else true endif
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endif;
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%-----------------------------------------------------------------------------%
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% Multiplication and division
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predicate int_div(var int: x, var int: y, var int: q) =
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q == aux_int_division_modulo_fn(x,y)[1];
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predicate int_mod(var int: x, var int: y, var int: r) =
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r == aux_int_division_modulo_fn(x,y)[2];
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function array[int] of var int: aux_int_division_modulo_fn(var int: x, var int: y) =
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let {
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%% Domain of q
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set of int: dom_q =
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if lb(y)*ub(y)>0 then
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let {
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set of int: EP = { ub(x) div ub(y), ub(x) div lb(y), lb(x) div ub(y), lb(x) div lb(y) },
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} in min(EP)..max(EP)
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else
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let {
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int: mm = max( abs(lb(x)), abs(ub(x)) ),
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} in -mm..mm %% TODO case when -1 or 1 not in dom(x)
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endif,
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var dom_q: q;
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int: by = max(abs(lb(y)), abs(ub(y)));
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var -by+1..by-1: r;
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constraint x = y * q + r,
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constraint 0 <= x -> 0 <= r, %% which is 0 > x \/ 0 <= r
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constraint x < 0 -> r <= 0, %% which is x >= 0 \/ r <= 0
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% abs(r) < abs(y)
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var 1.. max(abs(lb(y)), abs(ub(y))): w = abs(y),
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constraint w > r /\ w > -r,
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} in
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[ q, r ];
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%% Can also have int_times(var float, var int) ......... TODO
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predicate int_times(int: x, var int: y, var int: z);
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predicate int_times(var int: x, int: y, var int: z) = int_times(y, x, z);
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predicate int_times(var int: x, var int: y, var int: z) =
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if 0..1==dom(x) /\ 0..1==dom(y) then bool_and__INT(x,y,z)
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elseif card(dom(x))==2 /\ card(dom(y))==2 /\ 0 in dom(x) /\ 0 in dom(y)
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then let {
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var 0..1: xn;
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var 0..1: yn;
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var 0..1: zn;
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constraint x=xn*max(dom(x) diff {0});
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constraint y=yn*max(dom(y) diff {0});
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constraint z=zn*max(dom(x) diff {0})*max(dom(y) diff {0});
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} in
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bool_and__INT(xn,yn,zn)
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elseif min(card(dom(x)), card(dom(y))) >= MZN__QuadrIntCard then
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fzn_int_times(x, y, z)
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elseif card(dom(x)) * card(dom(y)) > nMZN__UnarySizeMax_intTimes
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\/ ( fIntTimesBool /\ (
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%% Peter's idea for *bool. More optimal but worse values on carpet cutting.
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(card(dom(x))==2 /\ 0 in dom(x))
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\/ (card(dom(y))==2 /\ 0 in dom(y))
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) )
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then %% PARAM
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%% ALSO NO POINT IF <=4. TODO
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if card(dom(x)) > card(dom(y)) \/
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( card(dom(x))==card(dom(y)) /\ 0 in dom(y) /\ not (0 in dom(x)) )
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then int_times(y,x,z)
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else
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let {
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set of int: s = lb(x)..ub(x),
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set of int: r = {lb(x)*lb(y), lb(x)*ub(y), ub(x)*lb(y), ub(x)*ub(y)},
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array[s] of var min(r)..max(r): ady = array1d(s, [
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if d in dom(x) then d*y else min(r) endif | d in s ]) }
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in
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ady[x] = z %% use element()
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endif
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else
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int_times_unary(x, { }, y, z)
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endif;
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%% domx__ can be used to narrow domain... NOT IMPL.
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predicate int_times_unary(var int: x, set of int: domx__, var int: y, var int: z) =
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let {
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set of int: r = {lb(x)*lb(y), lb(x)*ub(y), ub(x)*lb(y), ub(x)*ub(y)},
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%% set of int: domx = if card(domx__)>0 then domx__ else dom(x) endif,
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array[int, int] of var int: pp=eq_encode(x, y)
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} in
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z>=min(r) /\ z<=max(r) /\
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z==sum(i in index_set_1of2(pp), j in index_set_2of2(pp))
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(i * j * pp[i, j]) /\
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forall(i in index_set_1of2(pp), j in index_set_2of2(pp)
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where not ((i*j) in dom(z))
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)(pp[i, j]==0)
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;
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predicate int_times_unary__NOFN(var int: x, set of int: domx__, var int: y, var int: z) =
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let {
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set of int: r = {lb(x)*lb(y), lb(x)*ub(y), ub(x)*lb(y), ub(x)*ub(y)},
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%% set of int: domx = if card(domx__)>0 then domx__ else dom(x) endif,
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array[int] of var int: pX = eq_encode(x),
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array[int] of var int: pY = eq_encode(y),
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array[int] of int: valX = [ v | v in index_set(pX) ], %% NOT domx.
