1 | // $Id: IP.lib,v 1.1.1.1 2000-05-02 12:58:31 Singular Exp $ |
---|
2 | // |
---|
3 | // author : Christine Theis |
---|
4 | // |
---|
5 | |
---|
6 | //version="$Id: IP.lib,v 1.1.1.1 2000-05-02 12:58:31 Singular Exp $"; |
---|
7 | |
---|
8 | /////////////////////////////////////////////////////////////////////////////// |
---|
9 | |
---|
10 | info=" |
---|
11 | LIBRARY: IP.lib PROCEDURES FOR INTEGER PROGRAMMING USING GROEBNER BASIS METHODS |
---|
12 | |
---|
13 | |
---|
14 | Let A an integral (mxn)-matrix, b a vector with m integral |
---|
15 | coefficients and c a vector with n nonnegative integral coefficients. The |
---|
16 | solution of the IP-problem |
---|
17 | |
---|
18 | (*) minimize{ cx | Ax=b, all components of x are nonnegative integers } |
---|
19 | |
---|
20 | proceeds in two steps: |
---|
21 | |
---|
22 | 1. We compute the toric ideal of A and its Groebner basis with respect |
---|
23 | to a term ordering refining the cost function c (such an ordering |
---|
24 | exists because c is nonnegative). |
---|
25 | |
---|
26 | 2. We reduce the right hand vector b or an initial solution of the problem |
---|
27 | modulo this ideal. |
---|
28 | |
---|
29 | For these purposes, we can use seven different algorithms: |
---|
30 | The algorithm of Conti/Traverso (ct) can compute an optimal solution |
---|
31 | of the IP-problem directly from the right hand vector b. The same is |
---|
32 | true for its `positive' variant (pct) which can only be applied if A |
---|
33 | and b have nonnegative entries, but should be faster in that case. |
---|
34 | All other algorithms need initial solutions of the IP-problem. Except |
---|
35 | from the Conti-Traverso algorithm with elimination (ect), |
---|
36 | they should be more efficient than the algorithm mentionned before. |
---|
37 | These are the algorithms of Pottier (pt), Bigatti/La Scala/Robbiano |
---|
38 | (blr), Hosten/Sturmfels (hs) and Di Biase/Urbanke (du). The last two |
---|
39 | seem to be the fastest in the actual implementation. |
---|
40 | |
---|
41 | |
---|
42 | solve_IP(intmat A, intvec bx, intvec c, string alg); |
---|
43 | solve_IP(intmat A, list bx, intvec c, string alg); |
---|
44 | solve_IP(intmat A, intvec bx, intvec c, string alg, intvec prsv); |
---|
45 | solve_IP(intmat A, list bx, intvec c, string alg, intvec prsv); |
---|
46 | |
---|
47 | procedures for solving the IP-problem (*) |
---|
48 | They return the solution(s) of the given problem(s) or the |
---|
49 | message `not solvable'. |
---|
50 | `alg' may be one of the algorithm abbreviations as above. |
---|
51 | If `alg' is chosen to be `ct' or `pct', bx is read as the right |
---|
52 | hand vector b of the system Ax=b. b should then be an intvec of |
---|
53 | size m where m is the number of rows of A. Furthermore, bx and |
---|
54 | A should be nonnegative if `pct' is used. |
---|
55 | If `alg' is chosen to be `ect',`pt',`blr',`hs' or `du', bx is |
---|
56 | read as an initial solution x of the system Ax=b. bx should |
---|
57 | then be a nonnegative intvec of size n where n is the number |
---|
58 | of columns of A. |
---|
59 | If `alg' is chosen to be `blr' or `hs', the algorithm needs a |
---|
