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yap-6.3/CLPQR/clpqr/examples/simplex.pl

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This commit was generated by cvs2svn to compensate for changes in r4, which included commits to RCS files with non-trunk default branches. git-svn-id: https://yap.svn.sf.net/svnroot/yap/trunk@5 b08c6af1-5177-4d33-ba66-4b1c6b8b522a
2001-04-09 20:54:03 +01:00
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% clp(q,r) version 1.3.2 %
% %
% (c) Copyright 1992,1993,1994,1995 %
% Austrian Research Institute for Artificial Intelligence (OFAI) %
% Schottengasse 3 %
% A-1010 Vienna, Austria %
% %
% File: simplex.pl %
% Author: Christian Holzbaur christian@ai.univie.ac.at %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% b152 p.32 40/160/17200
example( 1, [X1,X2], Z) :-
{
X1=<50,
X2=<200,
X1+0.2*X2=<72,
150*X1+25*X2=<10000,
Z = 250*X1+45*X2
},
maximize(Z).
% p.33 1/0/1.5/7
example( 2,[X1,X2,X3], Z) :-
{
X1=<2,
X1+X2+2*X3=<4,
3*X2+4*X3=<6,
X1>=0,
X2>=0,
X3>=0,
Z = X1+2*X2+4*X3
},
maximize(Z).
% p.38 38/170/18850
example( 3, [X1,X2], Z) :-
{
X1=<50,
X2=<200,
X1+0.2*X2=<72,
150*X1+25*X2=<10000,
10*X1+X2>=550,
Z = 250*X1+55*X2
},
maximize(Z).
% 7/2/310
example( 4, [X,Y], Z) :-
{
2*X+Y =< 16,
X+2*Y =< 11,
X+3*Y =< 15,
Z = 30*X+50*Y
},
maximize(Z).
% b30313 p.315 0/0/2.5/5
example( 5, [X,Y,Z], Min) :-
{
X+3*Y+2*Z >= 5,
2*X+2*Y+Z >= 2,
4*X-2*Y+3*Z >= -1,
X >= 0,
Y >= 0,
Z >= 0,
Min = 6*X+5*Y+2*Z
},
minimize(Min).
% -7
example( 6, [X1,X2,X3], Min) :-
{
X1=<2,
X1+X2+2*X3=<4,
3*X2+4*X3=<6,
X1>=0,
X2>=0,
X3>=0,
Min = -X1-2*X2-4*X3
},
minimize( Min).
% -70
example( 7, [X1,X2,X3,X4,X5,X6,X7], Min) :-
{
X1 + X3 - X4 + X5 + 2*X6 + X7 =< 6,
X2 + X4 - 2*X5 + X6 - 2*X7 =< 4,
X3 - X4 + 2*X6 + X7 =< 1,
0 =< X1, X1 =< 6,
0 =< X2, X2 =< 6,
0 =< X3,
0 =< X4, X4 =< 4,
0 =< X5, X5 =< 2,
0 =< X6, X6 =< 10,
0 =< X7,
Min = -3*X1 + 4*X2 + 2*X3 - 2*X4 - 14*X5 + 11*X6 - 5*X7
},
minimize( Min).
% -39/2
example( 8, [X1,X2,X3,X4,X5,X6,X7], Min) :-
{
X1 + X3 - X4 + X5 + 2*X6 + X7 =< 6,
X2 + X4 - 2*X5 + X6 - 2*X7 =< 4,
X3 - X4 + 2*X6 + X7 =< 1,
0 =< X1, X1 =< 6,
0 =< X2, X2 =< 6,
0 =< X3,
0 =< X4, X4 =< 4,
0 =< X5, X5 =< 2,
0 =< X6, X6 =< 10,
0 =< X7,
Min = 3*X1 - 4*X2 - 2*X3 + 2*X4 + 14*X5 - 11*X6 + 5*X7
},
minimize( Min).