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array[int] of int: valY = [ v | v in index_set(pY) ], %% -- according to eq_encode!
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array[index_set(valX), index_set(valY)] of var 0..1: pp %% both dim 1..
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} in
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if is_fixed(x) \/ is_fixed(y) then
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z==x*y
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else
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z>=min(r) /\ z<=max(r) /\
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sum(pp)==1 /\
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z==sum(i in index_set(valX), j in index_set(valY))
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(valX[i] * valY[j] * pp[i, j]) /\
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forall(i in index_set(valX))
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( pX[valX[i]] == sum(j in index_set(valY))( pp[i, j] ) ) /\
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forall(j in index_set(valY))
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( pY[valY[j]] == sum(i in index_set(valX))( pp[i, j] ) )
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endif;
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predicate float_times(var float: x, var float: y, var float: z) =
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if is_fixed(x) then
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z==fix(x)*y %%%%% Need to use fix() otherwise added to CSE & nothing happens
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elseif is_fixed(y) then
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z==x*fix(y)
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elseif MZN__QuadrFloat then
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fzn_float_times(x, y, z)
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else
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abort("Unable to create linear formulation for the `float_times(\(x), \(y), \(z))` constraint." ++
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" Define QuadrFloat=true if your linear solver supports quadratic constraints," ++
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" or use integer variables.")
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endif;
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%%%Define int_pow
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predicate int_pow( var int: x, var int: y, var int: r ) =
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let {
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array[ int, int ] of int: x2y = array2d( lb(x)..ub(x), lb(y)..ub(y),
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[ pow( X, Y ) | X in lb(x)..ub(x), Y in lb(y)..ub(y) ] )
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} in
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r == x2y[ x, y ];
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%%% Adding a version returning float for efficiency
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/** @group builtins.arithmetic Return \(\a x ^ {\a y}\) */
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function var float: pow_float(var int: x, var int: y) =
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let {
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int: yy = if is_fixed(y) then fix(y) else -1 endif;
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} in
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if yy = 0 then 1
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elseif yy = 1 then x else
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let { var float: r ::is_defined_var;
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constraint int_pow_float(x,y,r) ::defines_var(r);
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} in r
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endif;
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%%%Define int_pow_float
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predicate int_pow_float( var int: x, var int: y, var float: r ) =
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let {
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array[ int, int ] of float: x2y = array2d( lb(x)..ub(x), lb(y)..ub(y),
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[ pow( X, Y ) | X in lb(x)..ub(x), Y in lb(y)..ub(y) ] )
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} in
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r == x2y[ x, y ];