60 | vector with positive coefficcients in the row space of A. If |
---|
61 | no row of A contains only positive entries, one must use the |
---|
62 | versions of solve_IP which take such a vector prsv as |
---|
63 | argument. |
---|
64 | solve_IP may also be called with a list bx of intvecs instead |
---|
65 | of a single intvec. |
---|
66 | |
---|
67 | |
---|
68 | "; |
---|
69 | |
---|
70 | /////////////////////////////////////////////////////////////////////////////// |
---|
71 | |
---|
72 | |
---|
73 | |
---|
74 | static proc solve_IP_1(intmat A, intvec bx, intvec c, string alg) |
---|
75 | { |
---|
76 | intvec v; |
---|
77 | // to be returned |
---|
78 | |
---|
79 | // check arguments as far as necessary |
---|
80 | // other inconsistencies are detected by the external program |
---|
81 | if(size(c)!=ncols(A)) |
---|
82 | { |
---|
83 | "ERROR: number of matrix columns must equal size of cost vector"; |
---|
84 | return(v); |
---|
85 | } |
---|
86 | |
---|
87 | // create first temporary file with that the external program is |
---|
88 | // called |
---|
89 | |
---|
90 | int process=system("pid"); |
---|
91 | string matrixfile="temp_MATRIX"+string(process); |
---|
92 | link MATRIX=":w "+matrixfile; |
---|
93 | open(MATRIX); |
---|
94 | |
---|
95 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
---|
96 | int i,j; |
---|
97 | for(j=1;j<=ncols(A);j++) |
---|
98 | { |
---|
99 | write(MATRIX,c[j]); |
---|
100 | } |
---|
101 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
---|
102 | for(i=1;i<=nrows(A);i++) |
---|
103 | { |
---|
104 | for(j=1;j<=ncols(A);j++) |
---|
105 | { |
---|
106 | write(MATRIX,A[i,j]); |
---|
107 | } |
---|
108 | } |
---|
109 | |
---|
110 | // search for positive row space vector, if required by the |
---|
111 | // algorithm |
---|
112 | int found=0; |
---|
113 | if((alg=="blr") || (alg=="hs")) |
---|
114 | { |
---|
115 | for(i=1;i<=nrows(A);i++) |
---|
116 | { |
---|
117 | found=i; |
---|
118 | for(j=1;j<=ncols(A);j++) |
---|
119 | { |
---|
120 | if(A[i,j]<=0) |
---|
121 | { |
---|
122 | found=0; |
---|
123 | } |
---|
124 | } |
---|
125 | if(found>0) |
---|
126 | { |
---|
127 | break; |
---|
128 | } |
---|
129 | } |
---|
130 | if(found==0) |
---|
131 | { |
---|
132 | "ERROR: algorithm needs positive vector in the row space of the matrix"; |
---|
133 | close(MATRIX); |
---|
134 | system("sh","rm -f "+matrixfile); |
---|
135 | return(v); |
---|
136 | } |
---|
137 | write(MATRIX,"positive row space vector:"); |
---|
138 | for(j=1;j<=ncols(A);j++) |
---|
139 | { |
---|
140 | write(MATRIX,A[found,j]); |
---|
141 | } |
---|
142 | } |
---|
143 | close(MATRIX); |
---|
144 | |
---|
145 | // create second temporary file for the external program |
---|
146 | |
---|
147 | string problemfile="temp_PROBLEM"+string(process); |
---|
148 | link PROBLEM=":w "+problemfile; |
---|
149 | open(PROBLEM); |
---|
150 | |
---|
151 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
---|
152 | for(i=1;i<=size(bx);i++) |
---|
153 | { |
---|
154 | write(PROBLEM,bx[i]); |
---|
155 | } |
---|
156 | close(PROBLEM); |
---|
157 | |
---|
158 | // call external program |
---|
159 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
---|
160 | |
---|
161 | // read solution from created file |
