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buildtools/ppl/tests/MIP_Problem/mipproblem1.cc
Jerome Duval 5873a060ca imported PPL 0.11.1 and CLooG 0.18.0. 
* these are dependencies for gcc 4 Graphite engine build.
* CLooG 0.18.0 includes ISL 0.11.1 which is the backend that the build script enables.
* PPL is needed by GCC build even if it isn't the chosen backend.
2013-04-06 15:10:34 +02:00

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/* Test the MIP_Problem class.
Copyright (C) 2001-2010 Roberto Bagnara <bagnara@cs.unipr.it>
Copyright (C) 2010-2011 BUGSENG srl (http://bugseng.com)
This file is part of the Parma Polyhedra Library (PPL).
The PPL is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 3 of the License, or (at your
option) any later version.
The PPL is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02111-1307, USA.
For the most up-to-date information see the Parma Polyhedra Library
site: http://www.cs.unipr.it/ppl/ . */
#include "ppl_test.hh"
namespace {
bool
test01() {
Variable X01(0);
Variable X02(1);
Variable X03(2);
Variable X04(3);
Variable X05(4);
Variable X06(5);
Variable X07(6);
Variable X08(7);
Variable X09(8);
Variable X10(9);
Variable X11(10);
Variable X12(11);
Variable X13(12);
Variable X14(13);
Variable X15(14);
Variable X16(15);
Variable X17(16);
Variable X18(17);
Variable X19(18);
Variable X20(19);
Variable X21(20);
Variable X22(21);
Variable X23(22);
Variable X24(23);
Variable X25(24);
Variable X26(25);
Variable X27(26);
Variable X28(27);
Variable X29(28);
Variable X30(29);
Variable X31(30);
Variable X32(31);
Variable X33(32);
Variable X34(33);
Variable X35(34);
Variable X36(35);
Variable X37(36);
Variable X38(37);
Variable X39(38);
Constraint_System cs;
cs.insert(X01 - X02 - X03 + 0*X39 == 0);
cs.insert(Coefficient("2386907802506363")*X01 - X04 == 0);
cs.insert(-X01 >= -80);
cs.insert(X02 - Coefficient("3152519739159347")*X14 >= 0);
cs.insert(X06 + X07 + X08 + X09 - X14 - X15 == 0);
cs.insert(Coefficient("2386907802506363")*X06
+ Coefficient("2386907802506363")*X07
+ Coefficient("1080863910568919")*X08
+ Coefficient("7746191359077253")*X09
- X16 == 0);
cs.insert(-X06 + X10 >= -80);
cs.insert(-X07 + X11 >= 0);
cs.insert(-X08 + X12 >= 0);
cs.insert(-X09 + X13 >= 0);
cs.insert(X22 - X23 - X24 - X25 == 0);
cs.insert(Coefficient("7746191359077253")*X22 - X26 == 0);
cs.insert(-X22 >= -500);
cs.insert(X23 - Coefficient("3152519739159347")*X36 >= 0);
cs.insert(Coefficient("7746191359077253")*X28
+ Coefficient("7746191359077253")*X29
+ Coefficient("3512807709348987")*X30
+ Coefficient("3332663724254167")*X31
- X38 == 0);
cs.insert(X28 + X29 + X30 + X31 - X36 + X37 + X39 == 44);
cs.insert(-X28 + X32 >= -500);
cs.insert(-X29 + X33 >= 0);
cs.insert(-X30 + X34 >= 0);
cs.insert(-X31 + X35 >= 0);
cs.insert(Coefficient("-2661627379775963")*X10
- Coefficient("2686397177726501")*X11
- Coefficient("5422333951354077")*X12
- Coefficient("5469621747441467")*X13
+ X25
- Coefficient("2466846695892189")*X32
- Coefficient("4996743786567565")*X33
- Coefficient("5064297780978123")*X34
- Coefficient("641481471923585")*X35 >= 0);
cs.insert(X03 - Coefficient("7854277750134145")*X22 >= 0);
cs.insert(X15
- Coefficient("7854277750134145")*X28
- Coefficient("7782220156096217")*X29
- Coefficient("7782220156096217")*X30
- Coefficient("7710162562058289")*X31 >= 0);
cs.insert(Coefficient("-5422333951354077")*X01 + X24 >= 0);
cs.insert(X21 >= 2);
cs.insert(-X16 - X38 >= -300);
for (dimension_type i = X01.id(); i <= X39.id(); ++i)
cs.insert(Variable(i) >= 0);
// Cost function.
Linear_Expression cost(-10*X02 - 8*X14 - 15*X23 - 12*X36 + 250*X39);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
if (mip.solve() != OPTIMIZED_MIP_PROBLEM)
return false;
// Computed numerator and denominator.
Coefficient num;
Coefficient den;
mip.optimal_value(num, den);
nout << "Optimum value = " << num << "/" << den << endl;
Coefficient num_kr = 11000;
Coefficient den_kr = 1;
if (num != num_kr || den != den_kr)
return false;
// The feasible / optimizing point.
Generator pg = mip.optimizing_point();
nout << "Optimizing point = ";
print_generator(pg);
// Making mip unfeasible.
Constraint_System further_cs;
further_cs.insert(X05 >= 5);
further_cs.insert(X05 <= 3);
mip.add_constraints(further_cs);
return !mip.is_satisfiable();
}
bool
test02() {
Variable A(0);
Variable B(1);
Variable C(2);
Variable D(3);
Variable E(4);
Variable F(5);
Variable G(6);
Variable H(7);
// Cost function
Linear_Expression cost(-26*A + 343*B + 1233*D - C + F);
// Feasible region.
Constraint_System cs;
cs.insert(A - B + C >= 24);
cs.insert(B <= 320);
cs.insert(A + B + 2*D == 23);
cs.insert(A + 2*B + E == 4112);
cs.insert(7*A + 5*B + F <= 200);
cs.insert(138*A + 2*G == 25);
cs.insert(23*A + 342*B - 34*H == 99);
for (dimension_type i = A.id(); i <= H.id(); ++i)
cs.insert(Variable(i) >= 0);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
Generator pg = mip.optimizing_point();
nout << "Optimizing point = ";
print_generator(pg);
Generator pg_kr = point();
pg_kr = point(22*B + 1846*C + 863*D + 312468*E + 15090*F + 950*G + 0*H, 76);
if (pg != pg_kr)
return false;
Coefficient num;
Coefficient den;
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
Coefficient num_kr = 1084869;
Coefficient den_kr = 76;
if (num != num_kr || den != den_kr)
return false;
// Reoptimize using another objective function.