%
% min = 11429082625/9792 = 1167185.7255923203
%
example( 9, Vs, Obj) :-
Vs = [ Anm1,Anm2,Anm3,Anm4,Anm5,Anm6,
Stm1,Stm2,Stm3,Stm4,Stm5,Stm6,
UE1,UE2,UE3,UE4,UE5,UE6
],
allpos( Vs),
{
+1*Stm1 = 60,
+0.9*Stm1 +1*Anm1 -1*Stm2 = 0,
+0.9*Stm2 +1*Anm2 -1*Stm3 = 0,
+0.9*Stm3 +1*Anm3 -1*Stm4 = 0,
+0.9*Stm4 +1*Anm4 -1*Stm5 = 0,
+0.9*Stm5 +1*Anm5 -1*Stm6 = 0,
+150*Stm1 -100*Anm1 +1*UE1 >= 8000,
+150*Stm2 -100*Anm2 +1*UE2 >= 9000,
+150*Stm3 -100*Anm3 +1*UE3 >= 8000,
+150*Stm4 -100*Anm4 +1*UE4 >= 10000,
+150*Stm5 -100*Anm5 +1*UE5 >= 9000,
+150*Stm6 -100*Anm6 +1*UE6 >= 12000,
-20*Stm1 +1*UE1 =< 0,
-20*Stm2 +1*UE2 =< 0,
-20*Stm3 +1*UE3 =< 0,
-20*Stm4 +1*UE4 =< 0,
-20*Stm5 +1*UE5 =< 0,
-20*Stm6 +1*UE6 =< 0,
Anm1 =< 18,
57 =< Stm2,
Stm2 =< 75,
Anm2 =< 18,
57 =< Stm3,
Stm3 =< 75,
Anm3 =< 18,
57 =< Stm4,
Stm4 =< 75,
Anm4 =< 18,
57 =< Stm5,
Stm5 =< 75,
Anm5 =< 18,
57 =< Stm6,
Stm6 =< 75,
Anm6 =< 18,
Obj = +2700*Stm1 +1500*Anm1 +30*UE1
+2700*Stm2 +1500*Anm2 +30*UE2
+2700*Stm3 +1500*Anm3 +30*UE3
+2700*Stm4 +1500*Anm4 +30*UE4
+2700*Stm5 +1500*Anm5 +30*UE5
+2700*Stm6 +1500*Anm6 +30*UE6
},
minimize( Obj).
% b20011, p144
%
example( utility, Vs, Min) :-
Vs = [ X11, X12, X13, X14, X15,
X21, X22, X23, X24, X25,
Y11, Y12, Y13, Y14,
Y21, Y22, Y23, Y24, Y25,
Z11, Z12, Z13, Z14,
Z21, Z22, Z23, Z24, Z25],
{
X11 + X12 + X13 + X14 + X15 = 1000,
X21 + X22 + X23 + X24 + X25 = 1000,
3*X11 + 2*X21 - Y11 - Y14 - Z11 - Z14 =< 0,
-3*X12 - 2*X22 + Y11 - Y12 + Z11 - Z12 = 0,
-3*X13 - 2*X23 - Y13 + Y14 - Z13 + Z14 = 0,
-3*X14 - 2*X24 + Y12 + Z12 = 0,
-3*X15 - 2*X25 + Y13 + Z13 = 0,
4*X11 + 5*X21 - Y21 - Z21 =< 0,
-4*X12 - 5*X22 + Y22 + Z22 = 0,
-4*X13 - 5*X23 + Y24 - Y25 + Z24 - Z25 = 0,
-4*X14 - 5*X24 + Y21 - Y22 - Y23 + Y25
+ Z21 - Z22 - Z23 + Z25 = 0,
-4*X15 - 5*X25 + Y23 - Y24 + Z23 - Z24 = 0,
7*X11 + 9*X21 >= 0,
7*X12 + 9*X22 =< 3000,
7*X13 + 9*X23 =< 200,
7*X14 + 9*X24 =< 10000,
7*X15 + 9*X25 =< 7000,
Z11 =< 1000,
Z12 =< 500,
Z13 =< 2000,
Z14 =< 100,
Z21 =< 5000,
Z22 =< 250,
Z23 =< 600,
Z24 =< 7000,
Z25 =< 4000,
X11 >= 0, X12 >= 0, X13 >= 0, X14 >= 0, X15 >= 0,
X21 >= 0, X22 >= 0, X23 >= 0, X24 >= 0, X25 >= 0,
Y11 >= 0, Y12 >= 0, Y13 >= 0, Y14 >= 0,
Y21 >= 0, Y22 >= 0, Y23 >= 0, Y24 >= 0, Y25 >= 0,
Z11 >= 0, Z12 >= 0, Z13 >= 0, Z14 >= 0,
Z21 >= 0, Z22 >= 0, Z23 >= 0, Z24 >= 0, Z25 >= 0,
M = 99999,
Min = M*X11 + M*X21 + 3*Y11 + 7*Y12 + 9*Y13 + Y14 + 4*Y21 + 7*Y22 + 3*Y23 +
8*Y24 + 5*Y25
},
minimize(Min).