---|
162 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
---|
163 | string solution=read(SOLUTION); |
---|
164 | int pos; |
---|
165 | string s; |
---|
166 | if(alg=="ct" || alg=="pct") |
---|
167 | { |
---|
168 | pos=find(solution,"NO"); |
---|
169 | if(pos!=0) |
---|
170 | { |
---|
171 | "not solvable"; |
---|
172 | } |
---|
173 | else |
---|
174 | { |
---|
175 | pos=find(solution,"YES"); |
---|
176 | pos=find(solution,":",pos); |
---|
177 | pos++; |
---|
178 | for(j=1;j<=ncols(A);j++) |
---|
179 | { |
---|
180 | while(solution[pos]==" " || solution[pos]==newline) |
---|
181 | { |
---|
182 | pos++; |
---|
183 | } |
---|
184 | s=""; |
---|
185 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
186 | { |
---|
187 | s=s+solution[pos]; |
---|
188 | pos++; |
---|
189 | } |
---|
190 | execute("v[j]="+s+";"); |
---|
191 | } |
---|
192 | } |
---|
193 | } |
---|
194 | else |
---|
195 | { |
---|
196 | pos=find(solution,"optimal"); |
---|
197 | pos=find(solution,":",pos); |
---|
198 | pos++; |
---|
199 | for(j=1;j<=ncols(A);j++) |
---|
200 | { |
---|
201 | while(solution[pos]==" " || solution[pos]==newline) |
---|
202 | { |
---|
203 | pos++; |
---|
204 | } |
---|
205 | s=""; |
---|
206 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
207 | { |
---|
208 | s=s+solution[pos]; |
---|
209 | pos++; |
---|
210 | } |
---|
211 | execute("v[j]="+s+";"); |
---|
212 | } |
---|
213 | } |
---|
214 | |
---|
215 | // delete all created files |
---|
216 | dummy=system("sh","rm -f "+matrixfile); |
---|
217 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
---|
218 | dummy=system("sh","rm -f "+problemfile); |
---|
219 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
---|
220 | |
---|
221 | return(v); |
---|
222 | } |
---|
223 | |
---|
224 | |
---|
225 | |
---|
226 | static proc solve_IP_2(intmat A, list bx, intvec c, string alg) |
---|
227 | { |
---|
228 | list l;; |
---|
229 | // to be returned |
---|
230 | |
---|
231 | // check arguments as far as necessary |
---|
232 | // other inconsistencies are detected by the external program |
---|
233 | if(size(c)!=ncols(A)) |
---|
234 | { |
---|
235 | "ERROR: number of matrix columns must equal size of cost vector"; |
---|
236 | return(l); |
---|
237 | } |
---|
238 | |
---|
239 | int k; |
---|
240 | for(k=2;k<=size(bx);k++) |
---|
241 | { |
---|
242 | if(size(bx[k])!=size(bx[1])) |
---|
243 | { |
---|
244 | "ERROR: size of all right hand vectors must be equal"; |
---|
245 | return(l); |
---|
246 | } |
---|
247 | } |
---|
248 | |
---|
249 | // create first temporary file with that the external program is |
---|
250 | // called |
---|
251 | |
---|
252 | int process=system("pid"); |
---|
253 | string matrixfile="temp_MATRIX"+string(process); |
---|
254 | link MATRIX=":w "+matrixfile; |
---|
255 | open(MATRIX); |
---|
256 | |
---|
257 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
---|
258 | int i,j; |
---|
259 | for(j=1;j<=ncols(A);j++) |
---|
260 | { |
---|
261 | write(MATRIX,c[j]); |
---|
262 | } |
---|
263 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
---|
264 | for(i=1;i<=nrows(A);i++) |
---|
265 | { |
---|
266 | for(j=1;j<=ncols(A);j++) |
---|
267 | { |
---|
268 | write(MATRIX,A[i,j]); |