Linear_Expression new_cost = -51*A + 632*B;
mip.set_objective_function(new_cost);
pg = mip.optimizing_point();
nout << "Optimizing point = ";
print_generator(pg);
pg_kr = point(782*B + 1598*C + 138244*E + 2890*F + 425*G + 7767*H, 34);
if (pg != pg_kr)
return false;
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
num_kr = 14536;
den_kr = 1;
if (num != num_kr || den != den_kr)
return false;
// Reoptimize after changing optimization mode.
mip.set_optimization_mode(MINIMIZATION);
pg = mip.optimizing_point();
nout << "Optimizing point = ";
print_generator(pg);
pg_kr = point(17100*A + 26174*B + 2274482*C
+ 1063871*D + 388070456*E + 18627830*F + 0*H,
94392);
if (pg != pg_kr)
return false;
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
num_kr = 3917467;
den_kr = 23598;
return num == num_kr && den == den_kr;
}
bool
test03() {
Variable A(0);
Variable B(1);
Variable C(2);
Variable D(3);
Constraint_System cs;
cs.insert(Coefficient("2251799813685248")*A
>= Coefficient("-5895288448651847"));
cs.insert(Coefficient("5895288437392848")*A
+ Coefficient("3643488632714799")*B
- Coefficient("2251799813685248")*C
>= Coefficient("-19077554137963492"));
cs.insert(Coefficient("5895288437392848")*A +
Coefficient("3643488632714799")*B
+ Coefficient("2251799813685248")*C >=
Coefficient("-19077554137963492"));
cs.insert(Coefficient("11790576874785696")*A
+ Coefficient("4503599627370496")*B
+ Coefficient("7286977274436797")*D
>= Coefficient("-38155108284934184"));
cs.insert(Coefficient("11790576874785696")*A
+ Coefficient("4503599627370496")*B
- Coefficient("7286977274436797")*D
>= Coefficient("-38155108284934184"));
cs.insert(Coefficient("11790576879289294")*A
+ Coefficient("7286977274436797")*C
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("11790576879289294")*A
+ Coefficient("7286977274436797")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("11790576879289294")*A
- Coefficient("7286977274436797")*C
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("11790576879289294")*A
- Coefficient("7286977274436797")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("2947644225451823")*A
- Coefficient("1125899906842624")*B
+ Coefficient("1821744319735099")*D
>= Coefficient("-9538777088122044"));
cs.insert(Coefficient("11790576892800094")*A
- Coefficient("4503599627370496")*B
- Coefficient("7286977274436797")*D
>= Coefficient("-38155108325466584"));
cs.insert(Coefficient("5895288437392848")*A
- Coefficient("3643488630462999")*B
+ Coefficient("2251799813685248")*C
>= Coefficient("-19077554133459892"));
cs.insert(Coefficient("2947644218696424")*A
- Coefficient("1821744320860999")*B
- Coefficient("1125899906842624")*C
>= Coefficient("-9538777072359446"));
cs.insert(Coefficient("7286977269933197")*A
+ Coefficient("11790576924325290")*B
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108379509776"));
cs.insert(Coefficient("7286977269933197")*A
+ Coefficient("11790576924325290")*B
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108379509776"));
cs.insert(Coefficient("562949953421312")*A
+ Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644226577723"));
cs.insert(Coefficient("562949953421312")*A
+ Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
- Coefficient("562949953421312")*D
>= Coefficient("-2947644226577723"));
cs.insert(Coefficient("562949953421312")*A
+ Coefficient("562949953421312")*B
- Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644225451823"));
cs.insert(Coefficient("562949953421312")*A
+ Coefficient("562949953421312")*B
- Coefficient("562949953421312")*C
- Coefficient("562949953421312")*D
>= Coefficient("-2947644225451823"));
cs.insert(Coefficient("7286977269933197")*A
+ Coefficient("4503599627370496")*B
+ Coefficient("11790576865778496")*C
>= Coefficient("-38155108266919784"));
cs.insert(Coefficient("7286977251918799")*A
+ Coefficient("4503599627370496")*B
- Coefficient("11790576870282096")*C
>= Coefficient("-38155108244401792"));
cs.insert(Coefficient("1821744320860999")*A
+ Coefficient("1125899906842624")*C
+ Coefficient("2947644226577723")*D
>= Coefficient("-9538777093751544"));
cs.insert(Coefficient("1821744320860999")*A
+ Coefficient("1125899906842624")*C
- Coefficient("2947644226577723")*
D >= Coefficient("-9538777093751544"));
cs.insert(Coefficient("1821744320860999")*A
- Coefficient("1125899906842624")*C
+ Coefficient("2947644228829523")*D
>= Coefficient("-9538777096003344"));
cs.insert(Coefficient("1821744320860999")*A
- Coefficient("1125899906842624")*C
- Coefficient("2947644228829523")*D
>= Coefficient("-9538777096003344"));
cs.insert(Coefficient("3643488664239996")*A
- Coefficient("2251799813685248")*B
+ Coefficient("5895288468918045")*C
>= Coefficient("-19077554257308884"));
cs.insert(Coefficient("3643488652980997")*A
- Coefficient("2251799813685248")*B
- Coefficient("5895288468918045")*C
>= Coefficient("-19077554232539084"));
cs.insert(Coefficient("562949953421312")*A
- Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644226577723"));
cs.insert(Coefficient("562949953421312")*A
- Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
- Coefficient("562949953421312")*D
>= Coefficient("-2947644229392473"));
cs.insert(Coefficient("562949953421312")*A
- Coefficient("562949953421312")*B
- Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644227140673"));
cs.insert(Coefficient("562949953421312")*A
- Coefficient("562949953421312")*B
- Coefficient("562949953421312")*C
- Coefficient("562949953421312")*D
>= Coefficient("-2947644227703623"));
cs.insert(Coefficient("7286977314969193")*A
- Coefficient("11790576906310892")*B
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108447063768"));
cs.insert(Coefficient("3643488655232797")*A
- Coefficient("5895288446400047")*B
- Coefficient("2251799813685248")*D
>= Coefficient("-19077554203265688"));
cs.insert(Coefficient("4503599627370496")*A
+ Coefficient("11790576753188506")*B
+ Coefficient("7286977179861205")*C
>= Coefficient("-38155107920142616"));
cs.insert(Coefficient("4503599627370496")*A
+ Coefficient("11790576766699304")*B
- Coefficient("7286977179861205")*C
>= Coefficient("-38155107965178608"));
cs.insert(Coefficient("4503599627370496")*A
+ Coefficient("7286977157343207")*B
+ Coefficient("11790576712656108")*D
>= Coefficient("-38155107816559824"));
cs.insert(Coefficient("2251799813685248")*A
+ Coefficient("3643488592182402")*B
- Coefficient("5895288374342453")*D
>= Coefficient("-19077553960071308"));
cs.insert(Coefficient("4503599627370496")*A
+ Coefficient("11790576753188506")*C
+ Coefficient("7286977175357605")*D
>= Coefficient("-38155107924646216"));
cs.insert(Coefficient("2251799813685248")*A
+ Coefficient("5895288390105051")*C
