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LAKES.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME LAKES
* Problem:
* ********
* A problem of water resource management in Canada, which may be
* formulated as
*
* Min SUM SUM (T(i,j)- R(i,j))^2 + (O(i,j)-R(N+i,j))^2)
* i=1,N j=1,5
*
* subject to
*
* T(i+1,1)-T(i,1)+O(i,1) = G(i,1)
* T(i+1,2)-T(i,2)-O(i,1)+O(i,2) = G(i,2)
* T(i+1,3)-T(i,3)-O(i,2)+O(i,3) = G(i,3)
* T(i+1,4)-T(i,4)-O(i,3)+O(i,4) = G(i,4)
* T(i+1,5)-T(i,5)-O(i,4)+O(i,5) = G(i,5)
*
* i=1,N and T(N+1,j) = T(1,j) for j=1,5
*
* O(i,2)-a*((T(i,2)/480.8+T(i,3)/4.6)/2-543.4)^2 *
* (T(i,2)/480.8-T(i,3)/4.6)^.5=0
* O(i,3)-b*((T(i,3)/4.6-543.4)^2*(T(i,3)/4.6-T(i,4)/105.15)^0.5) = 0
* O(i,4)-c*(T(i,4)/105.15-550.11)^2.2 = 0
*
* where T(i,j) and O(i,j) are variables, R(i,j) are given and
* a=.0841168 b=.1280849 and c=0.2605.
*
* Extra variables
*
* v(i,2) = T(i,2) / 961.6 + T(i,3) / 9.2 - 543.4
* w(i,2) = T(i,2) / 480.8 - T(i,3) / 4.6
* v(i,3) = T(i,3) / 4.6 - 543.4
* w(i,3) = T(i,3) / 4.6 - T(i,4) / 105.15
* v(i,4) = T(i,4) / 105.15 - 550.11
*
* are introduced so that the nonlinear constraints may be rewritten as
*
* O(i,2)-a*v(i,2)^2 * w(i,2)^0.5 = 0 ; w(i,2) > 0
* O(i,3)-b*v(i,3)^2 * w(i,3)^0.5 = 0 ; w(i,3) > 0
* O(i,4)-c*v(i,4)^2.2 = 0 ; v(i,4) > 0
*
* Source:
* S Jafar Sadjadi
* Dept. of Systems Design Engineering
* University of Waterloo
* Ontario, N2L 3G1 Canada
* SIF input: Nick Gould and Jafar Sadjadi, November 1995
* classification QOR2-RN-90-78
IE N 6
IA N-1 N -1
IA N+1 N 1
IM NN N 2
IE 1 1
IE 2 2
IE 3 3
IE 4 4
IE 5 5
IE 6 6
IE 7 7
IE 8 8
IE 9 9
IE 10 10
IE 11 11
IE 12 12
* Target value S_hat and O_hat
RE S1s1 202761.072
RE S1s2 277791.816
RE S1s3 2636.996
RE S1s4 59987.0235
RE S1s5 19490.4
RE S2s1 202703.646
RE S2s2 277849.512
RE S2s3 2638.1
RE S2s4 59998.59
RE S2s5 19555.2
RE S3s1 202720.536
RE S3s2 277955.288
RE S3s3 2639.894
RE S3s4 60046.959
RE S3s5 19597.6
RE S4s1 202808.364
RE S4s2 278104.336
RE S4s3 2640.906
RE S4s4 60074.298
RE S4s5 19652.8
RE S5s1 202916.46
RE S5s2 278224.536
RE S5s3 2641.458
RE S5s4 60091.122
RE S5s5 19708.8
RE S6s1 202953.618
RE S6s2 278277.424
RE S6s3 2641.458
RE S6s4 60082.71
RE S6s5 19706.4
RE O1o1 83.728
RE O1o2 174.665
