Substance

A Nonlinear Integer/Discrete/Continuous Solver Applied to an Oil Production Problem with 200 Oil Wells and 5 Oil Platforms

Jsun Yui Wong   

The following computer program tries to solve a location-allocation problem of searching for locations for five platforms and allocating 200 wells to these platforms.  Rectangular distances are used in line 1371 below.

The locations of wells given in line 23 through line line 34 below are from Table 2 of Cheung, Langevin, and Delmaire [1].

0 DEFSNG A-Z
3 DEFINT I,J,K,H
4 DIM X(1111),A(1111),L(1111),K(1111),PNEM(1111),ILO(1111),J(1111)
18 FOR IL=1 TO 400
19 READ L(IL)
20 NEXT IL
23 DATA 5,0,43,24,24,36,2,8,32,91,3,86,72,70,75,95,64,63,21,58,30,35,68,76,40,0,8,45,8,61
24 DATA 7,6,74,99,4,59,41,11,55,64,28,69,23,25,75,2,86,42,86,36,59,90,50,66,44,87,6,5,2,97
25 DATA 94,53,44,92,91,91,36,31,56,52,19,29,3,66,59,100,40,41,83,10,89,41,39,14,24,53,25,27,42,21,94,92,5,89,51,60,59,5,89,38
27 DATA 26,72,67,90,100,65,95,36,45,33,32,3,35,22,13,60,24,9,33,40,42,96,23,41,95,36,59,56,40,72
28 DATA 54,64,55,26,47,4,22,25,1,62,23,87,21,11,46,14,61,32,39,18
29 DATA 56,72,98,98,85,11,49,27,69,0,44,31,20,86,1,40,41,90,89,2,71,51,40,69,5,55,53,86,46,72,3,59,94,93,90,39,92,46,75,89,28,74,0,42,10,0,99,35,79,72
30 DATA 18,66,81,22,39,93,75,26,49,12,1,70,73,45,6,14,39,11,13,49,73,14,56,27,56,22,50,32,34,1,64,94,16,71,66,28,11,75,2,79,92,4,43,83,64,39,86,79,77,95,32,86,63,14,65,61
31 DATA 47,75,16,76,32,63,62,92,89,31,18,76,36,91,9,10,11,42,11,4,46,83,17,44,79,6,64,48,1,90,39,30,1,54,17,3,99,84,1,11,56,37,95,50
32 DATA 41,91,6,2,69,87,53,39,6,97,82,44,11,10,98,41,43,4,3,19,18,24,45,18,76,75,31,12,1,79,54,71,27,31,58,42,15,94,14,28
33 DATA 43,98,38,46,47,57,1,25,4,69,46,41,69,45,71,71,48,29,98,1,5,15,92,45,27,31,24,4,4,93,89,80,60,90,49,76,86,3,54,86
34 DATA 68,26,34,1,81,57,6,11,63,12,75,55,26,53,19,55,26,81,22,29
75 FOR JJJJ=-32000 TO 32000
76 RANDOMIZE JJJJ
77 M=-1.7E+38
88 FOR IAA=1 TO 10
89 A(IAA)=RND*100
90 NEXT IAA
111 FOR IBB= 11 TO 1010 STEP 1
112 A(IBB)=0
113 NEXT IBB
121 FOR IBB= 11 TO 1010 STEP 5
122 A(IBB)=1
123 NEXT IBB
126 REM   IMAR=10+FIX(RND*32700)
128 FOR I=1 TO 3270
129 FOR K=1 TO 1010
131 X(K)=A(K)
132 NEXT K
141 IF RND<.5 THEN 181 ELSE 244
181 J=1+FIX(RND*10)
183 R=RND*(1-RND*2)*A(J)
191 IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
192 GOTO 1333
244 IF RND<1/200 THEN JJ=11 ELSE IF RND<1/199 THEN JJ=16 ELSE IF RND<1/198 THEN JJ=21 ELSE IF RND<1/197 THEN JJ=26 ELSE IF RND<1/196 THEN JJ=31 ELSE IF RND<1/195 THEN JJ=36 ELSE IF RND<1/194 THEN JJ=41 ELSE 246
245 GOTO 705
246 IF RND<1/193 THEN JJ=46 ELSE IF RND<1/192 THEN JJ=51 ELSE IF RND<1/191 THEN JJ=56 ELSE IF RND<1/190 THEN JJ=61 ELSE IF RND<1/189 THEN JJ=66 ELSE IF RND<1/188 THEN JJ=71 ELSE IF RND<1/187 THEN JJ=76 ELSE 248
247 GOTO 705
248 IF RND<1/186 THEN JJ=81 ELSE IF RND<1/185 THEN JJ=86 ELSE IF RND<1/184 THEN JJ=91 ELSE IF RND<1/183 THEN JJ=96 ELSE IF RND<1/182 THEN JJ=101 ELSE IF RND<1/181 THEN JJ=106 ELSE IF RND<1/180 THEN JJ=111 ELSE 250
249 GOTO 705
250 IF RND<1/179 THEN JJ=116 ELSE IF RND<1/178 THEN JJ=121 ELSE IF RND<1/177 THEN JJ=126 ELSE IF RND<1/176 THEN JJ=131 ELSE IF RND<1/175 THEN JJ=136 ELSE IF RND<1/174 THEN JJ=141 ELSE IF RND<1/173 THEN JJ=146 ELSE 252
251 GOTO 705
252 IF RND<1/172 THEN JJ=151 ELSE IF RND<1/171 THEN JJ=156 ELSE IF RND<1/170 THEN JJ=161 ELSE IF RND<1/169 THEN JJ=166 ELSE IF RND<1/168 THEN JJ=171 ELSE IF RND<1/167 THEN JJ=176 ELSE IF RND<1/166 THEN JJ=181 ELSE 254
253 GOTO 705
254 IF RND<1/165 THEN JJ=186 ELSE IF RND<1/164 THEN JJ=191 ELSE IF RND<1/163 THEN JJ=196 ELSE IF RND<1/162 THEN JJ=201 ELSE IF RND<1/161 THEN JJ=206 ELSE IF RND<1/160 THEN JJ=211 ELSE IF RND<1/159 THEN JJ=216 ELSE 256
255 GOTO 705
256 IF RND<1/158 THEN JJ=221 ELSE IF RND<1/157 THEN JJ=226 ELSE IF RND<1/156 THEN JJ=231 ELSE IF RND<1/155 THEN JJ=236 ELSE IF RND<1/154 THEN JJ=241 ELSE IF RND<1/153 THEN JJ=246 ELSE IF RND<1/152 THEN JJ=251 ELSE 258
257 GOTO 705
258 IF RND<1/151 THEN JJ=256 ELSE IF RND<1/150 THEN JJ=261 ELSE IF RND<1/149 THEN JJ=266 ELSE IF RND<1/148 THEN JJ=271 ELSE IF RND<1/147 THEN JJ=276 ELSE IF RND<1/146 THEN JJ=281 ELSE IF RND<1/145 THEN JJ=286 ELSE 260
259 GOTO 705
260 IF RND<1/144 THEN JJ=291 ELSE IF RND<1/143 THEN JJ=296 ELSE IF RND<1/142 THEN JJ=301 ELSE IF RND<1/141 THEN JJ=306 ELSE IF RND<1/140 THEN JJ=311 ELSE IF RND<1/139 THEN JJ=316 ELSE IF RND<1/138 THEN JJ=321 ELSE 262
261 GOTO 705
262 IF RND<1/137 THEN JJ=326 ELSE IF RND<1/136 THEN JJ=331 ELSE IF RND<1/135 THEN JJ=336 ELSE IF RND<1/134 THEN JJ=341 ELSE IF RND<1/133 THEN JJ=346 ELSE IF RND<1/132 THEN JJ=351 ELSE IF RND<1/131 THEN JJ=356 ELSE 264
263 GOTO 705
264 IF RND<1/130 THEN JJ=361 ELSE IF RND<1/129 THEN JJ=366 ELSE IF RND<1/128 THEN JJ=371 ELSE IF RND<1/127 THEN JJ=376 ELSE IF RND<1/126 THEN JJ=381 ELSE IF RND<1/125 THEN JJ=386 ELSE IF RND<1/124 THEN JJ=391 ELSE 266
265 GOTO 705
266 IF RND<1/123 THEN JJ=396 ELSE IF RND<1/122 THEN JJ=401 ELSE IF RND<1/121 THEN JJ=406 ELSE IF RND<1/120 THEN JJ=411 ELSE IF RND<1/119 THEN JJ=416 ELSE IF RND<1/118 THEN JJ=421 ELSE IF RND<1/117 THEN JJ=426 ELSE 268
267 GOTO 705