- Coefficient("3643488594434202")*D
>= Coefficient("-19077553996100104"));
cs.insert(Coefficient("2251799813685248")*A
- Coefficient("5895288421630249")*C
+ Coefficient("3643488619204000")*D
>= Coefficient("-19077554088423896"));
cs.insert(Coefficient("4503599627370496")*A
- Coefficient("11790576865778496")*C
- Coefficient("7286977247415199")*D
>= Coefficient("-38155108244401792"));
cs.insert(Coefficient("4503599627370496")*A
- Coefficient("7286977247415199")*B
+ Coefficient("11790576888296494")*D
>= Coefficient("-38155108307452184"));
cs.insert(Coefficient("2251799813685248")*A
- Coefficient("3643488639470198")*B
- Coefficient("5895288464414445")*D
>= Coefficient("-19077554210021088"));
cs.insert(Coefficient("2251799813685248")*A
- Coefficient("5895288428385648")*B
+ Coefficient("3643488630462999")*C
>= Coefficient("-19077554131208092"));
cs.insert(Coefficient("4503599627370496")*A
- Coefficient("11790576843260498")*B
- Coefficient("7286977224897201")*C
>= Coefficient("-38155108163336992"));
cs.insert(Coefficient("1125899906842624")*B
>= Coefficient("-2947644227703623"));
cs.insert(Coefficient("5895288459910846")*B
+ Coefficient("2251799813685248")*C
+ Coefficient("3643488630462999")*D
>= Coefficient("-19077554198762088"));
cs.insert(Coefficient("5895288457659046")*B
+ Coefficient("2251799813685248")*C
- Coefficient("3643488628211199")*D
>= Coefficient("-19077554189754888"));
cs.insert(Coefficient("11790576915318092")*B
- Coefficient("4503599627370496")*C
+ Coefficient("7286977269933197")*D
>= Coefficient("-38155108393020576"));
cs.insert(Coefficient("5895288457659046")*B
- Coefficient("2251799813685248")*C
- Coefficient("3643488632714799")*D
>= Coefficient("-19077554187503088"));
cs.insert(Coefficient("7286977292451195")*B
+ Coefficient("11790576919821692")*C
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108433552976"));
cs.insert(Coefficient("3643488664239996")*B
+ Coefficient("5895288486932443")*C
- Coefficient("2251799813685248")*D
>= Coefficient("-19077554304596680"));
cs.insert(Coefficient("3643488643973798")*B
- Coefficient("5895288446400047")*C
+ Coefficient("2251799813685248")*D
>= Coefficient("-19077554180747688"));
cs.insert(Coefficient("7286977314969193")*B
- Coefficient("11790576937836090")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108510114168"));
cs.insert(Coefficient("4503599627370496")*B
+ Coefficient("7286977247415199")*C
+ Coefficient("11790576883792894")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("4503599627370496")*B
+ Coefficient("7286977251918799")*C
- Coefficient("11790576883792894")*D
>= Coefficient("-38155108280430584"));
cs.insert(Coefficient("4503599627370496")*B
- Coefficient("7286977229400801")*C
+ Coefficient("11790576852267696")*D
>= Coefficient("-38155108181351392"));
cs.insert(Coefficient("1125899906842624")*D
>= Coefficient("-2947644225451823"));
cs.insert(Coefficient("4503599627370496")*B
- Coefficient("7286977229400801")*C
- Coefficient("11790576852267696")*D
>= Coefficient("-38155108167840592"));
cs.insert(Coefficient("-2251799813685248")*D
>= Coefficient("-5895288448651847"));
cs.insert(Coefficient("2251799813685248")*C
>= Coefficient("-5895288446400047"));
cs.insert(Coefficient("-2251799813685248")*C
>= Coefficient("-5895288444148247"));
cs.insert(Coefficient("-1125899906842624")*B
+ Coefficient("1821744321986899")*C
+ Coefficient("2947644226577723")*D
>= Coefficient("-9538777088122044"));
cs.insert(Coefficient("-3643488607945001")*B
+ Coefficient("5895288414874849")*C
+ Coefficient("2251799813685248")*D
>= Coefficient("-19077554059150500"));
cs.insert(Coefficient("-4503599627370496")*B
+ Coefficient("7286977292451195")*C
- Coefficient("11790576906310892")*D
>= Coefficient("-38155108343480984"));
cs.insert(Coefficient("-7286977220393601")*B
+ Coefficient("11790576829749698")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108086775800"));
cs.insert(Coefficient("-4503599627370496")*B
- Coefficient("7286977274436797")*C
+ Coefficient("11790576901807292")*D
>= Coefficient("-38155108325466584"));
cs.insert(Coefficient("-3643488605693201")*B
- Coefficient("5895288414874849")*C
+ Coefficient("2251799813685248")*D
>= Coefficient("-19077554059150500"));
cs.insert(Coefficient("-1125899906842624")*B
- Coefficient("1821744319735099")*C
- Coefficient("2947644225451823")*D
>= Coefficient("-9538777079114846"));
cs.insert(Coefficient("-7286977220393601")*B
- Coefficient("11790576834253298")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108113797400"));
cs.insert(Coefficient("-5895288462162645")*B
+ Coefficient("2251799813685248")*C
+ Coefficient("3643488639470198")*D
>= Coefficient("-19077554144718892"));
cs.insert(Coefficient("-11790576924325290")*B
- Coefficient("4503599627370496")*C
+ Coefficient("7286977292451195")*D
>= Coefficient("-38155108320962984"));
cs.insert(Coefficient("-5895288468918045")*B
+ Coefficient("2251799813685248")*C
- Coefficient("3643488641721998")*D
>= Coefficient("-19077554160481492"));
cs.insert(Coefficient("-11790576928828890")*B
- Coefficient("4503599627370496")*C
- Coefficient("7286977292451195")*D
>= Coefficient("-38155108329970184"));
cs.insert(Coefficient("-281474976710656")*B
>= Coefficient("-736911053829681"));
cs.insert(Coefficient("-4503599627370496")*A
+ Coefficient("11790576658612912")*B
+ Coefficient("7286977125818009")*C
>= Coefficient("-38155107627408640"));
cs.insert(Coefficient("-2251799813685248")*A
+ Coefficient("5895288336061856")*B
- Coefficient("3643488560657205")*C
>= Coefficient("-19077553829466920"));
cs.insert(Coefficient("-2251799813685248")*A
+ Coefficient("3643488535887407")*B
+ Coefficient("5895288288774060")*D
>= Coefficient("-19077553683099932"));
cs.insert(Coefficient("-7286977274436797")*A
+ Coefficient("11790576766699304")*B
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108032732608"));
cs.insert(Coefficient("-4503599627370496")*A
+ Coefficient("7286977098796411")*B
- Coefficient("11790576609073318")*D
>= Coefficient("-38155107483293448"));
cs.insert(Coefficient("-7286977301458395")*A
+ Coefficient("11790576735174106")*B
- Coefficient("4503599627370496")*D
>= Coefficient("-38155107983193008"));
cs.insert(Coefficient("-4503599627370496")*A
+ Coefficient("11790576708152508")*C
+ Coefficient("7286977148336007")*D
>= Coefficient("-38155107771523824"));
cs.insert(Coefficient("-281474976710656")*A
+ Coefficient("281474976710656")*B
+ Coefficient("281474976710656")*C
+ Coefficient("281474976710656")*D
>= Coefficient("-1473822119481311"));
cs.insert(Coefficient("-1125899906842624")*A
+ Coefficient("2947644178164027")*C
- Coefficient("1821744285958102")*D