RE O1o3 180.539
RE O1o4 211.558
RE O1o5 232.252
RE O2o1 83.789
RE O2o2 173.255
RE O2o3 179.917
RE O2o4 210.585
RE O2o5 215.254
RE O3o1 82.9160
RE O3o2 173.721
RE O3o3 182.676
RE O3o4 207.838
RE O3o5 203.855
RE O4o1 80.134
RE O4o2 178.654
RE O4o3 185.917
RE O4o4 206.416
RE O4o5 186.308
RE O5o1 65.345
RE O5o2 188.01
RE O5o3 192.568
RE O5o4 204.3
RE O5o5 201.1
RE O6o1 72.005
RE O6o2 193.833
RE O6o3 196.651
RE O6o4 204.25
RE O6o5 241.079
* Defining the variables
VARIABLES
DO I 1 N
DO J 1 5
X T(I,J)
X O(I,J)
OD J
X V(I,2)
X W(I,2)
X V(I,3)
X W(I,3)
X V(I,4)
OD I
* Objective function groups
GROUPS
DO i 1 N
I+ n+i N i
DO j 1 5
XN R(i,j) T(i,j) 1.0
XN R(n+i,j) O(i,j) 1.0
ND
* Linear Constraints
DO i 1 N-1
IA k+1 i 1
DO j 1 5
XE G(i,j) T(k+1,j) 1.0 T(i,j) -1.0
XE G(i,j) O(i,j) 1.0
OD j
DO j 2 5
IA j-1 j -1
XE G(i,j) O(i,j-1) -1.0
ND
DO j 1 5
XE G(N,j) T(1,j) 1.0 T(N,j) -1.0
XE G(N,j) O(N,j) 1.0
ND
DO j 2 5
IA j-1 j -1
XE G(N,j) O(N,j-1) -1.0
ND
DO i 1 N
* Nonlinear constraints
XE A(i,1) O(i,2) -1.0
XE A(i,2) O(i,3) -1.0
XE A(i,3) O(i,4) -1.0
* Artificial linear constraints
XE V(i,2) V(i,2) -1.0
RE C 961.6
RD C C 1.0
ZE V(i,2) T(i,2) C
RE C 9.2
RD C C 1.0
ZE V(i,2) T(i,3) C
XE W(i,2) W(i,2) -1.0
RE C 480.8
RD C C 1.0
ZE W(i,2) T(i,2) C
RE C -4.6
RD C C 1.0
ZE W(i,2) T(i,3) C
XE V(i,3) V(i,3) -1.0
RE C 4.6
RD C C 1.0
ZE V(i,3) T(i,3) C
XE W(i,3) W(i,3) -1.0
RE C 4.6
RD C C 1.0
ZE W(i,3) T(i,3) C
RE C -105.15
RD C C 1.0
ZE W(i,3) T(i,4) C
XE V(i,4) V(i,4) -1.0
RE C 105.15
RD C C 1.0
ZE V(i,4) T(i,4) C
ND
CONSTANTS
Z LAKES R(1,1) S1s1
Z LAKES R(1,2) S1s2
Z LAKES R(1,3) S1s3
Z LAKES R(1,4) S1s4
Z LAKES R(1,5) S1s5
Z LAKES R(2,1) S2s1
Z LAKES R(2,2) S2s2
Z LAKES R(2,3) S2s3
Z LAKES R(2,4) S2s4
Z LAKES R(2,5) S2s5
Z LAKES R(3,1) S3s1
Z LAKES R(3,2) S3s2
Z LAKES R(3,3) S3s3
Z LAKES R(3,4) S3s4
Z LAKES R(3,5) S3s5
Z LAKES R(4,1) S4s1
Z LAKES R(4,2) S4s2
Z LAKES R(4,3) S4s3
Z LAKES R(4,4) S4s4
Z LAKES R(4,5) S4s5
Z LAKES R(5,1) S5s1
Z LAKES R(5,2) S5s2
Z LAKES R(5,3) S5s3
Z LAKES R(5,4) S5s4
Z LAKES R(5,5) S5s5
Z LAKES R(6,1) S6s1
Z LAKES R(6,2) S6s2
Z LAKES R(6,3) S6s3
Z LAKES R(6,4) S6s4
Z LAKES R(6,5) S6s5
Z LAKES R(7,1) O1o5
Z LAKES R(7,2) O1o2
Z LAKES R(7,3) O1o3
Z LAKES R(7,4) O1o4
Z LAKES R(7,5) O1o5