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%-----------------------------------------------------------------------------%
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% Array 'element' constraints
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predicate array_bool_element(var int: x, array[int] of bool: a, var bool: z) =
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array_int_element(x, arrayXd(a, [bool2int(a[i]) | i in index_set(a)]), bool2int(z));
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predicate array_var_bool_element(var int: x, array[int] of var bool: a,
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var bool: z) =
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array_var_int_element(x, arrayXd(a, [bool2int(a[i]) | i in index_set(a)]), bool2int(z));
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predicate array_int_element(var int: i00, array[int] of int: a, var int: z) =
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let {
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set of int: ix = index_set(a),
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constraint i00 in { i | i in ix where a[i] in dom(z) },
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} in %%% Tighten domain of i00 before dMin/dMax
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let {
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int: dMin = min(i in dom(i00))(a[i]),
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int: dMax = max(i in dom(i00))(a[i]),
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} in
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if dMin==dMax then
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z==dMin
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else
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z >= dMin /\
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z <= dMax /\
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let {
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int: nUBi00 = max(dom(i00)),
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int: nLBi00 = min(dom(i00)),
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int: nMinDist = min(i in nLBi00 .. nUBi00-1)(a[i+1]-a[i]),
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int: nMaxDist = max(i in nLBi00 .. nUBi00-1)(a[i+1]-a[i]),
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} in
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if nMinDist == nMaxDist then %% The linear case
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z == a[nLBi00] + nMinDist*(i00-nLBi00)
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else
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let {
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array[int] of var int: p = eq_encode(i00) %% this needs i00 in ix
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} %% Faster flattening than (i==i00) @2a9df1f7
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in
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sum(i in dom(i00))( a[i] * p[i] ) == z
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endif
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endif;
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predicate array_var_int_element(var int: i00, array[int] of var int: a,
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var int: z) =
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let {
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constraint i00 in { i | i in index_set(a) where
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0 < card(dom(a[i]) intersect dom(z)) },
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} in %% finish domain first
|
|
let {
|
|
int: minLB=min(i in dom(i00))(lb(a[i])),
|
|
int: maxUB=max(i in dom(i00))(ub(a[i]))
|
|
} in
|
|
if minLB==maxUB then
|
|
z==minLB
|
|
else
|
|
z >= minLB /\
|
|
z <= maxUB /\
|
|
if {0,1}==dom(i00) /*ub(i00)-lb(i00)==1*/ /*2==card( dom( i00 ) )*/ then
|
|
aux_int_eq_if_1(z, a[lb(i00)], (ub(i00)-i00)) /\
|
|
aux_int_eq_if_1(z, a[ub(i00)], (i00-lb(i00)))
|
|
else
|
|
let {
|
|
array[int] of var int: p = eq_encode(i00) %% this needs i00 in ix
|
|
} %% Faster flattening than (i==i00) @2a9df1f7
|
|
in
|
|
forall (i in dom(i00))(
|
|
aux_int_eq_if_1(z, a[i], p[i])
|
|
)
|
|
endif
|
|
endif;
|
|
|
|
predicate array_float_element(var int: i00, array[int] of float: a,
|
|
var float: z) =
|
|
let { set of int: ix = index_set(a),
|
|
constraint i00 in { i | i in ix where a[i]>=lb(z) /\ a[i]<=ub(z) },
|
|
} in %%% Tighten domain of i00 before dMin/dMax
|
|
let {
|
|
float: dMin = min(i in dom(i00))(a[i]),
|
|
float: dMax = max(i in dom(i00))(a[i]),
|
|
} in
|