---|
269 | } |
---|
270 | } |
---|
271 | |
---|
272 | // search for positive row space vector, if required by the |
---|
273 | // algorithm |
---|
274 | int found=0; |
---|
275 | if((alg=="blr") || (alg=="hs")) |
---|
276 | { |
---|
277 | for(i=1;i<=nrows(A);i++) |
---|
278 | { |
---|
279 | found=i; |
---|
280 | for(j=1;j<=ncols(A);j++) |
---|
281 | { |
---|
282 | if(A[i,j]<=0) |
---|
283 | { |
---|
284 | found=0; |
---|
285 | } |
---|
286 | } |
---|
287 | if(found>0) |
---|
288 | { |
---|
289 | break; |
---|
290 | } |
---|
291 | } |
---|
292 | if(found==0) |
---|
293 | { |
---|
294 | "ERROR: algorithm needs positive vector in the row space of the matrix"; |
---|
295 | close(MATRIX); |
---|
296 | system("sh","rm -f "+matrixfile); |
---|
297 | return(l); |
---|
298 | } |
---|
299 | write(MATRIX,"positive row space vector:"); |
---|
300 | for(j=1;j<=ncols(A);j++) |
---|
301 | { |
---|
302 | write(MATRIX,A[found,j]); |
---|
303 | } |
---|
304 | } |
---|
305 | close(MATRIX); |
---|
306 | |
---|
307 | // create second temporary file for the external program |
---|
308 | |
---|
309 | string problemfile="temp_PROBLEM"+string(process); |
---|
310 | link PROBLEM=":w "+problemfile; |
---|
311 | open(PROBLEM); |
---|
312 | |
---|
313 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
---|
314 | for(k=1;k<=size(bx);k++) |
---|
315 | { |
---|
316 | for(i=1;i<=size(bx[1]);i++) |
---|
317 | { |
---|
318 | write(PROBLEM,bx[k][i]); |
---|
319 | } |
---|
320 | } |
---|
321 | close(PROBLEM); |
---|
322 | |
---|
323 | // call external program |
---|
324 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
---|
325 | |
---|
326 | // read solution from created file |
---|
327 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
---|
328 | string solution=read(SOLUTION); |
---|
329 | intvec v; |
---|
330 | int pos,pos1,pos2; |
---|
331 | string s; |
---|
332 | if(alg=="ct" || alg=="pct") |
---|
333 | { |
---|
334 | pos=1; |
---|
335 | for(k=1;k<=size(bx);k++) |
---|
336 | { |
---|
337 | pos1=find(solution,"NO",pos); |
---|
338 | pos2=find(solution,"YES",pos); |
---|
339 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
---|
340 | // first problem not solvable |
---|
341 | { |
---|
342 | pos=find(solution,":",pos1); |
---|
343 | l=insert(l,"not solvable",size(l)); |
---|
344 | } |
---|
345 | else |
---|
346 | // first problem solvable |
---|
347 | { |
---|
348 | pos=find(solution,":",pos2); |
---|
349 | pos++; |
---|
350 | for(j=1;j<=ncols(A);j++) |
---|
351 | { |
---|
352 | while(solution[pos]==" " || solution[pos]==newline) |
---|
353 | { |
---|
354 | pos++; |
---|
355 | } |
---|
356 | s=""; |
---|
357 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
358 | { |
---|
359 | s=s+solution[pos]; |
---|
360 | pos++; |
---|
361 | } |
---|
362 | execute("v[j]="+s+";"); |
---|
363 | } |
---|
364 | l=insert(l,v,size(l)); |
---|
365 | } |
---|
366 | } |
---|
367 | } |
---|
368 | else |
---|
369 | { |
---|
370 | pos=1; |
---|
371 | for(k=1;k<=size(bx);k++) |
---|
372 | { |
---|
373 | pos=find(solution,"optimal",pos); |
---|
374 | pos=find(solution,":",pos); |
---|
375 | pos++; |
---|
376 | for(j=1;j<=ncols(A);j++) |
---|
377 | { |
---|
378 | while(solution[pos]==" " || solution[pos]==newline) |