>= Coefficient("-9538776941755056"));
cs.insert(Coefficient("-1125899906842624")*A
+ Coefficient("1125899906842624")*B
+ Coefficient("1125899906842624")*C
- Coefficient("1125899906842624")*D
>= Coefficient("-5895288471169845"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("11790576856771296")*C
+ Coefficient("7286977247415199")*D
>= Coefficient("-38155108221883792"));
cs.insert(Coefficient("-1125899906842624")*A
+ Coefficient("1125899906842624")*B
- Coefficient("1125899906842624")*C
+ Coefficient("1125899906842624")*D
>= Coefficient("-5895288471169845"));
cs.insert(Coefficient("-140737488355328")*A
- Coefficient("368455526774103")*C
- Coefficient("227718038700250")*D
>= Coefficient("-1192347131793131"));
cs.insert(Coefficient("-1125899906842624")*A
+ Coefficient("1125899906842624")*B
- Coefficient("1125899906842624")*C
- Coefficient("1125899906842624")*D
>= Coefficient("-5895288464414445"));
cs.insert(Coefficient("-3643488643973798")*A
+ Coefficient("2251799813685248")*B
+ Coefficient("5895288441896447")*C
>= Coefficient("-19077554158229692"));
cs.insert(Coefficient("-7286977296954795")*A
+ Coefficient("4503599627370496")*B
- Coefficient("11790576892800094")*C
>= Coefficient("-38155108352488176"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("7286977269933197")*B
+ Coefficient("11790576924325290")*D
>= Coefficient("-38155108411034976"));
cs.insert(Coefficient("-3643488639470198")*A
+ Coefficient("2251799813685248")*C
+ Coefficient("5895288466666245")*D
>= Coefficient("-19077554219028288"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("7286977296954795")*B
- Coefficient("11790576955850488")*D
>= Coefficient("-38155108514617768"));
cs.insert(Coefficient("-7286977251918799")*A
+ Coefficient("4503599627370496")*C
- Coefficient("11790576892800094")*D
>= Coefficient("-38155108311955784"));
cs.insert(Coefficient("-3643488655232797")*A
- Coefficient("2251799813685248")*C
+ Coefficient("5895288480177044")*D
>= Coefficient("-19077554264064284"));
cs.insert(Coefficient("-1821744320860999")*A
- Coefficient("1125899906842624")*C
- Coefficient("2947644229955423")*D
>= Coefficient("-9538777099381044"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("11790576874785696")*B
+ Coefficient("7286977269933197")*C
>= Coefficient("-38155108302948584"));
cs.insert(Coefficient("-7286977274436797")*A
- Coefficient("4503599627370496")*B
+ Coefficient("11790576937836090")*C
>= Coefficient("-38155108424545776"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("11790576802728102")*B
- Coefficient("7286977197875603")*C
>= Coefficient("-38155108019221808"));
cs.insert(Coefficient("-3643488664239996")*A
- Coefficient("2251799813685248")*B
- Coefficient("5895288493687843")*C
>= Coefficient("-19077554284330480"));
cs.insert(Coefficient("-562949953421312")*A
- Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644250784571"));
cs.insert(Coefficient("-281474976710656")*A
- Coefficient("281474976710656")*B
+ Coefficient("281474976710656")*C
- Coefficient("281474976710656")*D
>= Coefficient("-1473822131021785"));
cs.insert(Coefficient("-1125899906842624")*A
- Coefficient("1125899906842624")*B
- Coefficient("1125899906842624")*C
+ Coefficient("1125899906842624")*D
>= Coefficient("-5895288464414445"));
cs.insert(Coefficient("-1125899906842624")*A
- Coefficient("1125899906842624")*B
- Coefficient("1125899906842624")*C
- Coefficient("1125899906842624")*D
>= Coefficient("-5895288468918045"));
cs.insert(Coefficient("-3643488412038417")*A
- Coefficient("5895288318047457")*B
+ Coefficient("2251799813685248")*D
>= Coefficient("-19077553665085532"));
cs.insert(Coefficient("-1821744199263809")*A
- Coefficient("2947644153394229")*B
- Coefficient("1125899906842624")*D
>= Coefficient("-9538776813402468"));
cs.insert(Coefficient("-5895288378846052")*A
+ Coefficient("3643488632714799")*B
+ Coefficient("2251799813685248")*C
>= Coefficient("-19077554023121704"));
cs.insert(Coefficient("-11790576834253298")*A
+ Coefficient("7286977314969193")*B
- Coefficient("4503599627370496")*C
>= Coefficient("-38155108302948584"));
cs.insert(Coefficient("-736911041726257")*A
+ Coefficient("281474976710656")*B
+ Coefficient("455436077400500")*D
>= Coefficient("-2384694241068264"));
cs.insert(Coefficient("-5895288347320855")*A
+ Coefficient("2251799813685248")*B
- Coefficient("3643488616952200")*D
>= Coefficient("-19077553951064108"));
cs.insert(Coefficient("-2947644201807925")*A
+ Coefficient("1821744319735099")*C
+ Coefficient("1125899906842624")*D
>= Coefficient("-9538777048715548"));
cs.insert(Coefficient("-11790576820742500")*A
+ Coefficient("7286977296954795")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108248905384"));
cs.insert(Coefficient("-11790576996382886")*A
- Coefficient("7286977251918799")*C
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108523624968"));
cs.insert(Coefficient("-5895288507198642")*A
- Coefficient("3643488632714799")*C
- Coefficient("2251799813685248")*D
>= Coefficient("-19077554291085880"));
cs.insert(Coefficient("-11790577113476476")*A
- Coefficient("4503599627370496")*B
+ Coefficient("7286977319472793")*D
>= Coefficient("-38155108861394936"));
cs.insert(Coefficient("-5895288572500836")*A
- Coefficient("2251799813685248")*B
- Coefficient("3643488652980997")*D
>= Coefficient("-19077554450963668"));
cs.insert(Coefficient("-5895288484680644")*A
- Coefficient("3643488607945001")*B
+ Coefficient("2251799813685248")*C
>= Coefficient("-19077554212272888"));
cs.insert(Coefficient("-2947644274991419")*A
- Coefficient("1821744320860999")*B
- Coefficient("1125899906842624")*C
>= Coefficient("-9538777190578936"));
cs.insert(Coefficient("-2251799813685248")*A
>= Coefficient("-5895288448651847"));
// Cost function
Linear_Expression cost(10*A + 21*B + 31*C + 45*D);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
Generator pg = mip.optimizing_point();
nout << "Optimizing point obtained by simplex:\n";
print_generator(pg);
Coefficient num;
Coefficient den;
mip.evaluate_objective_function(pg, num, den);
nout << "\nOptimum value = " << num << "/" << den << endl;
C_Polyhedron ph(cs);
Coefficient num1;
Coefficient den1;
bool maximum;
Generator pg1 = point();
ph.maximize(cost, num1, den1, maximum, pg1);
nout << "\nOptimizing point obtained by enumeration:\n";
print_generator(pg1);
nout << "\nOptimum value = " << num1 << "/" << den1 << endl;
return maximum && num == num1 && den == den1 && pg == pg1;
}
bool
test04() {
Variable A(0);
Variable B(1);
Variable C(2);
Variable D(3);
Variable E(4);
Variable F(5);
Variable G(6);
Variable H(7);
// Cost function
Linear_Expression cost(-26*A + 343*B + 1233*D - C + F);
// Feasible region.