|
if dMin==dMax then
|
|
z==dMin
|
|
else
|
|
z >= dMin /\
|
|
z <= dMax /\
|
|
let {
|
|
int: nUBi00 = max(dom(i00)),
|
|
int: nLBi00 = min(dom(i00)),
|
|
float: nMinDist = min(i in nLBi00 .. nUBi00-1)(a[i+1]-a[i]),
|
|
float: nMaxDist = max(i in nLBi00 .. nUBi00-1)(a[i+1]-a[i]),
|
|
} in
|
|
if nMinDist == nMaxDist then %% The linear case
|
|
z == a[nLBi00] + nMinDist*(i00-nLBi00)
|
|
else
|
|
let {
|
|
array[int] of var int: p = eq_encode(i00) %% this needs i00 in ix
|
|
} %% Faster flattening than (i==i00) @2a9df1f7
|
|
in
|
|
sum(i in dom(i00))( a[i] * p[i] ) == z
|
|
endif
|
|
endif;
|
|
|
|
predicate array_var_float_element(var int: i00, array[int] of var float: a,
|
|
var float: z) =
|
|
let { set of int: ix = index_set(a),
|
|
constraint i00 in { i | i in ix where
|
|
lb(a[i])<=ub(z) /\ ub(a[i])>=lb(z)
|
|
},
|
|
} in %% finish domain first
|
|
let {
|
|
float: minLB=min(i in dom(i00))(lb(a[i])),
|
|
float: maxUB=max(i in dom(i00))(ub(a[i]))
|
|
} in
|
|
if minLB==maxUB then
|
|
z==minLB
|
|
else
|
|
z >= minLB /\
|
|
z <= maxUB /\
|
|
if {0,1}==dom(i00) /*ub(i00)-lb(i00)==1*/ /*2==card( dom( i00 ) )*/ then
|
|
aux_float_eq_if_1(z, a[lb(i00)], (ub(i00)-i00)) /\
|
|
aux_float_eq_if_1(z, a[ub(i00)], (i00-lb(i00)))
|
|
else
|
|
%%% The convexified bounds seem slow for ^2 and ^3 equations:
|
|
% sum(i in dom(i01))( lb(a[i]) * (i==i00) ) <= z /\ %% convexify lower bounds
|
|
% sum(i in dom(i01))( ub(a[i]) * (i==i00) ) >= z /\ %% convexify upper bounds
|
|
let {
|
|
array[int] of var int: p = eq_encode(i00) %% this needs i00 in ix
|
|
} %% Faster flattening than (i==i00) @2a9df1f7
|
|
in
|
|
forall (i in dom(i00))(
|
|
aux_float_eq_if_1(z, a[i], p[i])
|
|
)
|
|
%% Cuts:
|
|
/\
|
|
if fElementCutsXZ then
|
|
array_var_float_element__ROOF([ a[i] | i in dom(i00) ], z) :: MIP_cut %% these 2 as user cuts - too slow
|
|
/\ array_var_float_element__ROOF([ -a[i] | i in dom(i00) ], -z) :: MIP_cut %% or even skip them
|
|
else true endif
|
|
/\
|
|
if fElementCutsXZB then
|
|
array_var_float_element__XBZ_lb([ a[i] | i in dom(i00) ], [ p[i] | i in dom(i00) ], z) :: MIP_cut
|
|
/\ array_var_float_element__XBZ_lb([ -a[i] | i in dom(i00) ], [ p[i] | i in dom(i00) ], -z) :: MIP_cut
|
|
else true endif
|
|
endif
|
|
endif;
|
|
|
|
%%% Facets on the upper surface of the z-a polytope
|
|
%%% Possible parameter: maximal number of first cuts taken only
|
|
predicate array_var_float_element__ROOF(array[int] of var float: a,
|
|
var float: z) =
|
|
let { set of int: ix = index_set(a),
|
|
int: n = length(a),
|
|
array[int] of float: AU = [ ub(a[i]) | i in 1..n],
|
|
array[int] of int: srt_ub = sort_by([i | i in 1..n], AU),
|
|
%indices of ub sorted up
|
|
array[int] of float: AU_srt_ub = [ub(a[srt_ub[i]]) | i in 1..n],
|
|
array[int] of float: AL_srt_ub = [lb(a[srt_ub[i]]) | i in 1..n],
|
|
array[int] of float: MaxLBFrom =
|
|
[ max(j in index_set(AL_srt_ub) where j>=i)(AL_srt_ub[j])
|
|
| i in 1..n ], %% direct, O(n^2)
|
|
array[int] of float: ULB = [
|
|
if 1==i then MaxLBFrom[1]
|
|
else max([AU_srt_ub[i-1], MaxLBFrom[i]])
|
|
endif | i in 1..n ]
|
|
} in
|
|
%%% "ROOF"
|
|
forall (i in 1..n where
|
|
if i==n then true else ULB[i]!=ULB[i+1] endif %% not the same base bound
|
|
)(
|
|
z <= ULB[i]
|
|
+ sum( j in i..n where AU_srt_ub[i] != AL_srt_ub[i] ) %% not a const
|
|
( (AU_srt_ub[j]-ULB[i]) * (a[srt_ub[j]]-AL_srt_ub[j]) / (AU_srt_ub[j]-AL_srt_ub[j]) ) )
|
|
;
|
|
|
|
predicate array_var_float_element__XBZ_lb(array[int] of var float: x, array[int] of var int: b, var float: z) =
|
|
if fUseXBZCutGen then
|
|
array_var_float_element__XBZ_lb__cutgen(x, b, z) :: MIP_cut
|
|
else
|
|
%% Adding some cuts a priori, also to make solver extract the variables
|
|
let {
|
|
int: i1 = min(index_set(x))
|
|
} in
|
|
(z <= sum(i in index_set(x))(ub(x[i]) * b[i])) %:: MIP_cut -- does not work to put them here TODO
|
|
/\
|
|
forall(i in index_set(x) intersect i1..(i1+19)) %% otherwise too many on amaze2
|
|
( assert(lb(x[i]) == -ub(-x[i]) /\ ub(x[i]) == -lb(-x[i]), " negated var's bounds should swap " ) /\
|
|
z <= x[i] + sum(j in index_set(x) where i!=j)((ub(x[j])-lb(x[i]))*b[j])) %:: MIP_cut %% (ub_j-lb_i) * b_j
|
|
/\
|
|
forall(i in index_set(x) intersect i1..(i1+19))
|
|
( z <= ub(x[i])*b[i] + sum(j in index_set(x) where i!=j)(x[j]+lb(x[j])*(b[j]-1)) ) %:: MIP_cut
|
|
/\
|
|
(z <= sum(i in index_set(x))(x[i] + lb(x[i]) * (b[i]-1))) %:: MIP_cut
|
|
endif;
|
|
|
|
%-----------------------------------------------------------------------------%
|
|
% Set constraints
|
|
%% ----------------------------------------------- (NO) SETS ----------------------------------------------
|
|
% XXX only for a fixed set here, general see below.