---|
379 | { |
---|
380 | pos++; |
---|
381 | } |
---|
382 | s=""; |
---|
383 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
384 | { |
---|
385 | s=s+solution[pos]; |
---|
386 | pos++; |
---|
387 | } |
---|
388 | execute("v[j]="+s+";"); |
---|
389 | } |
---|
390 | l=insert(l,v,size(l)); |
---|
391 | } |
---|
392 | } |
---|
393 | |
---|
394 | // delete all created files |
---|
395 | dummy=system("sh","rm -f "+matrixfile); |
---|
396 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
---|
397 | dummy=system("sh","rm -f "+problemfile); |
---|
398 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
---|
399 | |
---|
400 | return(l); |
---|
401 | } |
---|
402 | |
---|
403 | |
---|
404 | |
---|
405 | static proc solve_IP_3(intmat A, intvec bx, intvec c, string alg, intvec prsv) |
---|
406 | { |
---|
407 | intvec v; |
---|
408 | // to be returned |
---|
409 | |
---|
410 | // check arguments as far as necessary |
---|
411 | // other inconsistencies are detected by the external program |
---|
412 | if(size(c)!=ncols(A)) |
---|
413 | { |
---|
414 | "ERROR: number of matrix columns must equal size of cost vector"; |
---|
415 | return(v); |
---|
416 | } |
---|
417 | |
---|
418 | if(size(prsv)!=ncols(A)) |
---|
419 | { |
---|
420 | "ERROR: number of matrix columns must equal size of positive row space vector"; |
---|
421 | return(v); |
---|
422 | } |
---|
423 | |
---|
424 | // create first temporary file with that the external program is |
---|
425 | // called |
---|
426 | |
---|
427 | int process=system("pid"); |
---|
428 | string matrixfile="temp_MATRIX"+string(process); |
---|
429 | link MATRIX=":w "+matrixfile; |
---|
430 | open(MATRIX); |
---|
431 | |
---|
432 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
---|
433 | int i,j; |
---|
434 | for(j=1;j<=ncols(A);j++) |
---|
435 | { |
---|
436 | write(MATRIX,c[j]); |
---|
437 | } |
---|
438 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
---|
439 | for(i=1;i<=nrows(A);i++) |
---|
440 | { |
---|
441 | for(j=1;j<=ncols(A);j++) |
---|
442 | { |
---|
443 | write(MATRIX,A[i,j]); |
---|
444 | } |
---|
445 | } |
---|
446 | |
---|
447 | // enter positive row space vector, if required by the algorithm |
---|
448 | if((alg=="blr") || (alg=="hs")) |
---|
449 | { |
---|
450 | write(MATRIX,"positive row space vector:"); |
---|
451 | for(j=1;j<=ncols(A);j++) |
---|
452 | { |
---|
453 | write(MATRIX,prsv[j]); |
---|
454 | } |
---|
455 | } |
---|
456 | close(MATRIX); |
---|
457 | |
---|
458 | // create second temporary file for the external program |
---|
459 | |
---|
460 | string problemfile="temp_PROBLEM"+string(process); |
---|
461 | link PROBLEM=":w "+problemfile; |
---|
462 | open(PROBLEM); |
---|
463 | |
---|
464 | write(PROBLEM,"PROBLEM","vector size:",size(bx),"number of instances:",1,"right hand or initial solution vectors:"); |
---|
465 | for(i=1;i<=size(bx);i++) |
---|
466 | { |
---|
467 | write(PROBLEM,bx[i]); |
---|
468 | } |
---|
469 | close(PROBLEM); |
---|
470 | |
---|
471 | // call external program |
---|
472 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
---|
473 | |
---|
474 | // read solution from created file |
---|
475 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