Constraint_System cs;
cs.insert(A - B + C >= 24);
cs.insert(B <= 320);
cs.insert(A + B + 2*D == 23);
cs.insert(A + 2*B + E == 4112);
cs.insert(7*A + 5*B + F <= 200);
cs.insert(138*A + 2*G == 25);
cs.insert(23*A + 342*B - 34*H == 99);
for (dimension_type i = A.id(); i <= H.id(); ++i)
cs.insert(Variable(i) >= 0);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
Generator pg = mip.optimizing_point();
nout << "Optimizing point = ";
print_generator(pg);
Generator pg_kr = point();
pg_kr = point(22*B + 1846*C + 863*D + 312468*E + 15090*F + 950*G + 0*H, 76);
if (pg != pg_kr)
return false;
Coefficient num;
Coefficient den;
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
Coefficient num_kr = 1084869;
Coefficient den_kr = 76;
if (num != num_kr || den != den_kr)
return false;
// Reoptimize using another objective function.
Linear_Expression new_cost = -51*A + 632*B;
mip.set_objective_function(new_cost);
pg = mip.optimizing_point();
nout << "Optimizing point = ";
print_generator(pg);
pg_kr = point(782*B + 1598*C + 138244*E + 2890*F + 425*G + 7767*H, 34);
if (pg != pg_kr)
return false;
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
num_kr = 14536;
den_kr = 1;
if (num != num_kr || den != den_kr)
return false;
// Reoptimize after changing optimization mode.
mip.set_optimization_mode(MINIMIZATION);
pg = mip.optimizing_point();
nout << "Optimizing point = ";
print_generator(pg);
pg_kr = point(17100*A + 26174*B + 2274482*C
+ 1063871*D + 388070456*E + 18627830*F + 0*H,
94392);
if (pg != pg_kr)
return false;
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
num_kr = 3917467;
den_kr = 23598;
if (num != num_kr || den != den_kr)
return false;
return true;
}
bool
test05() {
Variable A(0);
Variable B(1);
Variable C(2);
Variable D(3);
Constraint_System cs;
cs.insert(Coefficient("2251799813685248")*A
>= Coefficient("-5895288448651847"));
cs.insert(Coefficient("5895288437392848")*A
+ Coefficient("3643488632714799")*B
- Coefficient("2251799813685248")*C
>= Coefficient("-19077554137963492"));
cs.insert(Coefficient("5895288437392848")*A +
Coefficient("3643488632714799")*B
+ Coefficient("2251799813685248")*C >=
Coefficient("-19077554137963492"));
cs.insert(Coefficient("11790576874785696")*A
+ Coefficient("4503599627370496")*B
+ Coefficient("7286977274436797")*D
>= Coefficient("-38155108284934184"));
cs.insert(Coefficient("11790576874785696")*A
+ Coefficient("4503599627370496")*B
- Coefficient("7286977274436797")*D
>= Coefficient("-38155108284934184"));
cs.insert(Coefficient("11790576879289294")*A
+ Coefficient("7286977274436797")*C
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("11790576879289294")*A
+ Coefficient("7286977274436797")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("11790576879289294")*A
- Coefficient("7286977274436797")*C
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("11790576879289294")*A
- Coefficient("7286977274436797")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("2947644225451823")*A
- Coefficient("1125899906842624")*B
+ Coefficient("1821744319735099")*D
>= Coefficient("-9538777088122044"));
cs.insert(Coefficient("11790576892800094")*A
- Coefficient("4503599627370496")*B
- Coefficient("7286977274436797")*D
>= Coefficient("-38155108325466584"));
cs.insert(Coefficient("5895288437392848")*A
- Coefficient("3643488630462999")*B
+ Coefficient("2251799813685248")*C
>= Coefficient("-19077554133459892"));
cs.insert(Coefficient("2947644218696424")*A
- Coefficient("1821744320860999")*B
- Coefficient("1125899906842624")*C
>= Coefficient("-9538777072359446"));
cs.insert(Coefficient("7286977269933197")*A
+ Coefficient("11790576924325290")*B
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108379509776"));
cs.insert(Coefficient("7286977269933197")*A
+ Coefficient("11790576924325290")*B
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108379509776"));
cs.insert(Coefficient("562949953421312")*A
+ Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644226577723"));
cs.insert(Coefficient("562949953421312")*A
+ Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
- Coefficient("562949953421312")*D
>= Coefficient("-2947644226577723"));
cs.insert(Coefficient("562949953421312")*A
+ Coefficient("562949953421312")*B
- Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644225451823"));
cs.insert(Coefficient("562949953421312")*A
+ Coefficient("562949953421312")*B
- Coefficient("562949953421312")*C
- Coefficient("562949953421312")*D
>= Coefficient("-2947644225451823"));
cs.insert(Coefficient("7286977269933197")*A
+ Coefficient("4503599627370496")*B
+ Coefficient("11790576865778496")*C
>= Coefficient("-38155108266919784"));
cs.insert(Coefficient("7286977251918799")*A
+ Coefficient("4503599627370496")*B
- Coefficient("11790576870282096")*C
>= Coefficient("-38155108244401792"));
cs.insert(Coefficient("1821744320860999")*A
+ Coefficient("1125899906842624")*C
+ Coefficient("2947644226577723")*D
>= Coefficient("-9538777093751544"));
cs.insert(Coefficient("1821744320860999")*A
+ Coefficient("1125899906842624")*C
- Coefficient("2947644226577723")*
D >= Coefficient("-9538777093751544"));
cs.insert(Coefficient("1821744320860999")*A
- Coefficient("1125899906842624")*C
+ Coefficient("2947644228829523")*D
>= Coefficient("-9538777096003344"));
cs.insert(Coefficient("1821744320860999")*A
- Coefficient("1125899906842624")*C
- Coefficient("2947644228829523")*D
>= Coefficient("-9538777096003344"));
cs.insert(Coefficient("3643488664239996")*A
- Coefficient("2251799813685248")*B
+ Coefficient("5895288468918045")*C
>= Coefficient("-19077554257308884"));
cs.insert(Coefficient("3643488652980997")*A
- Coefficient("2251799813685248")*B
- Coefficient("5895288468918045")*C
>= Coefficient("-19077554232539084"));
cs.insert(Coefficient("562949953421312")*A
- Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644226577723"));
cs.insert(Coefficient("562949953421312")*A
- Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
- Coefficient("562949953421312")*D
>= Coefficient("-2947644229392473"));
cs.insert(Coefficient("562949953421312")*A
- Coefficient("562949953421312")*B
- Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644227140673"));
cs.insert(Coefficient("562949953421312")*A
- Coefficient("562949953421312")*B
- Coefficient("562949953421312")*C
- Coefficient("562949953421312")*D
>= Coefficient("-2947644227703623"));
cs.insert(Coefficient("7286977314969193")*A
- Coefficient("11790576906310892")*B
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108447063768"));
cs.insert(Coefficient("3643488655232797")*A
- Coefficient("5895288446400047")*B
- Coefficient("2251799813685248")*D
>= Coefficient("-19077554203265688"));
cs.insert(Coefficient("4503599627370496")*A