example( electricity, Vs, Min) :-
Vs = [ X11, X12, X13, X14, X15,
X21, X22, X23, X24, X25,
Y11, Y12, Y13, Y14,
Z11, Z12, Z13, Z14],
{
X11 + X12 + X13 + X14 + X15 = 1000,
X21 + X22 + X23 + X24 + X25 = 1000,
3*X11 + 2*X21 - Y11 - Y14 - Z11 - Z14 =< 0,
-3*X12 - 2*X22 + Y11 - Y12 + Z11 - Z12 = 0,
-3*X13 - 2*X23 - Y13 + Y14 - Z13 + Z14 = 0,
-3*X14 - 2*X24 + Y12 + Z12 = 0,
-3*X15 - 2*X25 + Y13 + Z13 = 0,
7*X11 + 9*X21 >= 0,
7*X12 + 9*X22 =< 3000,
7*X13 + 9*X23 =< 200,
7*X14 + 9*X24 =< 10000,
7*X15 + 9*X25 =< 7000,
Z11 =< 1000,
Z12 =< 500,
Z13 =< 2000,
Z14 =< 100,
X11 >= 0, X12 >= 0, X13 >= 0, X14 >= 0, X15 >= 0,
X21 >= 0, X22 >= 0, X23 >= 0, X24 >= 0, X25 >= 0,
Y11 >= 0, Y12 >= 0, Y13 >= 0, Y14 >= 0,
Z11 >= 0, Z12 >= 0, Z13 >= 0, Z14 >= 0,
M = 99999,
Min = M*X11 + M*X21 + 3*Y11 + 7*Y12 + 9*Y13 + Y14
},
minimize(Min).
example( water, Vs, Min) :-
Vs = [ X11, X12, X13, X14, X15,
X21, X22, X23, X24, X25,
Y21, Y22, Y23, Y24, Y25,
Z21, Z22, Z23, Z24, Z25],
{
X11 + X12 + X13 + X14 + X15 = 1000,
X21 + X22 + X23 + X24 + X25 = 1000,
4*X11 + 5*X21 - Y21 - Z21 =< 0,
-4*X12 - 5*X22 + Y22 + Z22 = 0,
-4*X13 - 5*X23 + Y24 - Y25 + Z24 - Z25 = 0,
-4*X14 - 5*X24 + Y21 - Y22 - Y23 + Y25
+ Z21 - Z22 - Z23 + Z25 = 0,
-4*X15 - 5*X25 + Y23 - Y24 + Z23 - Z24 = 0,
7*X11 + 9*X21 >= 0,
7*X12 + 9*X22 =< 3000,
7*X13 + 9*X23 =< 200,
7*X14 + 9*X24 =< 10000,
7*X15 + 9*X25 =< 7000,
Z21 =< 5000,
Z22 =< 250,
Z23 =< 600,
Z24 =< 7000,
Z25 =< 4000,
X11 >= 0, X12 >= 0, X13 >= 0, X14 >= 0, X15 >= 0,
X21 >= 0, X22 >= 0, X23 >= 0, X24 >= 0, X25 >= 0,
Y21 >= 0, Y22 >= 0, Y23 >= 0, Y24 >= 0, Y25 >= 0,
Z21 >= 0, Z22 >= 0, Z23 >= 0, Z24 >= 0, Z25 >= 0,
M = 99999,
Min = M*X11 + M*X21 + 4*Y21 + 7*Y22 + 3*Y23 + 8*Y24 + 5*Y25
},
minimize(Min).
allpos( []).
allpos( [V|Vs]) :-
{ V >= 0 },
allpos( Vs).
% --------------------------------------------------------------------------
test(0) :- { A=<2,B=<3,C=<4,A+B+C=10 }. % must fail
test(5) :-
{
2*X1 + 4*X2 + 3*X3 - 4*W1 - 10*W2 = 0,
2*X1 + X2 + X3 = 4,
5*X1 + 3*X2 + 2*X3 = 10,
2*W1 + 5*W2 =< 2,
W1 + 3*W2 =< 4,
W1 + 2*W2 =< 3,
X1 >= 0,
X2 >= 0,
X3 >= 0
}.
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