268 IF RND<1/116 THEN JJ=431 ELSE IF RND<1/115 THEN JJ=436 ELSE IF RND<1/114 THEN JJ=441 ELSE IF RND<1/113 THEN JJ=446 ELSE IF RND<1/112 THEN JJ=451 ELSE IF RND<1/111 THEN JJ=456 ELSE IF RND<1/110 THEN JJ=461 ELSE 270
269 GOTO 705
270 IF RND<1/109 THEN JJ=466 ELSE IF RND<1/108 THEN JJ=471 ELSE IF RND<1/107 THEN JJ=476 ELSE IF RND<1/106 THEN JJ=481 ELSE IF RND<1/105 THEN JJ=486 ELSE IF RND<1/104 THEN JJ=491 ELSE IF RND<1/103 THEN JJ=496 ELSE 272
271 GOTO 705
272 REM
274 IF RND<1/102 THEN JJ=501 ELSE IF RND<1/101 THEN JJ=506 ELSE 292
275 GOTO 705
292 IF RND<1/100 THEN JJ=511 ELSE IF RND<1/99 THEN JJ=516 ELSE IF RND<1/98 THEN JJ=521 ELSE IF RND<1/97 THEN JJ=526 ELSE IF RND<1/96 THEN JJ=531 ELSE IF RND<1/95 THEN JJ=536 ELSE IF RND<1/94 THEN JJ=541 ELSE 296
294 REM original  IF RND<1/100 THEN JJ=11 ELSE IF RND<1/99 THEN JJ=16 ELSE IF RND<1/98 THEN JJ=21 ELSE IF RND<1/97 THEN JJ=26 ELSE IF RND<1/96 THEN JJ=31 ELSE IF RND<1/95 THEN JJ=36 ELSE IF RND<1/94 THEN JJ=41 ELSE 296
295 GOTO 705
296 IF RND<1/93 THEN JJ=546 ELSE IF RND<1/92 THEN JJ=551 ELSE IF RND<1/91 THEN JJ=556 ELSE IF RND<1/90 THEN JJ=561 ELSE IF RND<1/89 THEN JJ=566 ELSE IF RND<1/88 THEN JJ=571 ELSE IF RND<1/87 THEN JJ=576 ELSE 298
297 GOTO 705
298 IF RND<1/86 THEN JJ=581 ELSE IF RND<1/85 THEN JJ=586 ELSE IF RND<1/84 THEN JJ=591 ELSE IF RND<1/83 THEN JJ=596 ELSE IF RND<1/82 THEN JJ=601 ELSE IF RND<1/81 THEN JJ=606 ELSE IF RND<1/80 THEN JJ=611 ELSE 300
299 GOTO 705
300 IF RND<1/79 THEN JJ=616 ELSE IF RND<1/78 THEN JJ=621 ELSE IF RND<1/77 THEN JJ=626 ELSE IF RND<1/76 THEN JJ=631 ELSE IF RND<1/75 THEN JJ=636 ELSE IF RND<1/74 THEN JJ=641 ELSE IF RND<1/73 THEN JJ=646 ELSE 302
301 GOTO 705
302 IF RND<1/72 THEN JJ=651 ELSE IF RND<1/71 THEN JJ=656 ELSE IF RND<1/70 THEN JJ=661 ELSE IF RND<1/69 THEN JJ=666 ELSE IF RND<1/68 THEN JJ=671 ELSE IF RND<1/67 THEN JJ=676 ELSE IF RND<1/66 THEN JJ=681 ELSE 304
303 GOTO 705
304 IF RND<1/65 THEN JJ=686 ELSE IF RND<1/64 THEN JJ=691 ELSE IF RND<1/63 THEN JJ=696 ELSE IF RND<1/62 THEN JJ=701 ELSE IF RND<1/61 THEN JJ=706 ELSE IF RND<1/60 THEN JJ=711 ELSE IF RND<1/59 THEN JJ=716 ELSE 306
305 GOTO 705
306 IF RND<1/58 THEN JJ=721 ELSE IF RND<1/57 THEN JJ=726 ELSE IF RND<1/56 THEN JJ=731 ELSE IF RND<1/55 THEN JJ=736 ELSE IF RND<1/54 THEN JJ=741 ELSE IF RND<1/53 THEN JJ=746 ELSE IF RND<1/52 THEN JJ=751 ELSE 308
307 GOTO 705
308 IF RND<1/51 THEN JJ=756 ELSE IF RND<1/50 THEN JJ=761 ELSE IF RND<1/49 THEN JJ=766 ELSE IF RND<1/48 THEN JJ=771 ELSE IF RND<1/47 THEN JJ=776 ELSE IF RND<1/46 THEN JJ=781 ELSE IF RND<1/45 THEN JJ=786 ELSE 310
309 GOTO 705
310 IF RND<1/44 THEN JJ=791 ELSE IF RND<1/43 THEN JJ=796 ELSE IF RND<1/42 THEN JJ=801 ELSE IF RND<1/41 THEN JJ=806 ELSE IF RND<1/40 THEN JJ=811 ELSE IF RND<1/39 THEN JJ=816 ELSE IF RND<1/38 THEN JJ=821 ELSE 312
311 GOTO 705
312 IF RND<1/37 THEN JJ=826 ELSE IF RND<1/36 THEN JJ=831 ELSE IF RND<1/35 THEN JJ=836 ELSE IF RND<1/34 THEN JJ=841 ELSE IF RND<1/33 THEN JJ=846 ELSE IF RND<1/32 THEN JJ=851 ELSE IF RND<1/31 THEN JJ=856 ELSE 314
313 GOTO 705
314 IF RND<1/30 THEN JJ=861 ELSE IF RND<1/29 THEN JJ=866 ELSE IF RND<1/28 THEN JJ=871 ELSE IF RND<1/27 THEN JJ=876 ELSE IF RND<1/26 THEN JJ=881 ELSE IF RND<1/25 THEN JJ=886 ELSE IF RND<1/24 THEN JJ=891 ELSE 316
315 GOTO 705
316 IF RND<1/23 THEN JJ=896 ELSE IF RND<1/22 THEN JJ=901 ELSE IF RND<1/21 THEN JJ=906 ELSE IF RND<1/20 THEN JJ=911 ELSE IF RND<1/19 THEN JJ=916 ELSE IF RND<1/18 THEN JJ=921 ELSE IF RND<1/17 THEN JJ=926 ELSE 318
317 GOTO 705
318 IF RND<1/16 THEN JJ=931 ELSE IF RND<1/15 THEN JJ=936 ELSE IF RND<1/14 THEN JJ=941 ELSE IF RND<1/13 THEN JJ=946 ELSE IF RND<1/12 THEN JJ=951 ELSE IF RND<1/11 THEN JJ=956 ELSE IF RND<1/10 THEN JJ=961 ELSE 320
319 GOTO 705
320 IF RND<1/9 THEN JJ=966 ELSE IF RND<1/8 THEN JJ=971 ELSE IF RND<1/7 THEN JJ=976 ELSE IF RND<1/6 THEN JJ=981 ELSE IF RND<1/5 THEN JJ=986 ELSE IF RND<1/4 THEN JJ=991 ELSE IF RND<1/3 THEN JJ=996 ELSE 322
321 GOTO 705
322 REM
323 REM
324 IF RND<1/2 THEN JJ=1001 ELSE JJ=1006
705 IF RND<.2 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=1 ELSE IF RND<.4 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=1:X(JJ+4)=0 ELSE IF RND<.6 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=1:X(JJ+3)=0:X(JJ+4)=0 ELSE 711
708 GOTO 1333
711 IF RND<.5 THEN X(JJ)=0:X(JJ+1)=1:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0 ELSE X(JJ)=1:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0
1333 GOTO 1367
1367 FOR H=1 TO 200
1371 PNEM(H)=-(ABS(L(H*2-1)-X(1))+ABS(L(H*2)-X(6)))*X(5*H+6)-(ABS(L(H*2-1)-X(2))+ABS(L(H*2)-X(7)))*X(5*H+7)-(ABS(L(H*2-1)-X(3))+ABS(L(H*2)-X(8)))*X(5*H+8)-(ABS(L(H*2-1)-X(4))+ABS(L(H*2)-X(9)))*X(5*H+9)-(ABS(L(H*2-1)-X(5))+ABS(L(H*2)-X(10)))*X(5*H+10)
1379 NEXT H
1389 PSUM=0
1391 FOR HH=1 TO 200
1393 PSUM=PSUM+PNEM(HH)
1396 NEXT HH
1401 P=PSUM
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 1010
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-4500 THEN 1912 ELSE 2999
1912 LPRINT A(1),A(2),A(3),A(4),A(5),A(6),A(7),A(8),A(9),A(10),M,JJJJ
1921 FOR IPR=11 TO 1006 STEP 5
1923 LPRINT A(IPR),A(IPR+1),A(IPR+2),A(IPR+3),A(IPR+4)
1928 NEXT IPR
2999 NEXT JJJJ

