1/*  $Id$
    2
    3    Part of CPL(R) (Constraint Logic Programming over Reals)
    4
    5    Author:        Leslie De Koninck
    6    E-mail:        Leslie.DeKoninck@cs.kuleuven.be
    7    WWW:           http://www.swi-prolog.org
    8		   http://www.ai.univie.ac.at/cgi-bin/tr-online?number+95-09
    9    Copyright (C): 2004, K.U. Leuven and
   10		   1992-1995, Austrian Research Institute for
   11		              Artificial Intelligence (OFAI),
   12			      Vienna, Austria
   13
   14    This software is part of Leslie De Koninck's master thesis, supervised
   15    by Bart Demoen and daily advisor Tom Schrijvers.  It is based on CLP(Q,R)
   16    by Christian Holzbaur for SICStus Prolog and distributed under the
   17    license details below with permission from all mentioned authors.
   18
   19    This program is free software; you can redistribute it and/or
   20    modify it under the terms of the GNU General Public License
   21    as published by the Free Software Foundation; either version 2
   22    of the License, or (at your option) any later version.
   23
   24    This program is distributed in the hope that it will be useful,
   25    but WITHOUT ANY WARRANTY; without even the implied warranty of
   26    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   27    GNU General Public License for more details.
   28
   29    You should have received a copy of the GNU Lesser General Public
   30    License along with this library; if not, write to the Free Software
   31    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
   32
   33    As a special exception, if you link this library with other files,
   34    compiled with a Free Software compiler, to produce an executable, this
   35    library does not by itself cause the resulting executable to be covered
   36    by the GNU General Public License. This exception does not however
   37    invalidate any other reasons why the executable file might be covered by
   38    the GNU General Public License.
   39*/
   40
   41:- module(clpcd_bb,
   42	[
   43	    bb_inf/5
   44	]).   45
   46:- use_module(library(clpcd/domain_ops)).   47:- use_module(library(clpcd/bv)).   48:- use_module(library(clpcd/nf)).   49:- use_module(library(clpcd/solve)).   50:- use_module(library(clpcd/detact)).   51
   52% bb_inf(Ints,Term,Inf)
   53%
   54% Finds the infimum of Term where the variables Ints are to be integers.
   55% The infimum is stored in Inf.
   56
   57bb_inf(CLP, Is, Term, Inf, Vertex) :-
   58	wait_linear(CLP, Term, Nf, bb_inf_internal(CLP, Is, Nf, Inf, Vertex)).
   59
   60% ---------------------------------------------------------------------
   61
   62% bb_inf_internal(Is,Lin,Inf,Vertex)
   63%
   64% Finds an infimum Inf for linear expression in normal form Lin, where
   65% all variables in Is are to be integers.
   66
   67bb_inf_internal(CLP, Is, Lin, _, _) :-
   68	bb_intern(Is, CLP, IsNf),
   69	nb_delete(prov_opt),
   70	repair(CLP, Lin, LinR),	% bb_narrow ...
   71	deref(CLP,LinR,Lind),
   72	var_with_def_assign(CLP, Dep, Lind),
   73	determine_active_dec(CLP, Lind),
   74	bb_loop(CLP, Dep, IsNf),
   75	fail.
   76bb_inf_internal(CLP, _, _, Inf, Vertex) :-
   77	nb_current(prov_opt,InfVal-Vertex),
   78	add_constraint(Inf =:= InfVal, CLP),
   79	nb_delete(prov_opt).
   80
   81% bb_loop(CLP, Opt, Is)
   82%
   83% Minimizes the value of Opt where variables Is have to be integer values.
   84% This predicate can be backtracked to try different strategies.
   85
   86bb_loop(CLP, Opt, Is) :-
   87	bb_reoptimize(CLP, Opt, Inf),
   88	bb_better_bound(CLP, Inf),
   89	vertex_value(Is, CLP, Ivs),
   90	(   bb_first_nonint(CLP, Is, Ivs, Viol, Floor, Ceiling)
   91	->  bb_branch(CLP, Viol, Floor, Ceiling),
   92	    bb_loop(CLP, Opt, Is)
   93	;   round_values(Ivs,CLP,RoundVertex),
   94	    nb_setval(prov_opt,Inf-RoundVertex) % new provisional optimum
   95	).
   96
   97% bb_reoptimize(Obj,Inf)
   98%
   99% Minimizes the value of Obj and puts the result in Inf.
  100% This new minimization is necessary as making a bound integer may yield a
  101% different optimum. The added inequalities may also have led to binding.
  102
  103bb_reoptimize(CLP, Obj, Inf) :-
  104	var(Obj),
  105        !,
  106	iterate_dec(CLP, Obj, Inf).