|
|
% Normally not called because all plugged into the domain.
|
|
% Might be called instead of set_in(x, var set of int s) if s gets fixed?
|
|
predicate set_in(var int: x, set of int: s__) =
|
|
let {
|
|
set of int: s = if has_bounds(x) then s__ intersect dom(x) else s__ endif,
|
|
constraint min(s) <= x,
|
|
constraint x <= max(s),
|
|
} in
|
|
if s = min(s)..max(s) then true
|
|
elseif fPostprocessDomains then
|
|
set_in__POST(x, s)
|
|
else %% Update eq_encode
|
|
let {
|
|
array[int] of var int: p = eq_encode(x);
|
|
} in
|
|
forall(i in index_set(p) diff s)(p[i]==0)
|
|
% let {
|
|
% array[int] of int: sL = [ e | e in s where not (e - 1 in s) ];
|
|
% array[int] of int: sR = [ e | e in s where not (e + 1 in s) ];
|
|
% array [index_set(sR)] of var 0..1: B;
|
|
% constraint assert(length(sR)==length(sL), "N of lb and ub of sub-intervals of a set should be equal");
|
|
% } in
|
|
% sum(B) = 1 %% use indicators
|
|
% /\
|
|
% x >= sum(i in index_set(sL))(B[i]*sL[i])
|
|
% /\
|
|
% x <= sum(i in index_set(sR))(B[i]*sR[i])
|
|
endif;
|
|
|
|
%%% for a fixed set
|
|
predicate set_in_reif(var int: x, set of int: s__, var bool: b) =
|
|
if is_fixed(b) then
|
|
if fix(b) then x in s__ else x in dom(x) diff s__ endif
|
|
elseif has_bounds(x) /\ not (s__ subset dom(x)) then
|
|
b <-> x in s__ intersect dom(x) %% Use CSE
|
|
else
|
|
let {
|
|
set of int: s = if has_bounds(x) then s__ intersect dom(x) else s__ endif,
|
|
} in
|
|
(
|
|
if dom(x) subset s then b==true
|
|
elseif card(dom(x) intersect s)==0 then b==false
|
|
elseif fPostprocessDomains then
|
|
set_in_reif__POST(x, s, b)
|
|
%% Bad. Very much so for CBC. 27.06.2019: elseif s == min(s)..max(s) then
|
|
%% b <-> (min(s) <= x /\ x <= max(s))
|
|
else
|
|
if card(dom(x))<=nMZN__UnaryLenMax_setInReif then %% PARAM TODO
|
|
let {
|
|
array[int] of var int: p = eq_encode(x);
|
|
} in
|
|
sum(i in s intersect dom(x))(p[i]) == bool2int(b)
|
|
else
|
|
bool2int(b) == fVarInBigSetOfInt(x, s)
|
|
endif
|
|
endif
|
|
)
|
|
endif;
|
|
|
|
% Alternative
|
|
predicate alt_set_in_reif(var int: x, set of int: s, var bool: b) =
|
|
b <->
|
|
exists(i in 1..length([ 0 | e in s where not (e - 1 in s) ]))(
|
|
let { int: l = [ e | e in s where not (e - 1 in s) ][i],
|
|
int: r = [ e | e in s where not (e + 1 in s) ][i] }
|
|
in
|
|
l <= x /\ x <= r
|
|
);
|
|
|
|
%%% for a fixed set
|
|
predicate set_in_imp(var int: x, set of int: s__, var bool: b) =
|
|
if is_fixed(b) then
|
|
if fix(b) then x in s__ else true endif
|
|
elseif has_bounds(x) /\ not (s__ subset dom(x)) then
|
|
b -> x in s__ intersect dom(x) %% Use CSE
|
|
else
|
|
let {
|
|
set of int: s = if has_bounds(x) then s__ intersect dom(x) else s__ endif,
|
|
} in
|
|
(
|
|
if dom(x) subset s then true
|
|
elseif card(dom(x) intersect s)==0 then b==false
|
|
elseif s == min(s)..max(s) then
|
|
(b -> min(s) <= x) /\ (b -> x <= max(s))
|
|
else
|
|
if card(dom(x))<=nMZN__UnaryLenMax_setInReif then %% PARAM TODO
|
|
let {
|
|
array[int] of var int: p = eq_encode(x);
|
|
} in
|
|
sum(i in s intersect dom(x))(p[i]) >= bool2int(b)
|
|
else
|
|
bool2int(b) <= fVarInBigSetOfInt(x, s)
|
|
endif
|
|
endif
|
|
)
|
|
endif;
|
|
|
|
function var 0..1: fVarInBigSetOfInt(var int: x, set of int: s)
|
|
= let {
|
|
array[int] of int: sL = [ e | e in s where not (e - 1 in s) ];
|
|