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  Its output through JJJJ=-31997 is presented below; not all of the 200 allocations of wells to platforms are shown below.  What immediately follows is a hand copy from the output on paper.

85.99997   59.00007   43.99956   12.30693   9.463252
38.93289   86.00018   27.00034   68.99996   9.991962
-4312.998   -31997
00001
00100
00100
00001
01000
00010
01000
01000
01000
00010
.
.
.
.
.

Interpreted in accordance with line 1912 through line 1928, the output above was obtained in fifteen minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter.  With the present algorithm, a usable solution may come early, late, or worse.

References

[1] B. K.-S. Cheung, A. Langevin and H. Delmaire, Coupling Genetic Algorithm with a Grid Search Method To Solve Mixed Integer Nonlinear Programming Problems, Computers Math. Applic. Vol. 34, No. 12, pp.13-23, 1997. 

[2] Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

A Nonlinear Integer/Discrete/Continuous Solver Applied to an Oil Production Problem with 100 Oil Wells and 5 Oil Platforms

A Nonlinear Integer/Discrete/Continuous Solver Applied to

Jsun Yui Wong   

The following computer program tries to solve a location-allocation problem of searching for locations for five platforms and allocating 100 wells to these platforms.  Rectangular distances are used in line 1371 below.

The locations of wells given in line 21, line 22, line 23, line 24, line 25, line 27, and line 28 are from Table 1 and from the first part of Table 2 of Cheung, Langevin, and Delmaire [1].