  107bb_reoptimize(_, Obj, Inf) :-
  108	Inf = Obj.
  109
  110% bb_better_bound(Inf)
  111%
  112% Checks if the new infimum Inf is better than the previous one (if such exists).
  113
  114bb_better_bound(CLP, Inf) :-
  115	nb_current(prov_opt,Inc-_), !,
  116	compare_d(CLP, <, Inf, Inc).
  117bb_better_bound(_, _).
  118
  119% bb_branch(V,U,L)
  120%
  121% Stores that V =< U or V >= L, can be used for different strategies within bb_loop/3.
  122
  123bb_branch(CLP, V, U, _) :- add_constraint(V =< U, CLP).
  124bb_branch(CLP, V, _, L) :- add_constraint(V >= L, CLP).
  125
  126% bb_first_nonint(Ints,Rhss,Viol,Floor,Ceiling)
  127%
  128% Finds the first variable in Ints which doesn't have an active integer bound.
  129% Rhss contain the Rhs (R + I) values corresponding to the variables.
  130% The first variable that hasn't got an active integer bound, is returned in
  131% Viol. The floor and ceiling of its actual bound is returned in Floor and Ceiling.
  132
  133bb_first_nonint(CLP, [I|Is], [Rhs|Rhss], Viol, F, C) :-
  134	(   floor_d(CLP, Rhs, Floor),
  135            ceiling_d(CLP, Rhs, Ceiling),
  136            compare_d(CLP, <, epsilon, min(Rhs-Floor, Ceiling-Rhs))
  137	->  Viol = I,
  138            F = Floor,
  139            C = Ceiling
  140        ;   bb_first_nonint(CLP, Is, Rhss, Viol, F, C)
  141	).
  142
  143% round_values([X|Xs],CLP,[Xr|Xrs])
  144%
  145% Rounds of the values of the first list into the second list.
  146
  147round_values([],_,[]).
  148round_values([X|Xs],CLP,[Y|Ys]) :-
  149        eval_d(CLP, round(X), Y),
  150	round_values(Xs,CLP,Ys).
  151
  152% bb_intern([X|Xs],[Xi|Xis])
  153%
  154% Turns the elements of the first list into integers into the second
  155% list via bb_intern/3.
  156
  157bb_intern([], _, []).
  158bb_intern([X|Xs], CLP, [Xi|Xis]) :-
  159	nf(X, CLP, Xnf),
  160	bb_intern(Xnf, CLP, Xi, X),
  161	bb_intern(Xs, CLP, Xis).
  162
  163
  164% bb_intern(Nf,X,Term)
  165%
  166% Makes sure that Term which is normalized into Nf, is integer.
  167% X contains the possibly changed Term. If Term is a variable,
  168% then its bounds are hightened or lowered to the next integer.
  169% Otherwise, it is checked it Term is integer.
  170
  171bb_intern([], _, X, _) :-
  172	!,
  173	X = 0.
  174bb_intern([v(I,[])], CLP, X, _) :-
  175	!,
  176	X = I,
  177        compare_d(CLP, =, I, integer(I)).
  178bb_intern([v(One,[V^1])], CLP, X, _) :-
  179        compare_d(CLP, =, One, 1),
  180	!,
  181	V = X,
  182	bb_narrow_lower(CLP, X),
  183	bb_narrow_upper(CLP, X).
  184bb_intern(_, CLP, _, Term) :-
  185	throw(instantiation_error(bb_inf(CLP, Term, _, _),1)).
  186
  187% bb_narrow_lower(X)
  188%
  189% Narrows the lower bound so that it is an integer bound.
  190% We do this by finding the infimum of X and asserting that X
  191% is larger than the first integer larger or equal to the infimum
  192% (second integer if X is to be strict larger than the first integer).
  193
  194bb_narrow_lower(CLP, X) :-
  195	(   inf(CLP, X, Inf)
  196	->  ceiling_d(CLP, Inf, Bound),
  197	    (   entailed(CLP, X > Bound)
  198            ->  add_constraint(X >= Bound+1, CLP)
  199	    ;   add_constraint(X >= Bound,   CLP)
  200	    )
  201	;   true
  202	).
  203
  204% bb_narrow_upper(X)
  205%
  206% See bb_narrow_lower/1. This predicate handles the upper bound.
  207
  208bb_narrow_upper(CLP, X) :-
  209	(   sup(CLP, X, Sup)
  210	->  floor_d(CLP, Sup, Bound),
  211	    (   entailed(CLP, X < Bound)
  212            ->  add_constraint(X =< Bound-1, CLP)
  213	    ;   add_constraint(X =< Bound,   CLP)
  214	    )
  215	;   true
  216	)