-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathLIN.SIF
368 lines (293 loc) · 9.32 KB
/
LIN.SIF
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
***************************
* SET UP THE INITIAL DATA *
***************************
NAME LIN
* Problem :
* *********
* A non-convex global optimization chemical equilibrium problem from the
* thesis of W.J. Lin.
* It has a nonlinear objective and linear constraints.
* Source: illustrative example (section 4.6) in
* C.M. McDonald and C.A. Floudas, "Global optimization for the phase
* and chemical equilibrium problem: application to the NRTL equation",
* Computers & Chemical Engineering, (submitted), 1994.
* SIF input: Marcel Mongeau, 9 February 1994.
* classification OLR2-AY-4-2
* PARAMETERS likely to be changed for different problems:
* Number of variable sets (# of phases)
IE P 2
* Number of components
IE C 2
IE 1 1
IE 2 2
* Constants
* (A for array, i.e. indexed names)
AE TAU(1,2) 3.00498
AE TAU(2,1) 4.69071
AE ALF(1,2) 0.391965
AE ALF(2,1) 0.391965
* Initial quantities of each component
AE INIT(1) 0.5
AE INIT(2) 0.5
VARIABLES
DO I 1 C
DO K 1 P
X X(I,K)
ND
GROUPS
* Linearities (none here) in the objective function:
N OBJ
* Mass-balance constraints
* (X or Z when using parametrized (indexed) names:
* X for numerical value; Z when assigning a named parameter)
DO I 1 C
DO K 1 P
XE MB(I) X(I,K) 1.0
ND
CONSTANTS
* Right-hand side of constraints
DO I 1 C
Z LIN MB(I) INIT(I)
OD I
* Other parameters:
* (A for arrays)
RE ZERO 0.0
RE ONE 1.0
DO I 1 C
A= ALF(I,I) ZERO
A= TAU(I,I) ZERO
OD I
DO I 1 C
DO J 1 C
AM MALF ALF(I,J) -1.0
A* PROD MALF TAU(I,J)
A( G(I,J) EXP PROD
ND
DO I 1 C
A= G(I,I) ONE
OD I
DO I 1 C
DO J 1 C
A* M(I,J) G(I,J) TAU(I,J)
ND
BOUNDS
XL LIN 'DEFAULT' 1.D-12
ZU LIN X(1,1) INIT1
ZU LIN X(1,2) INIT1
ZU LIN X(2,1) INIT2
ZU LIN X(2,2) INIT2
START POINT
XV LIN X(1,1) 0.5
XV LIN X(1,2) 0.0
XV LIN X(2,1) 0.0
XV LIN X(2,2) 0.5
ELEMENT TYPE
* With dependent elemental- and internal-variables
* (No indexed names allowed in sections TYPE)
* (P for parametrizing the definition of a type)
EV XTAUG1 Y1 Y2
EP XTAUG1 G11 G12
EP XTAUG1 G21 G22
EP XTAUG1 M11 M12
EP XTAUG1 M21 M22
EV XTAUG2 Y1 Y2
EP XTAUG2 G11 G12
EP XTAUG2 G21 G22
EP XTAUG2 M11 M12
EP XTAUG2 M21 M22
EV XLOGX X
EV XLOGXC X
EV XLOGXC Y1 Y2
IV XLOGXC XX YY
ELEMENT USES
* Assign an element type to each element fct and define the particular
* problem variables that will be assigned to the above elemental variables
DO K 1 P
XT A(1,K) XTAUG1
ZV A(1,K) Y1 X(1,K)
ZV A(1,K) Y2 X(2,K)
ZP A(1,K) G11 G(1,1)
ZP A(1,K) G12 G(1,2)
ZP A(1,K) G21 G(2,1)
ZP A(1,K) G22 G(2,2)
ZP A(1,K) M11 M(1,1)
ZP A(1,K) M12 M(1,2)
ZP A(1,K) M21 M(2,1)
ZP A(1,K) M22 M(2,2)
XT A(2,K) XTAUG2
ZV A(2,K) Y1 X(1,K)
ZV A(2,K) Y2 X(2,K)
ZP A(2,K) G11 G(1,1)
ZP A(2,K) G12 G(1,2)
ZP A(2,K) G21 G(2,1)
ZP A(2,K) G22 G(2,2)
ZP A(2,K) M11 M(1,1)
ZP A(2,K) M12 M(1,2)
ZP A(2,K) M21 M(2,1)
ZP A(2,K) M22 M(2,2)
ND
DO K 1 P
DO I 1 C
XT B(I,K) XLOGX
ZV B(I,K) X X(I,K)
ND
DO K 1 P
DO I 1 C
XT C(I,K) XLOGXC
ZV C(I,K) X X(I,K)
ZV C(I,K) Y1 X(1,K)
ZV C(I,K) Y2 X(2,K)
ND
GROUP USES
* Assign element functions to groups
DO K 1 P
XE OBJ A(1,K) A(2,K)
DO I 1 C
XE OBJ B(I,K)
XE OBJ C(I,K) -1.0
ND
OBJECT BOUND
* Solution
*Global minimum: -0.02020 :
* XV LIN X(1,1) 0.00071
* XV LIN X(1,2) 0.49929
* XV LIN X(2,1) 0.15588
* XV LIN X(2,2) 0.34412
*local minimum: -0.01961 :
* XV LIN X(1,1) 0.00213
* XV LIN X(1,2) 0.49787
* XV LIN X(2,1) 0.46547
* XV LIN X(2,2) 0.03453
*local maximum: -0.01730 :
* XV LIN X(1,1) 0.00173
* XV LIN X(1,2) 0.49827
* XV LIN X(2,1) 0.37544
* XV LIN X(2,2) 0.12456
*LO SOLTN -0.02020
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS LIN
TEMPORARIES
* Declare temporary variables and intrinsic (Machine) and external fct needed:
R INSUM1
R INSUM2
R SUM
R RATIO1
R RATIO2
R TERM1
R TERM2
R SQ1
R SQ2
R SQ11
R SQ12
R SQ21
R SQ22
R TRI1
R TRI2
R CUB1
R CUB2
R CUB11
R CUB12
R CUBM21
R CUBM22
R CUB21
R CUB22
R H1
R H2
R H3
R H4
R H5
R LOGX
M LOG
INDIVIDUALS
* Define the (linear) Relations that define each internal variable in terms
* of the elemental variables. Specify the actual nonlinear behaviour of the
* element types.