0 DEFSNG A-Z
3 DEFINT I,J,K,H
4 DIM X(555),A(555),L(555),K(555),PNEM(555),ILO(555),J(555)
18 FOR IL=1 TO 200
19 READ L(IL)
20 NEXT IL
21 DATA 22,3,69,44,44,50,70,12,97,51,94,35,100,62,94,26,13,75,65,99
22 DATA 58,59,82,31,13,95,87,29,41,87,47,94,15,89,20,85,31,50,12,99,86,75,47,98,0,52,54,92,90,79
23 DATA 5,0,43,24,24,36,2,8,32,91,3,86,72,70,75,95,64,63,21,58,30,35,68,76,40,0,8,45,8,61
24 DATA 7,6,74,99,4,59,41,11,55,64,28,69,23,25,75,2,86,42,86,36,59,90,50,66,44,87,6,5,2,97
25 DATA 94,53,44,92,91,91,36,31,56,52,19,29,3,66,50,100,40,41,83,10,89,41,39,14,24,53,25,27,42,21,94,92,5,89,51,60,59,5,89,38
27 DATA 26,72,67,90,100,65,95,36,45,33,32,3,35,22,13,60,24,9,33,40,42,96,23,41,95,36,59,56,40,72
28 DATA 54,64,55,26,47,4,22,25,1,62,23,87,21,11,46,14,61,32,39,18
75 FOR JJJJ=-32000 TO 32000
76 RANDOMIZE JJJJ
77 M=-1.7E+38
88 FOR IAA=1 TO 10
89 A(IAA)=RND*100
90 NEXT IAA
111 FOR IBB= 11 TO 510 STEP 1
112 A(IBB)=0
113 NEXT IBB
121 FOR IBB= 11 TO 510 STEP 5
122 A(IBB)=1
123 NEXT IBB
126 REM   IMAR=10+FIX(RND*32700)
128 FOR I=1 TO 3270
129 FOR K=1 TO 510
131 X(K)=A(K)
132 NEXT K
141 IF RND<.5 THEN 181 ELSE 194
181 J=1+FIX(RND*10)
183 R=RND*(1-RND*2)*A(J)
191 IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
192 GOTO 1333
194 GOTO 294
195 GOTO 205
196 IF RND<1/32 THEN JJ=51 ELSE IF RND<1/31 THEN JJ=56 ELSE IF RND<1/30 THEN JJ=61 ELSE IF RND<1/29 THEN JJ=66 ELSE IF RND<1/28 THEN JJ=71 ELSE IF RND<1/27 THEN JJ=76 ELSE IF RND<1/26 THEN JJ=81 ELSE IF RND<1/25 THEN JJ=86 ELSE 198
197 GOTO 205
198 IF RND<1/24 THEN JJ=91 ELSE IF RND<1/23 THEN JJ=96 ELSE IF RND<1/22 THEN JJ=101 ELSE IF RND<1/21 THEN JJ=106 ELSE IF RND<1/20 THEN JJ=111 ELSE IF RND<1/19 THEN JJ=116 ELSE IF RND<1/18 THEN JJ=121 ELSE IF RND<1/17 THEN JJ=126 ELSE 200
199       GOTO 205
200 IF RND<1/16 THEN JJ=131 ELSE IF RND<1/15 THEN JJ=136 ELSE IF RND<1/14 THEN JJ=141 ELSE IF RND<1/13 THEN JJ=146 ELSE IF RND<1/12 THEN JJ=151 ELSE IF RND<1/11 THEN JJ=156 ELSE IF RND<1/10 THEN JJ=161 ELSE IF RND<1/9 THEN JJ=166 ELSE 202
201     GOTO 205
202 IF RND<1/8 THEN JJ=171 ELSE IF RND<1/7 THEN JJ=176 ELSE IF RND<1/6 THEN JJ=181 ELSE IF RND<1/5 THEN JJ=186 ELSE IF RND<1/4 THEN JJ=191 ELSE IF RND<1/3 THEN JJ=196 ELSE IF RND<1/2 THEN JJ=201 ELSE JJ=206
205 IF RND<.2 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=1 ELSE IF RND<.4 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=1:X(JJ+4)=0 ELSE IF RND<.6 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=1:X(JJ+3)=0:X(JJ+4)=0 ELSE 211
208 GOTO 1333
211 IF RND<.5 THEN X(JJ)=0:X(JJ+1)=1:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0 ELSE X(JJ)=1:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0
294 IF RND<1/100 THEN JJ=11 ELSE IF RND<1/99 THEN JJ=16 ELSE IF RND<1/98 THEN JJ=21 ELSE IF RND<1/97 THEN JJ=26 ELSE IF RND<1/96 THEN JJ=31 ELSE IF RND<1/95 THEN JJ=36 ELSE IF RND<1/94 THEN JJ=41 ELSE 296
295 GOTO 705
296 IF RND<1/93 THEN JJ=46 ELSE IF RND<1/92 THEN JJ=51 ELSE IF RND<1/91 THEN JJ=56 ELSE IF RND<1/90 THEN JJ=61 ELSE IF RND<1/89 THEN JJ=66 ELSE IF RND<1/88 THEN JJ=71 ELSE IF RND<1/87 THEN JJ=76 ELSE 298
297 GOTO 705
298 IF RND<1/86 THEN JJ=81 ELSE IF RND<1/85 THEN JJ=86 ELSE IF RND<1/84 THEN JJ=91 ELSE IF RND<1/83 THEN JJ=96 ELSE IF RND<1/82 THEN JJ=101 ELSE IF RND<1/81 THEN JJ=106 ELSE IF RND<1/80 THEN JJ=111 ELSE 300
299 GOTO 705
300 IF RND<1/79 THEN JJ=116 ELSE IF RND<1/78 THEN JJ=121 ELSE IF RND<1/77 THEN JJ=126 ELSE IF RND<1/76 THEN JJ=131 ELSE IF RND<1/75 THEN JJ=136 ELSE IF RND<1/74 THEN JJ=141 ELSE IF RND<1/73 THEN JJ=146 ELSE 302
301 GOTO 705
302 IF RND<1/72 THEN JJ=151 ELSE IF RND<1/71 THEN JJ=156 ELSE IF RND<1/70 THEN JJ=161 ELSE IF RND<1/69 THEN JJ=166 ELSE IF RND<1/68 THEN JJ=171 ELSE IF RND<1/67 THEN JJ=176 ELSE IF RND<1/66 THEN JJ=181 ELSE 304
303 GOTO 705
304 IF RND<1/65 THEN JJ=186 ELSE IF RND<1/64 THEN JJ=191 ELSE IF RND<1/63 THEN JJ=196 ELSE IF RND<1/62 THEN JJ=201 ELSE IF RND<1/61 THEN JJ=206 ELSE IF RND<1/60 THEN JJ=211 ELSE IF RND<1/59 THEN JJ=216 ELSE 306
305 GOTO 705
306 IF RND<1/58 THEN JJ=221 ELSE IF RND<1/57 THEN JJ=226 ELSE IF RND<1/56 THEN JJ=231 ELSE IF RND<1/55 THEN JJ=236 ELSE IF RND<1/54 THEN JJ=241 ELSE IF RND<1/53 THEN JJ=246 ELSE IF RND<1/52 THEN JJ=251 ELSE 308
307 GOTO 705
308 IF RND<1/51 THEN JJ=256 ELSE IF RND<1/50 THEN JJ=261 ELSE IF RND<1/49 THEN JJ=266 ELSE IF RND<1/48 THEN JJ=271 ELSE IF RND<1/47 THEN JJ=276 ELSE IF RND<1/46 THEN JJ=281 ELSE IF RND<1/45 THEN JJ=286 ELSE 310
309 GOTO 705
310 IF RND<1/44 THEN JJ=291 ELSE IF RND<1/43 THEN JJ=296 ELSE IF RND<1/42 THEN JJ=301 ELSE IF RND<1/41 THEN JJ=306 ELSE IF RND<1/40 THEN JJ=311 ELSE IF RND<1/39 THEN JJ=316 ELSE IF RND<1/38 THEN JJ=321 ELSE 312
311 GOTO 705
312 IF RND<1/37 THEN JJ=326 ELSE IF RND<1/36 THEN JJ=331 ELSE IF RND<1/35 THEN JJ=336 ELSE IF RND<1/34 THEN JJ=341 ELSE IF RND<1/33 THEN JJ=346 ELSE IF RND<1/32 THEN JJ=351 ELSE IF RND<1/31 THEN JJ=356 ELSE 314
313 GOTO 705
314 IF RND<1/30 THEN JJ=361 ELSE IF RND<1/29 THEN JJ=366 ELSE IF RND<1/28 THEN JJ=371 ELSE IF RND<1/27 THEN JJ=376 ELSE IF RND<1/26 THEN JJ=381 ELSE IF RND<1/25 THEN JJ=386 ELSE IF RND<1/24 THEN JJ=391 ELSE 316
315 GOTO 705
316 IF RND<1/23 THEN JJ=396 ELSE IF RND<1/22 THEN JJ=401 ELSE IF RND<1/21 THEN JJ=406 ELSE IF RND<1/20 THEN JJ=411 ELSE IF RND<1/19 THEN JJ=416 ELSE IF RND<1/18 THEN JJ=421 ELSE IF RND<1/17 THEN JJ=426 ELSE 318
317 GOTO 705
318 IF RND<1/16 THEN JJ=431 ELSE IF RND<1/15 THEN JJ=436 ELSE IF RND<1/14 THEN JJ=441 ELSE IF RND<1/13 THEN JJ=446 ELSE IF RND<1/12 THEN JJ=451 ELSE IF RND<1/11 THEN JJ=456 ELSE IF RND<1/10 THEN JJ=461 ELSE 320
319 GOTO 705
320 IF RND<1/9 THEN JJ=466 ELSE IF RND<1/8 THEN JJ=471 ELSE IF RND<1/7 THEN JJ=476 ELSE IF RND<1/6 THEN JJ=481 ELSE IF RND<1/5 THEN JJ=486 ELSE IF RND<1/4 THEN JJ=491 ELSE IF RND<1/3 THEN JJ=496 ELSE 322
321 GOTO 705
322 IF RND<1/2 THEN JJ=501 ELSE JJ=506