+ Coefficient("11790576753188506")*B
+ Coefficient("7286977179861205")*C
>= Coefficient("-38155107920142616"));
cs.insert(Coefficient("4503599627370496")*A
+ Coefficient("11790576766699304")*B
- Coefficient("7286977179861205")*C
>= Coefficient("-38155107965178608"));
cs.insert(Coefficient("4503599627370496")*A
+ Coefficient("7286977157343207")*B
+ Coefficient("11790576712656108")*D
>= Coefficient("-38155107816559824"));
cs.insert(Coefficient("2251799813685248")*A
+ Coefficient("3643488592182402")*B
- Coefficient("5895288374342453")*D
>= Coefficient("-19077553960071308"));
cs.insert(Coefficient("4503599627370496")*A
+ Coefficient("11790576753188506")*C
+ Coefficient("7286977175357605")*D
>= Coefficient("-38155107924646216"));
cs.insert(Coefficient("2251799813685248")*A
+ Coefficient("5895288390105051")*C
- Coefficient("3643488594434202")*D
>= Coefficient("-19077553996100104"));
cs.insert(Coefficient("2251799813685248")*A
- Coefficient("5895288421630249")*C
+ Coefficient("3643488619204000")*D
>= Coefficient("-19077554088423896"));
cs.insert(Coefficient("4503599627370496")*A
- Coefficient("11790576865778496")*C
- Coefficient("7286977247415199")*D
>= Coefficient("-38155108244401792"));
cs.insert(Coefficient("4503599627370496")*A
- Coefficient("7286977247415199")*B
+ Coefficient("11790576888296494")*D
>= Coefficient("-38155108307452184"));
cs.insert(Coefficient("2251799813685248")*A
- Coefficient("3643488639470198")*B
- Coefficient("5895288464414445")*D
>= Coefficient("-19077554210021088"));
cs.insert(Coefficient("2251799813685248")*A
- Coefficient("5895288428385648")*B
+ Coefficient("3643488630462999")*C
>= Coefficient("-19077554131208092"));
cs.insert(Coefficient("4503599627370496")*A
- Coefficient("11790576843260498")*B
- Coefficient("7286977224897201")*C
>= Coefficient("-38155108163336992"));
cs.insert(Coefficient("1125899906842624")*B
>= Coefficient("-2947644227703623"));
cs.insert(Coefficient("5895288459910846")*B
+ Coefficient("2251799813685248")*C
+ Coefficient("3643488630462999")*D
>= Coefficient("-19077554198762088"));
cs.insert(Coefficient("5895288457659046")*B
+ Coefficient("2251799813685248")*C
- Coefficient("3643488628211199")*D
>= Coefficient("-19077554189754888"));
cs.insert(Coefficient("11790576915318092")*B
- Coefficient("4503599627370496")*C
+ Coefficient("7286977269933197")*D
>= Coefficient("-38155108393020576"));
cs.insert(Coefficient("5895288457659046")*B
- Coefficient("2251799813685248")*C
- Coefficient("3643488632714799")*D
>= Coefficient("-19077554187503088"));
cs.insert(Coefficient("7286977292451195")*B
+ Coefficient("11790576919821692")*C
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108433552976"));
cs.insert(Coefficient("3643488664239996")*B
+ Coefficient("5895288486932443")*C
- Coefficient("2251799813685248")*D
>= Coefficient("-19077554304596680"));
cs.insert(Coefficient("3643488643973798")*B
- Coefficient("5895288446400047")*C
+ Coefficient("2251799813685248")*D
>= Coefficient("-19077554180747688"));
cs.insert(Coefficient("7286977314969193")*B
- Coefficient("11790576937836090")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108510114168"));
cs.insert(Coefficient("4503599627370496")*B
+ Coefficient("7286977247415199")*C
+ Coefficient("11790576883792894")*D
>= Coefficient("-38155108289437784"));
cs.insert(Coefficient("4503599627370496")*B
+ Coefficient("7286977251918799")*C
- Coefficient("11790576883792894")*D
>= Coefficient("-38155108280430584"));
cs.insert(Coefficient("4503599627370496")*B
- Coefficient("7286977229400801")*C
+ Coefficient("11790576852267696")*D
>= Coefficient("-38155108181351392"));
cs.insert(Coefficient("1125899906842624")*D
>= Coefficient("-2947644225451823"));
cs.insert(Coefficient("4503599627370496")*B
- Coefficient("7286977229400801")*C
- Coefficient("11790576852267696")*D
>= Coefficient("-38155108167840592"));
cs.insert(Coefficient("-2251799813685248")*D
>= Coefficient("-5895288448651847"));
cs.insert(Coefficient("2251799813685248")*C
>= Coefficient("-5895288446400047"));
cs.insert(Coefficient("-2251799813685248")*C
>= Coefficient("-5895288444148247"));
cs.insert(Coefficient("-1125899906842624")*B
+ Coefficient("1821744321986899")*C
+ Coefficient("2947644226577723")*D
>= Coefficient("-9538777088122044"));
cs.insert(Coefficient("-3643488607945001")*B
+ Coefficient("5895288414874849")*C
+ Coefficient("2251799813685248")*D
>= Coefficient("-19077554059150500"));
cs.insert(Coefficient("-4503599627370496")*B
+ Coefficient("7286977292451195")*C
- Coefficient("11790576906310892")*D
>= Coefficient("-38155108343480984"));
cs.insert(Coefficient("-7286977220393601")*B
+ Coefficient("11790576829749698")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108086775800"));
cs.insert(Coefficient("-4503599627370496")*B
- Coefficient("7286977274436797")*C
+ Coefficient("11790576901807292")*D
>= Coefficient("-38155108325466584"));
cs.insert(Coefficient("-3643488605693201")*B
- Coefficient("5895288414874849")*C
+ Coefficient("2251799813685248")*D
>= Coefficient("-19077554059150500"));
cs.insert(Coefficient("-1125899906842624")*B
- Coefficient("1821744319735099")*C
- Coefficient("2947644225451823")*D
>= Coefficient("-9538777079114846"));
cs.insert(Coefficient("-7286977220393601")*B
- Coefficient("11790576834253298")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108113797400"));
cs.insert(Coefficient("-5895288462162645")*B
+ Coefficient("2251799813685248")*C
+ Coefficient("3643488639470198")*D
>= Coefficient("-19077554144718892"));
cs.insert(Coefficient("-11790576924325290")*B
- Coefficient("4503599627370496")*C
+ Coefficient("7286977292451195")*D
>= Coefficient("-38155108320962984"));
cs.insert(Coefficient("-5895288468918045")*B
+ Coefficient("2251799813685248")*C
- Coefficient("3643488641721998")*D
>= Coefficient("-19077554160481492"));
cs.insert(Coefficient("-11790576928828890")*B
- Coefficient("4503599627370496")*C
- Coefficient("7286977292451195")*D
>= Coefficient("-38155108329970184"));
cs.insert(Coefficient("-281474976710656")*B
>= Coefficient("-736911053829681"));
cs.insert(Coefficient("-4503599627370496")*A
+ Coefficient("11790576658612912")*B
+ Coefficient("7286977125818009")*C
>= Coefficient("-38155107627408640"));
cs.insert(Coefficient("-2251799813685248")*A
+ Coefficient("5895288336061856")*B
- Coefficient("3643488560657205")*C
>= Coefficient("-19077553829466920"));
cs.insert(Coefficient("-2251799813685248")*A
+ Coefficient("3643488535887407")*B
+ Coefficient("5895288288774060")*D
>= Coefficient("-19077553683099932"));
cs.insert(Coefficient("-7286977274436797")*A
+ Coefficient("11790576766699304")*B
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108032732608"));
cs.insert(Coefficient("-4503599627370496")*A