T XTAUG1
A INSUM1 Y1*G11 + Y2*G21
A INSUM2 Y1*G12 + Y2*G22
A RATIO1 M11/INSUM1
A RATIO2 M12/INSUM2
A TERM1 Y1*RATIO1
A TERM2 Y2*RATIO2
A SUM TERM1 + TERM2
A SQ1 TERM1/INSUM1
A SQ2 TERM2/INSUM2
A SQ11 SQ1*G11
A SQ12 SQ2*G12
A SQ21 SQ1*G21
A SQ22 SQ2*G22
A TRI1 RATIO1 - SQ11 - SQ12
A TRI2 RATIO2 - SQ21 - SQ22
A CUB1 SQ11/INSUM1
A CUB2 SQ12/INSUM2
A CUB11 CUB1*G11
A CUB12 CUB2*G12
A CUBM21 CUB1*G21
A CUBM22 CUB2*G22
A CUB21 SQ21*G21/INSUM1
A CUB22 SQ22*G22/INSUM2
A H1 RATIO2-SQ22-2*SQ21
A H2 M12*G12/INSUM2**2
A H3 SQ1*G21**2/INSUM1
A H4 M12*G22/INSUM2**2
A H5 SQ2*G22**2/INSUM2
F Y1 * SUM
G Y1 SUM + Y1*TRI1
G Y2 Y1*TRI2
H Y1 Y1 2*(TRI1 + Y1*(-SQ11+CUB11+CUB12))
H Y1 Y2 H1 + Y1*(-H2 + 2*(CUBM21+CUBM22))
H Y2 Y2 2*Y1*(H3 - H4 + H5)
T XTAUG2
A INSUM1 Y1*G11 + Y2*G21
A INSUM2 Y1*G12 + Y2*G22
A RATIO1 M21/INSUM1
A RATIO2 M22/INSUM2
A TERM1 Y1*RATIO1
A TERM2 Y2*RATIO2
A SUM TERM1 + TERM2
A SQ1 TERM1/INSUM1
A SQ2 TERM2/INSUM2
A SQ11 SQ1*G11
A SQ12 SQ2*G12
A SQ21 SQ1*G21
A SQ22 SQ2*G22
A TRI1 RATIO1 - SQ11 - SQ12
A TRI2 RATIO2 - SQ21 - SQ22
A CUB1 SQ11/INSUM1
A CUB2 SQ12/INSUM2
A CUB11 CUB1*G11
A CUB12 CUB2*G12
A CUBM21 CUB1*G21
A CUBM22 CUB2*G22
A CUB21 SQ21*G21/INSUM1
A CUB22 SQ22*G22/INSUM2
A H1 RATIO1-SQ11-2*SQ12
A H2 M21*G21/INSUM1**2
A H3 SQ1*G11**2/INSUM1
A H4 M21*G11/INSUM1**2
A H5 SQ2*G12**2/INSUM2
F Y2 * SUM
G Y1 Y2*TRI1
G Y2 SUM + Y2*TRI2
H Y1 Y1 2*Y2*(H3 - H4 + H5)
H Y1 Y2 H1 + Y2*(-H2 +2*(CUBM21+CUBM22))
H Y2 Y2 2*(TRI2 + Y2*(-SQ22+CUB21+CUB22))
T XLOGX
A LOGX LOG( X )
F X * LOGX
G X LOGX + 1.0
H X X 1.0 / X
T XLOGXC
R YY Y1 1.0 Y2 1.0
R XX X 1.0
A LOGX LOG( YY )
F XX * LOGX
G XX LOGX
G YY XX / YY
H XX YY 1.0 / YY
H YY YY - XX / YY**2
ENDATA