---|
476 | string solution=read(SOLUTION); |
---|
477 | int pos; |
---|
478 | string s; |
---|
479 | if(alg=="ct" || alg=="pct") |
---|
480 | { |
---|
481 | pos=find(solution,"NO"); |
---|
482 | if(pos!=0) |
---|
483 | { |
---|
484 | "not solvable"; |
---|
485 | } |
---|
486 | else |
---|
487 | { |
---|
488 | pos=find(solution,"YES"); |
---|
489 | pos=find(solution,":",pos); |
---|
490 | pos++; |
---|
491 | for(j=1;j<=ncols(A);j++) |
---|
492 | { |
---|
493 | while(solution[pos]==" " || solution[pos]==newline) |
---|
494 | { |
---|
495 | pos++; |
---|
496 | } |
---|
497 | s=""; |
---|
498 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
499 | { |
---|
500 | s=s+solution[pos]; |
---|
501 | pos++; |
---|
502 | } |
---|
503 | execute("v[j]="+s+";"); |
---|
504 | } |
---|
505 | } |
---|
506 | } |
---|
507 | else |
---|
508 | { |
---|
509 | pos=find(solution,"optimal"); |
---|
510 | pos=find(solution,":",pos); |
---|
511 | pos++; |
---|
512 | for(j=1;j<=ncols(A);j++) |
---|
513 | { |
---|
514 | while(solution[pos]==" " || solution[pos]==newline) |
---|
515 | { |
---|
516 | pos++; |
---|
517 | } |
---|
518 | s=""; |
---|
519 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
520 | { |
---|
521 | s=s+solution[pos]; |
---|
522 | pos++; |
---|
523 | } |
---|
524 | execute("v[j]="+s+";"); |
---|
525 | } |
---|
526 | } |
---|
527 | |
---|
528 | // delete all created files |
---|
529 | dummy=system("sh","rm -f "+matrixfile); |
---|
530 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
---|
531 | dummy=system("sh","rm -f "+problemfile); |
---|
532 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
---|
533 | |
---|
534 | return(v); |
---|
535 | } |
---|
536 | |
---|
537 | |
---|
538 | |
---|
539 | static proc solve_IP_4(intmat A, list bx, intvec c, string alg, intvec prsv) |
---|
540 | { |
---|
541 | list l; |
---|
542 | // to be returned |
---|
543 | |
---|
544 | // check arguments as far as necessary |
---|
545 | // other inconsistencies are detected by the external program |
---|
546 | if(size(c)!=ncols(A)) |
---|
547 | { |
---|
548 | "ERROR: number of matrix columns must equal size of cost vector"; |
---|
549 | return(l); |
---|
550 | } |
---|
551 | |
---|
552 | if(size(prsv)!=ncols(A)) |
---|
553 | { |
---|
554 | "ERROR: number of matrix columns must equal size of positive row space vector"; |
---|
555 | return(v); |
---|
556 | } |
---|
557 | |
---|
558 | int k; |
---|
559 | for(k=2;k<=size(bx);k++) |
---|
560 | { |
---|
561 | if(size(bx[k])!=size(bx[1])) |
---|
562 | { |
---|
563 | "ERROR: size of all right hand vectors must be equal"; |
---|
564 | return(l); |
---|
565 | } |
---|
566 | } |
---|
567 | |
---|
568 | // create first temporary file with that the external program is |
---|
569 | // called |
---|
570 | |
---|
571 | int process=system("pid"); |
---|
572 | string matrixfile="temp_MATRIX"+string(process); |
---|
573 | link MATRIX=":w "+matrixfile; |
---|
574 | open(MATRIX); |
---|
575 | |
---|
576 | write(MATRIX,"MATRIX","columns:",ncols(A),"cost vector:"); |
---|
577 | int i,j; |
---|
578 | for(j=1;j<=ncols(A);j++) |
---|
579 | { |
---|
580 | write(MATRIX,c[j]); |
---|
581 | } |
---|
582 | write(MATRIX,"rows:",nrows(A),"matrix:"); |