323 REM    GOTO 705
705 IF RND<.2 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=1 ELSE IF RND<.4 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=1:X(JJ+4)=0 ELSE IF RND<.6 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=1:X(JJ+3)=0:X(JJ+4)=0 ELSE 211
708 GOTO 1333
711 IF RND<.5 THEN X(JJ)=0:X(JJ+1)=1:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0 ELSE X(JJ)=1:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0
1333 GOTO 1367
1367 FOR H=1 TO 100
1371 PNEM(H)=-(ABS(L(H*2-1)-X(1))+ABS(L(H*2)-X(6)))*X(5*H+6)-(ABS(L(H*2-1)-X(2))+ABS(L(H*2)-X(7)))*X(5*H+7)-(ABS(L(H*2-1)-X(3))+ABS(L(H*2)-X(8)))*X(5*H+8)-(ABS(L(H*2-1)-X(4))+ABS(L(H*2)-X(9)))*X(5*H+9)-(ABS(L(H*2-1)-X(5))+ABS(L(H*2)-X(10)))*X(5*H+10)
1379 NEXT H
1389 PSUM=0
1391 FOR HH=1 TO 100
1393 PSUM=PSUM+PNEM(HH)
1396 NEXT HH
1401 P=PSUM
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 510
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-2100 THEN 1912 ELSE 2999
1912 LPRINT A(1),A(2),A(3),A(4),A(5),A(6),A(7),A(8),A(9),A(10),M,JJJJ
1941  LPRINT A(11),A(12),A(13),A(14),A(15)
1942  LPRINT A(16),A(17),A(18),A(19),A(20)
1943  LPRINT A(21),A(22),A(23),A(24),A(25)
1944  LPRINT A(26),A(27),A(28),A(29),A(30)
1945  LPRINT A(31),A(32),A(33),A(34),A(35)
1946  LPRINT A(36),A(37),A(38),A(39),A(40)
1947  LPRINT A(41),A(42),A(43),A(44),A(45)
1948  LPRINT A(46),A(47),A(48),A(49),A(50)
1949  LPRINT A(51),A(52),A(53),A(54),A(55)
1950  LPRINT A(56),A(57),A(58),A(59),A(60)
1951  LPRINT A(61),A(62),A(63),A(64),A(65)
1952  LPRINT A(66),A(67),A(68),A(69),A(70)
1953  LPRINT A(71),A(72),A(73),A(74),A(75)
1954  LPRINT A(76),A(77),A(78),A(79),A(80)
1955  LPRINT A(81),A(82),A(83),A(84),A(85)
1956  LPRINT A(86),A(87),A(88),A(89),A(90)
1957  LPRINT A(91),A(92),A(93),A(94),A(95)
1958  LPRINT A(96),A(97),A(98),A(99),A(100)
1959  LPRINT A(101),A(102),A(103),A(104),A(105)
1960  LPRINT A(106),A(107),A(108),A(109),A(110)
1961  LPRINT A(111),A(112),A(113),A(114),A(115)
1962  LPRINT A(116),A(117),A(118),A(119),A(120)
1963  LPRINT A(121),A(122),A(123),A(124),A(125)
1964  LPRINT A(126),A(127),A(128),A(129),A(130)
1965  LPRINT A(131),A(132),A(133),A(134),A(135)
1966  LPRINT A(136),A(137),A(138),A(139),A(140)
1967  LPRINT A(141),A(142),A(143),A(144),A(145)
1968  LPRINT A(146),A(147),A(148),A(149),A(150)
1969  LPRINT A(151),A(152),A(153),A(154),A(155)
1970  LPRINT A(156),A(157),A(158),A(159),A(160)
1971  LPRINT A(161),A(162),A(163),A(164),A(165)
1972  LPRINT A(166),A(167),A(168),A(169),A(170)
1973  LPRINT A(171),A(172),A(173),A(174),A(175)
1974  LPRINT A(176),A(177),A(178),A(179),A(180)
1975  LPRINT A(181),A(182),A(183),A(184),A(185)
1976  LPRINT A(186),A(187),A(188),A(189),A(190)
1977  LPRINT A(191),A(192),A(193),A(194),A(195)
1978  LPRINT A(196),A(197),A(198),A(199),A(200)
1979  LPRINT A(201),A(202),A(203),A(204),A(205)
1980  LPRINT A(206),A(207),A(208),A(209),A(210)
1981  LPRINT A(211),A(212),A(213),A(214),A(215)
1982  LPRINT A(216),A(217),A(218),A(219),A(220)
1983  LPRINT A(221),A(222),A(223),A(224),A(225)
1984  LPRINT A(226),A(227),A(228),A(229),A(230)
1985  LPRINT A(231),A(232),A(233),A(234),A(235)
1986  LPRINT A(236),A(237),A(238),A(239),A(240)
1987  LPRINT A(241),A(242),A(243),A(244),A(245)
1988  LPRINT A(246),A(247),A(248),A(249),A(250)
1989  LPRINT A(251),A(252),A(253),A(254),A(255)
1990  LPRINT A(256),A(257),A(258),A(259),A(260)
1991  LPRINT A(261),A(262),A(263),A(264),A(265)
1992  LPRINT A(266),A(267),A(268),A(269),A(270)
1993  LPRINT A(271),A(272),A(273),A(274),A(275)
1994  LPRINT A(276),A(277),A(278),A(279),A(280)
1995  LPRINT A(281),A(282),A(283),A(284),A(285)
1996  LPRINT A(286),A(287),A(288),A(289),A(290)
1997  LPRINT A(291),A(292),A(293),A(294),A(295)
1998  LPRINT A(296),A(297),A(298),A(299),A(300)
1999  LPRINT A(301),A(302),A(303),A(304),A(305)
2000  REM
2001  REM
2002  LPRINT A(306),A(307),A(308),A(309),A(310)
2003  LPRINT A(311),A(312),A(313),A(314),A(315)
2004  LPRINT A(316),A(317),A(318),A(319),A(320)
2005  LPRINT A(321),A(322),A(323),A(324),A(325)
2006  LPRINT A(326),A(327),A(328),A(329),A(330)
2007  LPRINT A(331),A(332),A(333),A(334),A(335)
2008  LPRINT A(336),A(337),A(338),A(339),A(340)
2009  LPRINT A(341),A(342),A(343),A(344),A(345)
2019  LPRINT A(346),A(347),A(348),A(349),A(350)
2020  LPRINT A(351),A(352),A(353),A(354),A(355)
2021  LPRINT A(356),A(357),A(358),A(359),A(360)
2022  LPRINT A(361),A(362),A(363),A(364),A(365)
2023  LPRINT A(366),A(367),A(368),A(369),A(370)
2024  LPRINT A(371),A(372),A(373),A(374),A(375)
2025  LPRINT A(376),A(377),A(378),A(379),A(380)
2026  LPRINT A(381),A(382),A(383),A(384),A(385)
2027  LPRINT A(386),A(387),A(388),A(389),A(390)
2028  LPRINT A(391),A(392),A(393),A(394),A(395)
2029  LPRINT A(396),A(397),A(398),A(399),A(400)
2030  LPRINT A(401),A(402),A(403),A(404),A(405)
2031  LPRINT A(406),A(407),A(408),A(409),A(410)
2032  LPRINT A(411),A(412),A(413),A(414),A(415)
2033  LPRINT A(416),A(417),A(418),A(419),A(420)
2034  LPRINT A(421),A(422),A(423),A(424),A(425)
2035  LPRINT A(426),A(427),A(428),A(429),A(430)
2036  LPRINT A(431),A(432),A(433),A(434),A(435)
2037  LPRINT A(436),A(437),A(438),A(439),A(440)
2038  LPRINT A(441),A(442),A(443),A(444),A(445)
2039  LPRINT A(446),A(447),A(448),A(449),A(450)
2040  LPRINT A(451),A(452),A(453),A(454),A(455)
2041  LPRINT A(456),A(457),A(458),A(459),A(460)
2042  LPRINT A(461),A(462),A(463),A(464),A(465)
2043  LPRINT A(466),A(467),A(468),A(469),A(470)
2044  LPRINT A(471),A(472),A(473),A(474),A(475)
2045  LPRINT A(476),A(477),A(478),A(479),A(480)
2046  LPRINT A(481),A(482),A(483),A(484),A(485)
2047  LPRINT A(486),A(487),A(488),A(489),A(490)
2048  LPRINT A(491),A(492),A(493),A(494),A(495)
2049  LPRINT A(496),A(497),A(498),A(499),A(500)
2050  LPRINT A(501),A(502),A(503),A(504),A(505)
2051  LPRINT A(506),A(507),A(508),A(509),A(510)
2999 NEXT JJJJ