Z LAKES R(8,1) O2o1
Z LAKES R(8,2) O2o2
Z LAKES R(8,3) O2o3
Z LAKES R(8,4) O2o4
Z LAKES R(8,5) O2o5
Z LAKES R(9,1) O3o1
Z LAKES R(9,2) O3o2
Z LAKES R(9,3) O3o3
Z LAKES R(9,4) O3o4
Z LAKES R(9,5) O3o5
Z LAKES R(10,1) O4o1
Z LAKES R(10,2) O4o2
Z LAKES R(10,3) O4o3
Z LAKES R(10,4) O4o4
Z LAKES R(10,5) O4o5
Z LAKES R(11,1) O5o1
Z LAKES R(11,2) O5o2
Z LAKES R(11,3) O5o3
Z LAKES R(11,4) O5o4
Z LAKES R(11,5) O5o5
Z LAKES R(12,1) O6o1
Z LAKES R(12,2) O6o2
Z LAKES R(12,3) O6o3
Z LAKES R(12,4) O6o4
Z LAKES R(12,5) O6o5
X LAKES G(1,1) -22.0
X LAKES G(1,2) -1.0
X LAKES G(1,3) 3.0
X LAKES G(1,4) -27.2
X LAKES G(1,5) 51.5
X LAKES G(2,1) 44.0
X LAKES G(2,2) 162.0
X LAKES G(2,3) 8.0
X LAKES G(2,4) 12.5
X LAKES G(2,5) 53.5
X LAKES G(3,1) -11.0
X LAKES G(3,2) 60.0
X LAKES G(3,3) 10.0
X LAKES G(3,4) 18.0
X LAKES G(3,5) 39.0
X LAKES G(4,1) 124.0
X LAKES G(4,2) 246.0
X LAKES G(4,3) 6.0
X LAKES G(4,4) 9.7
X LAKES G(4,5) 17.2
X LAKES G(5,1) 127.0
X LAKES G(5,2) 175.0
X LAKES G(5,3) 3.0
X LAKES G(5,4) 10.0
X LAKES G(5,5) 30.2
X LAKES G(6,1) 78.0
X LAKES G(6,2) 156.0
X LAKES G(6,3) 3.0
X LAKES G(6,4) 14.0
X LAKES G(6,5) 23.2
DO i 1 N
X LAKES V(i,2) 543.4
X LAKES W(i,2) 0.0
X LAKES V(i,3) 543.4
X LAKES W(i,3) 0.0
X LAKES V(i,4) 550.11
ND
BOUNDS
FR LAKES 'DEFAULT'
DO i 1 N
XL LAKES W(i,2) 0.0001
XL LAKES W(i,3) 0.0001
XL LAKES V(i,4) 0.0001
ND
START POINT
LAKES 'DEFAULT' 1.0
ELEMENT TYPE
EV 1VAR V
EP 1VAR P
EV 2VAR V
EV 2VAR W
EP 2VAR P
ELEMENT USES
DO i 1 N
XT B(i,1) 2VAR
ZV B(i,1) V V(i,2)
ZV B(i,1) W W(i,2)
XP B(i,1) P 0.0841168
XT B(i,2) 2VAR
ZV B(i,2) V V(i,3)
ZV B(i,2) W W(i,3)
XP B(i,2) P 0.1280849
XT B(i,3) 1VAR
ZV B(i,3) V V(i,4)
XP B(i,3) P 0.2605
ND
GROUP TYPE
GV L2 ALPHA
GROUP USES
DO i 1 N
XE A(i,1) B(i,1)
XE A(i,2) B(i,2)
XE A(i,3) B(i,3)
ND
DO i 1 N
I+ n+i N i
DO j 1 5
XT R(i,j) L2
XT R(n+i,j) L2
ND
*LO SOLUTION ?? ! Probably infeasible
ENDATA
ELEMENTS LAKES
TEMPORARIES
INDIVIDUALS
T 1VAR
F P * V ** 2.2
G V P * 2.2 * V ** 1.2
H V V P * 2.64 * V ** 0.2
T 2VAR
F P * V ** 2 * W ** 0.5
G V P * 2.0 * V * W ** 0.5
G W P * 0.5 * V ** 2 / W ** 0.5
H V V P * 2.0 * W ** 0.5
H V W P * V / W ** 0.5
H W W - P * 0.25 * V ** 2 / W ** 1.5
ENDATA
GROUPS LAKES
INDIVIDUALS
T L2
F ALPHA * ALPHA
G ALPHA + ALPHA
H 2.0
ENDATA