---|
583 | for(i=1;i<=nrows(A);i++) |
---|
584 | { |
---|
585 | for(j=1;j<=ncols(A);j++) |
---|
586 | { |
---|
587 | write(MATRIX,A[i,j]); |
---|
588 | } |
---|
589 | } |
---|
590 | |
---|
591 | // enter positive row space vector if required by the algorithm |
---|
592 | if((alg=="blr") || (alg=="hs")) |
---|
593 | { |
---|
594 | write(MATRIX,"positive row space vector:"); |
---|
595 | for(j=1;j<=ncols(A);j++) |
---|
596 | { |
---|
597 | write(MATRIX,prsv[j]); |
---|
598 | } |
---|
599 | } |
---|
600 | close(MATRIX); |
---|
601 | |
---|
602 | // create second temporary file for the external program |
---|
603 | |
---|
604 | string problemfile="temp_PROBLEM"+string(process); |
---|
605 | link PROBLEM=":w "+problemfile; |
---|
606 | open(PROBLEM); |
---|
607 | |
---|
608 | write(PROBLEM,"PROBLEM","vector size:",size(bx[1]),"number of instances:",size(bx),"right hand or initial solution vectors:"); |
---|
609 | for(k=1;k<=size(bx);k++) |
---|
610 | { |
---|
611 | for(i=1;i<=size(bx[1]);i++) |
---|
612 | { |
---|
613 | write(PROBLEM,bx[k][i]); |
---|
614 | } |
---|
615 | } |
---|
616 | close(PROBLEM); |
---|
617 | |
---|
618 | // call external program |
---|
619 | int dummy=system("sh","solve_IP -alg "+alg+" "+matrixfile+" "+problemfile); |
---|
620 | |
---|
621 | // read solution from created file |
---|
622 | link SOLUTION=":r "+matrixfile+".sol."+alg; |
---|
623 | string solution=read(SOLUTION); |
---|
624 | intvec v; |
---|
625 | int pos,pos1,pos2; |
---|
626 | string s; |
---|
627 | if(alg=="ct" || alg=="pct") |
---|
628 | { |
---|
629 | pos=1; |
---|
630 | for(k=1;k<=size(bx);k++) |
---|
631 | { |
---|
632 | pos1=find(solution,"NO",pos); |
---|
633 | pos2=find(solution,"YES",pos); |
---|
634 | if(pos1!=0 && (pos1<pos2 || pos2==0)) |
---|
635 | // first problem not solvable |
---|
636 | { |
---|
637 | pos=find(solution,":",pos1); |
---|
638 | l=insert(l,"not solvable",size(l)); |
---|
639 | } |
---|
640 | else |
---|
641 | // first problem solvable |
---|
642 | { |
---|
643 | pos=find(solution,":",pos2); |
---|
644 | pos++; |
---|
645 | for(j=1;j<=ncols(A);j++) |
---|
646 | { |
---|
647 | while(solution[pos]==" " || solution[pos]==newline) |
---|
648 | { |
---|
649 | pos++; |
---|
650 | } |
---|
651 | s=""; |
---|
652 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
653 | { |
---|
654 | s=s+solution[pos]; |
---|
655 | pos++; |
---|
656 | } |
---|
657 | execute("v[j]="+s+";"); |
---|
658 | } |
---|
659 | l=insert(l,v,size(l)); |
---|
660 | } |
---|
661 | } |
---|
662 | } |
---|
663 | else |
---|
664 | { |
---|
665 | pos=1; |
---|
666 | for(k=1;k<=size(bx);k++) |
---|
667 | { |
---|
668 | pos=find(solution,"optimal",pos); |
---|
669 | pos=find(solution,":",pos); |
---|
670 | pos++; |
---|
671 | for(j=1;j<=ncols(A);j++) |
---|
672 | { |
---|
673 | while(solution[pos]==" " || solution[pos]==newline) |
---|
674 | { |
---|
675 | pos++; |
---|
676 | } |
---|
677 | s=""; |
---|
678 | while(solution[pos]!=" " && solution[pos]!=newline) |
---|
679 | { |
---|
680 | s=s+solution[pos]; |
---|
681 | pos++; |
---|
682 | } |
---|
683 | execute("v[j]="+s+";"); |
---|
684 | } |
---|
685 | l=insert(l,v,size(l)); |
---|
686 | } |
---|
687 | } |