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  Its complete output through JJJJ=-31999 is presented below.  What immediately follows is a hand copy from the output on paper

12.46138     55.99959       32.00004       89.00004     51.00025
71.06358          63.99993     20.99991      36.00002    92.00004
-2072   -31999
00100
00010
01000
00010
00010
00010
00010
00010
10000
00001
01000
00010
10000
00010
00001
00001
10000
10000
00100
10000
01000
00001
10000
00001
00010
00100
00100
00100
00100
00001
10000
01000
00001
01000
10000
00100
01000
00100
10000
10000
00100
00001
10000
00100
01000
10000
00100
00010
00010
00010
00001
01000
00001
00100
10000
00010
00001
00001
00100
01000
00100
10000
00001
00100
00010
00010
00100
10000
00100
00100
00001
10000
01000
00100
00010
10000
00001
00010
00010
00100
00100
00100
10000
00100
00100
00001
00100
00010
01000
01000
01000
00100
00100
00100
10000
10000
00100
00100
00010
00100

Interpreted in accordance with line 1912 through line 2051, the output above was obtained in four minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter. 

References

[1] B. K.-S. Cheung, A. Langevin and H. Delmaire, Coupling Genetic Algorithm with a Grid Search Method To Solve Mixed Integer Nonlinear Programming Problems, Computers Math. Applic. Vol. 34, No. 12, pp.13-23, 1997. 

[2] Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

A Nonlinear Integer/Discrete/Continuous Solver Applied to an Oil Production Problem with 40 Oil Wells and 5 Oil Platforms

Jsun Yui Wong   

The following computer program tries to solve a location-allocation problem of searching for locations for five platforms and allocating forty wells to these platforms.  Rectangular distances are used in line 1371 below.

The locations of wells given in line 21, line 22, and line 23 are from Table 1 and from the first part of Table 2 of Cheung, Langevin, and Delmaire [1].