+ Coefficient("7286977098796411")*B
- Coefficient("11790576609073318")*D
>= Coefficient("-38155107483293448"));
cs.insert(Coefficient("-7286977301458395")*A
+ Coefficient("11790576735174106")*B
- Coefficient("4503599627370496")*D
>= Coefficient("-38155107983193008"));
cs.insert(Coefficient("-4503599627370496")*A
+ Coefficient("11790576708152508")*C
+ Coefficient("7286977148336007")*D
>= Coefficient("-38155107771523824"));
cs.insert(Coefficient("-281474976710656")*A
+ Coefficient("281474976710656")*B
+ Coefficient("281474976710656")*C
+ Coefficient("281474976710656")*D
>= Coefficient("-1473822119481311"));
cs.insert(Coefficient("-1125899906842624")*A
+ Coefficient("2947644178164027")*C
- Coefficient("1821744285958102")*D
>= Coefficient("-9538776941755056"));
cs.insert(Coefficient("-1125899906842624")*A
+ Coefficient("1125899906842624")*B
+ Coefficient("1125899906842624")*C
- Coefficient("1125899906842624")*D
>= Coefficient("-5895288471169845"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("11790576856771296")*C
+ Coefficient("7286977247415199")*D
>= Coefficient("-38155108221883792"));
cs.insert(Coefficient("-1125899906842624")*A
+ Coefficient("1125899906842624")*B
- Coefficient("1125899906842624")*C
+ Coefficient("1125899906842624")*D
>= Coefficient("-5895288471169845"));
cs.insert(Coefficient("-140737488355328")*A
- Coefficient("368455526774103")*C
- Coefficient("227718038700250")*D
>= Coefficient("-1192347131793131"));
cs.insert(Coefficient("-1125899906842624")*A
+ Coefficient("1125899906842624")*B
- Coefficient("1125899906842624")*C
- Coefficient("1125899906842624")*D
>= Coefficient("-5895288464414445"));
cs.insert(Coefficient("-3643488643973798")*A
+ Coefficient("2251799813685248")*B
+ Coefficient("5895288441896447")*C
>= Coefficient("-19077554158229692"));
cs.insert(Coefficient("-7286977296954795")*A
+ Coefficient("4503599627370496")*B
- Coefficient("11790576892800094")*C
>= Coefficient("-38155108352488176"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("7286977269933197")*B
+ Coefficient("11790576924325290")*D
>= Coefficient("-38155108411034976"));
cs.insert(Coefficient("-3643488639470198")*A
+ Coefficient("2251799813685248")*C
+ Coefficient("5895288466666245")*D
>= Coefficient("-19077554219028288"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("7286977296954795")*B
- Coefficient("11790576955850488")*D
>= Coefficient("-38155108514617768"));
cs.insert(Coefficient("-7286977251918799")*A
+ Coefficient("4503599627370496")*C
- Coefficient("11790576892800094")*D
>= Coefficient("-38155108311955784"));
cs.insert(Coefficient("-3643488655232797")*A
- Coefficient("2251799813685248")*C
+ Coefficient("5895288480177044")*D
>= Coefficient("-19077554264064284"));
cs.insert(Coefficient("-1821744320860999")*A
- Coefficient("1125899906842624")*C
- Coefficient("2947644229955423")*D
>= Coefficient("-9538777099381044"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("11790576874785696")*B
+ Coefficient("7286977269933197")*C
>= Coefficient("-38155108302948584"));
cs.insert(Coefficient("-7286977274436797")*A
- Coefficient("4503599627370496")*B
+ Coefficient("11790576937836090")*C
>= Coefficient("-38155108424545776"));
cs.insert(Coefficient("-4503599627370496")*A
- Coefficient("11790576802728102")*B
- Coefficient("7286977197875603")*C
>= Coefficient("-38155108019221808"));
cs.insert(Coefficient("-3643488664239996")*A
- Coefficient("2251799813685248")*B
- Coefficient("5895288493687843")*C
>= Coefficient("-19077554284330480"));
cs.insert(Coefficient("-562949953421312")*A
- Coefficient("562949953421312")*B
+ Coefficient("562949953421312")*C
+ Coefficient("562949953421312")*D
>= Coefficient("-2947644250784571"));
cs.insert(Coefficient("-281474976710656")*A
- Coefficient("281474976710656")*B
+ Coefficient("281474976710656")*C
- Coefficient("281474976710656")*D
>= Coefficient("-1473822131021785"));
cs.insert(Coefficient("-1125899906842624")*A
- Coefficient("1125899906842624")*B
- Coefficient("1125899906842624")*C
+ Coefficient("1125899906842624")*D
>= Coefficient("-5895288464414445"));
cs.insert(Coefficient("-1125899906842624")*A
- Coefficient("1125899906842624")*B
- Coefficient("1125899906842624")*C
- Coefficient("1125899906842624")*D
>= Coefficient("-5895288468918045"));
cs.insert(Coefficient("-3643488412038417")*A
- Coefficient("5895288318047457")*B
+ Coefficient("2251799813685248")*D
>= Coefficient("-19077553665085532"));
cs.insert(Coefficient("-1821744199263809")*A
- Coefficient("2947644153394229")*B
- Coefficient("1125899906842624")*D
>= Coefficient("-9538776813402468"));
cs.insert(Coefficient("-5895288378846052")*A
+ Coefficient("3643488632714799")*B
+ Coefficient("2251799813685248")*C
>= Coefficient("-19077554023121704"));
cs.insert(Coefficient("-11790576834253298")*A
+ Coefficient("7286977314969193")*B
- Coefficient("4503599627370496")*C
>= Coefficient("-38155108302948584"));
cs.insert(Coefficient("-736911041726257")*A
+ Coefficient("281474976710656")*B
+ Coefficient("455436077400500")*D
>= Coefficient("-2384694241068264"));
cs.insert(Coefficient("-5895288347320855")*A
+ Coefficient("2251799813685248")*B
- Coefficient("3643488616952200")*D
>= Coefficient("-19077553951064108"));
cs.insert(Coefficient("-2947644201807925")*A
+ Coefficient("1821744319735099")*C
+ Coefficient("1125899906842624")*D
>= Coefficient("-9538777048715548"));
cs.insert(Coefficient("-11790576820742500")*A
+ Coefficient("7286977296954795")*C
- Coefficient("4503599627370496")*D
>= Coefficient("-38155108248905384"));
cs.insert(Coefficient("-11790576996382886")*A
- Coefficient("7286977251918799")*C
+ Coefficient("4503599627370496")*D
>= Coefficient("-38155108523624968"));
cs.insert(Coefficient("-5895288507198642")*A
- Coefficient("3643488632714799")*C
- Coefficient("2251799813685248")*D
>= Coefficient("-19077554291085880"));
cs.insert(Coefficient("-11790577113476476")*A
- Coefficient("4503599627370496")*B
+ Coefficient("7286977319472793")*D
>= Coefficient("-38155108861394936"));
cs.insert(Coefficient("-5895288572500836")*A
- Coefficient("2251799813685248")*B
- Coefficient("3643488652980997")*D
>= Coefficient("-19077554450963668"));
cs.insert(Coefficient("-5895288484680644")*A
- Coefficient("3643488607945001")*B
+ Coefficient("2251799813685248")*C
>= Coefficient("-19077554212272888"));
cs.insert(Coefficient("-2947644274991419")*A
- Coefficient("1821744320860999")*B
- Coefficient("1125899906842624")*C
>= Coefficient("-9538777190578936"));
cs.insert(Coefficient("-2251799813685248")*A
>= Coefficient("-5895288448651847"));
// Cost function
Linear_Expression cost(10*A + 21*B + 31*C + 45*D);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
Generator pg = mip.optimizing_point();
nout << "Optimizing point = ";