array[int] of int: sR = [ e | e in s where not (e + 1 in s) ];
|
|
constraint assert(length(sR)==length(sL), "N of lb and ub of sub-intervals of a set should be equal");
|
|
} in
|
|
sum(i in index_set(sL)) (bool2int(x>=sL[i] /\ x<=sR[i])); %% use indicators
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% OTHER SET STUFF COMING FROM nosets.mzn %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%-----------------------------------------------------------------------------%
|
|
%-----------------------------------------------------------------------------%
|
|
|
|
annotation bool_search(array[$X] of var bool: x, ann:a1, ann:a2, ann:a3) =
|
|
let { array[int] of var bool: xx = array1d(x) } in
|
|
int_search([bool2int(xx[i]) | i in index_set(xx)],a1,a2,a3);
|
|
|
|
annotation warm_start( array[int] of var bool: x, array[int] of bool: v ) =
|
|
warm_start( [ bool2int(x[i]) | i in index_set(x) ], [ bool2int(v[i]) | i in index_set(v) ] );
|
|
|
|
|
|
annotation sat_goal(var bool: b) = int_max_goal(b);
|
|
annotation int_max_goal(var int: x);
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DOMAIN POSTPROCESSING BUILT-INS %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
% Single variable: x = d <-> x_eq_d[d]
|
|
predicate equality_encoding__POST(var int: x, array[int] of var int: x_eq_d);
|
|
|
|
%%%%%%% var int: b: bool2int is a reverse_map, not passed to .fzn
|
|
predicate set_in__POST(var int: x, set of int: s__);
|
|
predicate set_in_reif__POST(var int: x, set of int: s__, var int: b);
|
|
|
|
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LOGICAL CONSTRAINTS TO THE SOLVER %%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%%%%%%% var int: b: bool2int is a reverse_map, not passed to .fzn => REPEAT TESTS. TODO
|
|
predicate int_lin_eq_reif__IND(array[int] of int: c, array[int] of var int: x, int: d, var int: b);
|
|
predicate int_lin_le_reif__IND(array[int] of int: c, array[int] of var int: x, int: d, var int: b);
|
|
predicate int_lin_ne__IND(array[int] of int: c, array[int] of var int: x, int: d);
|
|
predicate aux_int_le_zero_if_0__IND(var int: x, var int: b);
|
|
predicate float_lin_le_reif__IND(array[int] of float: c, array[int] of var float: x, float: d, var int: b);
|
|
predicate aux_float_eq_if_1__IND(var float: x, var float: y, var int: b);
|
|
predicate aux_float_le_zero_if_0__IND(var float: x, var int: b);
|
|
|
|
predicate array_int_minimum__IND(var int: m, array[int] of var int: x);
|
|
predicate array_int_maximum__IND(var int: m, array[int] of var int: x);
|
|
predicate array_float_minimum__IND(var float: m, array[int] of var float: x);
|
|
predicate array_float_maximum__IND(var float: m, array[int] of var float: x);
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% XBZ cut generator, currently CPLEX only %%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
predicate array_var_float_element__XBZ_lb__cutgen(array[int] of var float: x, array[int] of var int: b, var float: z);
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Quadratic expressions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
|
|
predicate fzn_float_times(var float: a, var float: b, var float: c);
|
|
predicate fzn_int_times(var int: a, var int: b, var int: c);
|
|
predicate fzn_array_float_minimum(var float: m, array[int] of var float: x);
|