0 DEFSNG A-Z
3 DEFINT I,J,K,H
4 DIM X(355),A(333),L(590),K(333),PNEWM(555),ILO(355),J(333)
18 FOR IL=1 TO 80
19 READ L(IL)
20 NEXT IL
21 DATA 22,3,69,44,44,50,70,12,97,51,94,35,100,62,94,26,13,75,65,99
22 DATA 58,59,82,31,13,95,87,29,41,87,47,94,15,89,20,85,31,50,12,99,86,75,47,98,0,52,54,92,90,79
23 DATA 5,0,43,24,24,36,2,8,32,91,3,86,72,70,75,95,64,63,21,58,30,35,68,76,40,0,8,45,8,61
75 FOR JJJJ=-32000 TO 32000
76 RANDOMIZE JJJJ
77 M=-1.7E+38
88 FOR IAA=1 TO 10
89 A(IAA)=RND*100
90 NEXT IAA
111 FOR IBB= 11 TO 210 STEP 1
112 A(IBB)=0
113 NEXT IBB
121 FOR IBB= 11 TO 210 STEP 5
122 A(IBB)=1
123 NEXT IBB
126 REM   IMAR=10+FIX(RND*32700)
128 FOR I=1 TO 3270
129 FOR K=1 TO 210
131 X(K)=A(K)
132 NEXT K
141 IF RND<.5 THEN 181 ELSE 194
181 J=1+FIX(RND*10)
183 R=RND*(1-RND*2)*A(J)
191 IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
192 GOTO 1333
194 IF RND<1/40 THEN JJ=11 ELSE IF RND<1/39 THEN JJ=16 ELSE IF RND<1/38 THEN JJ=21 ELSE IF RND<1/37 THEN JJ=26 ELSE IF RND<1/36 THEN JJ=31 ELSE IF RND<1/35 THEN JJ=36 ELSE IF RND<1/34 THEN JJ=41 ELSE IF RND<1/33 THEN JJ=46 ELSE 196
195 GOTO 205
196 IF RND<1/32 THEN JJ=51 ELSE IF RND<1/31 THEN JJ=56 ELSE IF RND<1/30 THEN JJ=61 ELSE IF RND<1/29 THEN JJ=66 ELSE IF RND<1/28 THEN JJ=71 ELSE IF RND<1/27 THEN JJ=76 ELSE IF RND<1/26 THEN JJ=81 ELSE IF RND<1/25 THEN JJ=86 ELSE 198
197 GOTO 205
198 IF RND<1/24 THEN JJ=91 ELSE IF RND<1/23 THEN JJ=96 ELSE IF RND<1/22 THEN JJ=101 ELSE IF RND<1/21 THEN JJ=106 ELSE IF RND<1/20 THEN JJ=111 ELSE IF RND<1/19 THEN JJ=116 ELSE IF RND<1/18 THEN JJ=121 ELSE IF RND<1/17 THEN JJ=126 ELSE 200
199       GOTO 205
200 IF RND<1/16 THEN JJ=131 ELSE IF RND<1/15 THEN JJ=136 ELSE IF RND<1/14 THEN JJ=141 ELSE IF RND<1/13 THEN JJ=146 ELSE IF RND<1/12 THEN JJ=151 ELSE IF RND<1/11 THEN JJ=156 ELSE IF RND<1/10 THEN JJ=161 ELSE IF RND<1/9 THEN JJ=166 ELSE 202
201     GOTO 205
202 IF RND<1/8 THEN JJ=171 ELSE IF RND<1/7 THEN JJ=176 ELSE IF RND<1/6 THEN JJ=181 ELSE IF RND<1/5 THEN JJ=186 ELSE IF RND<1/4 THEN JJ=191 ELSE IF RND<1/3 THEN JJ=196 ELSE IF RND<1/2 THEN JJ=201 ELSE JJ=206
205 IF RND<.2 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=1 ELSE IF RND<.4 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=1:X(JJ+4)=0 ELSE IF RND<.6 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=1:X(JJ+3)=0:X(JJ+4)=0 ELSE 211
208 GOTO 1333
211 IF RND<.5 THEN X(JJ)=0:X(JJ+1)=1:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0 ELSE X(JJ)=1:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0
1333 GOTO 1367
1367 FOR H=1 TO 40
1371 PNEWM(H)=-(ABS(L(H*2-1)-X(1))+ABS(L(H*2)-X(6)))*X(5*H+6)-(ABS(L(H*2-1)-X(2))+ABS(L(H*2)-X(7)))*X(5*H+7)-(ABS(L(H*2-1)-X(3))+ABS(L(H*2)-X(8)))*X(5*H+8)-(ABS(L(H*2-1)-X(4))+ABS(L(H*2)-X(9)))*X(5*H+9)-(ABS(L(H*2-1)-X(5))+ABS(L(H*2)-X(10)))*X(5*H+10)
1379 NEXT H
1389 PSUM=0
1391 FOR HH=1 TO 40
1393 PSUM=PSUM+PNEWM(HH)
1396 NEXT HH
1401 P=PSUM
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 210
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-787.1 THEN 1912 ELSE 1999
1912 LPRINT A(1),A(2),A(3),A(4),A(5),A(6),A(7),A(8),A(9),A(10),M,JJJJ
1941  LPRINT A(11),A(12),A(13),A(14),A(15)
1942  LPRINT A(16),A(17),A(18),A(19),A(20)
1943  LPRINT A(21),A(22),A(23),A(24),A(25)
1944  LPRINT A(26),A(27),A(28),A(29),A(30)
1945  LPRINT A(31),A(32),A(33),A(34),A(35)
1946  LPRINT A(36),A(37),A(38),A(39),A(40)
1947  LPRINT A(41),A(42),A(43),A(44),A(45)
1948  LPRINT A(46),A(47),A(48),A(49),A(50)
1949  LPRINT A(51),A(52),A(53),A(54),A(55)
1950  LPRINT A(56),A(57),A(58),A(59),A(60)
1951  LPRINT A(61),A(62),A(63),A(64),A(65)
1952  LPRINT A(66),A(67),A(68),A(69),A(70)
1953  LPRINT A(71),A(72),A(73),A(74),A(75)
1954  LPRINT A(76),A(77),A(78),A(79),A(80)
1955  LPRINT A(81),A(82),A(83),A(84),A(85)
1956  LPRINT A(86),A(87),A(88),A(89),A(90)
1957  LPRINT A(91),A(92),A(93),A(94),A(95)
1958  LPRINT A(96),A(97),A(98),A(99),A(100)
1959  LPRINT A(101),A(102),A(103),A(104),A(105)
1960  LPRINT A(106),A(107),A(108),A(109),A(110)
1961  LPRINT A(111),A(112),A(113),A(114),A(115)
1962  LPRINT A(116),A(117),A(118),A(119),A(120)
1963  LPRINT A(121),A(122),A(123),A(124),A(125)
1964  LPRINT A(126),A(127),A(128),A(129),A(130)
1965  LPRINT A(131),A(132),A(133),A(134),A(135)
1966  LPRINT A(136),A(137),A(138),A(139),A(140)
1967  LPRINT A(141),A(142),A(143),A(144),A(145)
1968  LPRINT A(146),A(147),A(148),A(149),A(150)
1969  LPRINT A(151),A(152),A(153),A(154),A(155)
1970  LPRINT A(156),A(157),A(158),A(159),A(160)
1971  LPRINT A(161),A(162),A(163),A(164),A(165)
1972  LPRINT A(166),A(167),A(168),A(169),A(170)
1973  LPRINT A(171),A(172),A(173),A(174),A(175)
1974  LPRINT A(176),A(177),A(178),A(179),A(180)
1975  LPRINT A(181),A(182),A(183),A(184),A(185)
1976  LPRINT A(186),A(187),A(188),A(189),A(190)
1977  LPRINT A(191),A(192),A(193),A(194),A(195)
1978  LPRINT A(196),A(197),A(198),A(199),A(200)
1979  LPRINT A(201),A(202),A(203),A(204),A(205)
1980  LPRINT A(206),A(207),A(208),A(209),A(210)
1999 NEXT JJJJ

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  Its complete output through JJJJ=-31991 is presented below.  What immediately follows is a hand copy from the output on paper.

23.55757   93.99992   19.45316   22.00001   68.87894  
49.99995   30.9999   90.83935   2.99998   75.03171  
-787.0001   -31991
00010
00001
10000
01000
01000
01000
01000
01000
00100
00001
00001
01000
00100
01000
00100
00100
00100
00100
10000
00100
00001
00100
10000
00001
00001
00010
00010
10000
00010
00100
00100
00001
00001
00001
10000
10000
00001
00010
10000
10000

Interpreted in accordance with line 1912 through line 1980, the output above was obtained in six minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter. 

References

[1] B. K.-S. Cheung, A. Langevin and H. Delmaire, Coupling Genetic Algorithm with a Grid Search Method To Solve Mixed Integer Nonlinear Programming Problems, Computers Math. Applic. Vol. 34, No. 12, pp.13-23, 1997. 