print_generator(pg);
Coefficient num;
Coefficient den;
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
return true;
}
bool
test06() {
Variable A(0);
Variable B(1);
Linear_Expression cost(A + B);
Constraint_System cs;
cs.insert(-A - B >= -8);
cs.insert(-A - 3*B >= -18);
cs.insert(-A + B >= -4);
cs.insert(A >= 0);
cs.insert(A <= 3);
cs.insert(B >= 0);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
const Coefficient num_kr = 8;
const Coefficient den_kr = 1;
Coefficient num;
Coefficient den;
Generator pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
Generator pg_kr = point(3*A + 5*B);
if (pg != pg_kr)
return false;
// Set Variable A to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(A));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
// Set Variable B to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(B));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
return true;
}
bool
test07() {
Variable A(0);
Variable B(1);
Linear_Expression cost(A + B);
Constraint_System cs;
cs.insert(-A - 3*B >= -4);
cs.insert(-5*A - B >= -5);
cs.insert(-3*A - 2*B >= -2);
cs.insert(A + 3*B >= -1);
cs.insert(2*A - B >= -2);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
Coefficient num_kr = 8;
Coefficient den_kr = 7;
Coefficient num;
Coefficient den;
Generator pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
Generator pg_kr = point(-2*A + 10*B, 7);
if (pg != pg_kr)
return false;
// Set Variable A to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(A));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
num_kr = 1;
den_kr = 1;
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
pg_kr = point(B);
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
// Set Variable B to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(B));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
return true;
}
bool
test08() {
Variable A(0);
Variable B(1);
Variable C(2);
Variable D(3);
Linear_Expression cost(12*A + 6*B + 4*C + 3*D);
Constraint_System cs;
cs.insert(A >= 0);
cs.insert(B >= 0);
cs.insert(C >= 0);
cs.insert(D >= 0);
cs.insert(3008*A + 20980*B - 97775*C - 101225*D >= 0);
cs.insert(3985*A + 25643*B - 135871*C - 130580*D >= 0);
cs.insert(4324*A + 26978*B - 133655*C - 168473*D >= 0);
cs.insert(3534*A + 25361*B - 46243*C - 100407*D >= 0);
cs.insert(8836*A + 40796*B - 176661*C - 215616*D >= 0);
cs.insert(5376*A + 37562*B - 182576*C - 217615*D >= 0);
cs.insert(2491*A + 16544*B - 49440*C - 83639*D >= 0);
cs.insert(4775*A + 39122*B - 136701*C - 193393*D >= 0);
cs.insert(8046*A + 42958*B - 225138*C - 256575*D >= 0);
cs.insert(8554*A + 48955*B - 257370*C - 312877*D >= 0);
cs.insert(6147*A + 45514*B - 165274*C - 227099*D >= 0);
cs.insert(8366*A + 55140*B - 203989*C - 321623*D >= 0);
cs.insert(13479*A + 68037*B - 174270*C - 341743*D >= 0);
cs.insert(21808*A + 78302*B - 322990*C - 487539*D >= 0);
cs.insert(-8554*A - 48955*B >= -10000);
cs.insert(-257370*C - 312877*D >= -10000);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
Coefficient num_kr = Coefficient("8231960000");
Coefficient den_kr = 581120267;
Coefficient num;
Coefficient den;
Generator pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
Generator pg_kr = point(679355000*A + 19925000*C + 0*D, 581120267);
if (pg != pg_kr)
return false;
// Set Variable A to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(A));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
num_kr = Coefficient("81926256268");
den_kr = Coefficient("6651564805");
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
pg_kr = point(Coefficient("6651564805")*A + 196469466*B + 232165453*C + 0*D,
Coefficient("6651564805"));
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
// Set Variable B to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(B));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
num_kr = 1646392;
den_kr = 135871;
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
pg_kr = point(135871*A + 3985*C + 0*D, 135871);
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
// Set Variable C to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(C));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
num_kr = 2335041;
den_kr = 193393;
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
pg_kr = point(193393*A + 4775*D, 193393);
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
// Set Variable D to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(D));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
num_kr = 12;
den_kr = 1;
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
pg_kr = point(A + 0*D);
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
return true;
}
bool
test09() {
Variable A(0);
Variable B(1);
Variable C(2);
Linear_Expression cost(A + B + C);
Constraint_System cs;
cs.insert(A >= -1);
cs.insert(B >= -1);
cs.insert(C >= -1);
cs.insert(-A >= -1);
cs.insert(-B >= -1);
cs.insert(-C >= -1);
MIP_Problem mip = MIP_Problem(cs.space_dimension(), cs, cost, MAXIMIZATION);
Coefficient num_kr = 3;
Coefficient den_kr = 1;
Coefficient num;
Coefficient den;
Generator pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
Generator pg_kr = point(A + B + C);
if (pg != pg_kr)
return false;
// Set Variable A to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(A));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
// Set Variable B to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(B));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
// Set Variable C to be constrained to have an integer value.
mip.add_to_integer_space_dimensions(Variables_Set(C));
pg = mip.optimizing_point();
mip.evaluate_objective_function(pg, num, den);
nout << "Optimum value = " << num << "/" << den << endl;
if (num != num_kr || den != den_kr)
return false;
nout << "Optimizing point = ";
print_generator(pg);
if (pg != pg_kr)
return false;
return true;
}
bool
test10() {
Variable A(0);
Variable B(1);
Variable C(2);
// Feasible region.
Constraint_System cs;
cs.insert(A + B <= 1);
cs.insert(A + C <= 1);
cs.insert(B + C <= 1);
// All integer variables.
Variables_Set ivs(A, C);
// Cost function.
Linear_Expression cost(-2*A - 3*B - 4*C);
MIP_Problem mip(cs.space_dimension(), cs.begin(), cs.end(), ivs, cost,
MINIMIZATION);
if (mip.solve() != OPTIMIZED_MIP_PROBLEM)
return false;
Generator pg = mip.optimizing_point();
nout << "Optimizing point = ";
using namespace Parma_Polyhedra_Library::IO_Operators;
nout << pg << endl;
return true;
}
} // namespace
BEGIN_MAIN
DO_TEST_F64(test01);
DO_TEST_F32(test02);
DO_TEST_F64(test03);
DO_TEST_F32(test04);
DO_TEST_F64(test05);
DO_TEST(test06);
DO_TEST(test07);
DO_TEST_F64(test08);
DO_TEST(test09);
DO_TEST(test10);
END_MAIN
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