---|
688 | |
---|
689 | // delete all created files |
---|
690 | dummy=system("sh","rm -f "+matrixfile); |
---|
691 | dummy=system("sh","rm -f "+matrixfile+".GB."+alg); |
---|
692 | dummy=system("sh","rm -f "+problemfile); |
---|
693 | dummy=system("sh","rm -f "+matrixfile+".sol."+alg); |
---|
694 | |
---|
695 | return(l); |
---|
696 | } |
---|
697 | |
---|
698 | |
---|
699 | |
---|
700 | |
---|
701 | |
---|
702 | |
---|
703 | proc solve_IP |
---|
704 | "USAGE: |
---|
705 | solve_IP(A,bx,c,alg); A intmat, bx intvec, c intvec, alg string |
---|
706 | solve_IP(A,bx,c,alg); A intmat, bx list of intvec, c intvec, alg string |
---|
707 | solve_IP(A,bx,c,alg,prsv); A intmat, bx intvec, c intvec, alg string, |
---|
708 | prsv intvec |
---|
709 | solve_IP(A,bx,c,alg,prsv); A intmat, bx list of intvec, c intvec, alg string, |
---|
710 | prsv intvec |
---|
711 | RETURN: solution of the associated integer programming problem as explained |
---|
712 | in IP.lib |
---|
713 | return type = type of bx |
---|
714 | EXAMPLE: example solve_IP; shows an example" |
---|
715 | { |
---|
716 | if(size(#)==4) |
---|
717 | { |
---|
718 | if(typeof(#[2])=="intvec") |
---|
719 | { |
---|
720 | return(solve_IP_1(#[1],#[2],#[3],#[4])); |
---|
721 | } |
---|
722 | else |
---|
723 | { |
---|
724 | return(solve_IP_2(#[1],#[2],#[3],#[4])); |
---|
725 | } |
---|
726 | } |
---|
727 | else |
---|
728 | { |
---|
729 | if(typeof(#[2])=="intvec") |
---|
730 | { |
---|
731 | return(solve_IP_3(#[1],#[2],#[3],#[4],#[5])); |
---|
732 | } |
---|
733 | else |
---|
734 | { |
---|
735 | return(solve_IP_4(#[1],#[2],#[3],#[4],#[5])); |
---|
736 | } |
---|
737 | } |
---|
738 | } |
---|
739 | |
---|
740 | |
---|
741 | |
---|
742 | example |
---|
743 | { |
---|
744 | "EXAMPLE"; echo=2; |
---|
745 | |
---|
746 | // call with single right hand vector |
---|
747 | intmat A[2][3]=1,1,0,0,1,1; |
---|
748 | A; |
---|
749 | intvec b1=1,1; |
---|
750 | b1; |
---|
751 | intvec c=2,2,1; |
---|
752 | c; |
---|
753 | intvec solution_vector=solve_IP(A,b1,c,"pct"); |
---|
754 | solution_vector; |
---|
755 | |
---|
756 | // call with list of right hand vectors |
---|
757 | intvec b2=-1,1; |
---|
758 | list l=b1,b2; |
---|
759 | l; |
---|
760 | list solution_list=solve_IP(A,l,c,"ct"); |
---|
761 | solution_list; |
---|
762 | |
---|
763 | // call with single initial solution vector |
---|
764 | A=2,1,-1,-1,1,2; |
---|
765 | A; |
---|
766 | b1=3,4,5; |
---|
767 | solution_vector=solve_IP(A,b1,c,"du"); |
---|
768 | |
---|
769 | // call with single initial solution vector and algorithm needing a positive |
---|
770 | // row space vector |
---|
771 | solution_vector=solve_IP(A,b1,c,"hs"); |
---|
772 | |
---|
773 | // call with single initial solution vector and positive row space vector |
---|
774 | intvec prsv=1,2,1; |
---|
775 | prsv; |
---|
776 | solution_vector=solve_IP(A,b1,c,"hs",prsv); |
---|
777 | solution_vector; |
---|
778 | |
---|
779 | // call with list of initial solution vectors and positive row space vector |
---|
780 | b2=7,8,0; |
---|
781 | l=b1,b2; |
---|
782 | l; |
---|
783 | solution_list=solve_IP(A,l,c,"blr",prsv); |
---|
784 | solution_list; |
---|
785 | } |
---|
786 | |
---|
787 | |
---|
788 | |
---|