[2] Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

Line 1371 of the Last Two Posts

Jsun Yui Wong

Line 1371 of the last two posts should read as follows:

1371 PNEWM(H)=-(ABS(L(H*2-1)-X(1))+ABS(L(H*2)-X(6)))*X(5*H+6)

-(ABS(L(H*2-1)-X(2))+ABS(L(H*2)-X(7)))*X(5*H+7)

-(ABS(L(H*2-1)-X(3))+ABS(L(H*2)-X(8)))*X(5*H+8)

-(ABS(L(H*2-1)-X(4))+ABS(L(H*2)-X(9)))*X(5*H+9)

-(ABS(L(H*2-1)-X(5))+ABS(L(H*2)-X(10)))*X(5*H+10)

A Nonlinear Integer/Discrete/Continuous Solver Applied to an Oil Production Problem with 25 Oil Wells and 5 Oil Platforms, Fourth Edition

Jsun Yui Wong   

The following computer program tries to solve the problem in Cheung, Langevin, and Delmaire [1, page 17] of searching for locations for five platforms and allocating twenty-five wells to these platforms.  Rectangular distances are used in line 1371 below.

0 DEFSNG A-Z
3 DEFINT I,J,K,H
4 DIM X(155),A(155),L(590),K(33),PNEWM(555),ILO(55)
18 FOR IL=1 TO 50
19 READ L(IL)
20 NEXT IL
21 DATA 22,3,69,44,44,50,70,12,97,51,94,35,100,62,94,26,13,75,65,99
22 DATA 58,59,82,31,13,95,87,29,41,87,47,94,15,89,20,85,31,50,12,99,86,75,47,98,0,52,54,92,90,79
75 FOR JJJJ=-32000 TO 32000
76 RANDOMIZE JJJJ
77 M=-1.7E+38
88 FOR IAA=1 TO 10
89 A(IAA)=RND*100
90 NEXT IAA
111 FOR IBB= 11 TO 135 STEP 1
112 A(IBB)=0
113 NEXT IBB
121 FOR IBB= 11 TO 135 STEP 5
122 A(IBB)=1
123 NEXT IBB
126 REM   IMAR=10+FIX(RND*32700)
128 FOR I=1 TO 3270
129 FOR K=1 TO 135
131 X(K)=A(K)
132 NEXT K
141 IF RND<.5 THEN 181 ELSE 194
181 J=1+FIX(RND*10)
183 R=RND*(1-RND*2)*A(J)
191 IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
192 GOTO 1333
194 IF RND<1/25 THEN JJ=11 ELSE IF RND<1/24 THEN JJ=16 ELSE IF RND<1/23 THEN JJ=21 ELSE IF RND<1/22 THEN JJ=26 ELSE IF RND<1/21 THEN JJ=31 ELSE IF RND<1/20 THEN JJ=36 ELSE IF RND<1/19 THEN JJ=41 ELSE IF RND<1/18 THEN JJ=46 ELSE 196
195 GOTO 205
196 IF RND<1/17 THEN JJ=51 ELSE IF RND<1/16 THEN JJ=56 ELSE IF RND<1/15 THEN JJ=61 ELSE IF RND<1/14 THEN JJ=66 ELSE IF RND<1/13 THEN JJ=71 ELSE IF RND<1/12 THEN JJ=76 ELSE IF RND<1/11 THEN JJ=81 ELSE IF RND<1/10 THEN JJ=86 ELSE 198
197 GOTO 205
198 IF RND<1/9 THEN JJ=91 ELSE IF RND<1/8 THEN JJ=96 ELSE IF RND<1/7 THEN JJ=101 ELSE IF RND<1/6 THEN JJ=106 ELSE IF RND<1/5 THEN JJ=111 ELSE IF RND<1/4 THEN JJ=116 ELSE IF RND<1/3 THEN JJ=121 ELSE IF RND<1/2 THEN JJ=126 ELSE JJ=131
205 IF RND<.2 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=1 ELSE IF RND<.4 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=1:X(JJ+4)=0 ELSE IF RND<.6 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=1:X(JJ+3)=0:X(JJ+4)=0 ELSE 211
208 GOTO 1333
211 IF RND<.5 THEN X(JJ)=0:X(JJ+1)=1:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0 ELSE X(JJ)=1:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0
1333 GOTO 1367
1367 FOR H=1 TO 25
1371 PNEWM(H)=-(ABS(L(H*2-1)-X(1))+ABS(L(H*2)-X(6)))*X(5*H+6)-(ABS(L(H*2-1)-X(2))+ABS(L(H*2)-X(7)))*X(5*H+7)-(ABS(L(H*2-1)-X(3))+ABS(L(H*2)-X(8)))*X(5*H+8)-(ABS(L(H*2-1)-X(4))+ABS(L(H*2)-X(9)))*X(5*H+9)-(ABS(L(H*2-1)-X(5))+ABS(L(H*2)-X(10)))*X(5*H+10)
1379 NEXT H
1389 PSUM=0
1391 FOR HH=1 TO 25
1393 PSUM=PSUM+PNEWM(HH)
1396 NEXT HH
1401 P=PSUM
1402 GOTO 1451
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 135
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-389.1 THEN 1912 ELSE 1999
1912 LPRINT A(1),A(2),A(3),A(4),A(5),A(6),A(7),A(8),A(9),A(10),M,JJJJ
1941  LPRINT A(11),A(12),A(13),A(14),A(15)
1942  LPRINT A(16),A(17),A(18),A(19),A(20)
1943  LPRINT A(21),A(22),A(23),A(24),A(25)
1944  LPRINT A(26),A(27),A(28),A(29),A(30)
1945  LPRINT A(31),A(32),A(33),A(34),A(35)
1946  LPRINT A(36),A(37),A(38),A(39),A(40)
1947  LPRINT A(41),A(42),A(43),A(44),A(45)
1948  LPRINT A(46),A(47),A(48),A(49),A(50)
1949  LPRINT A(51),A(52),A(53),A(54),A(55)
1950  LPRINT A(56),A(57),A(58),A(59),A(60)
1951  LPRINT A(61),A(62),A(63),A(64),A(65)
1952  LPRINT A(66),A(67),A(68),A(69),A(70)
1953  LPRINT A(71),A(72),A(73),A(74),A(75)
1954  LPRINT A(76),A(77),A(78),A(79),A(80)
1955  LPRINT A(81),A(82),A(83),A(84),A(85)
1956  LPRINT A(86),A(87),A(88),A(89),A(90)
1957  LPRINT A(91),A(92),A(93),A(94),A(95)
1958  LPRINT A(96),A(97),A(98),A(99),A(100)
1959  LPRINT A(101),A(102),A(103),A(104),A(105)
1960  LPRINT A(106),A(107),A(108),A(109),A(110)
1961  LPRINT A(111),A(112),A(113),A(114),A(115)
1962  LPRINT A(116),A(117),A(118),A(119),A(120)
1963  LPRINT A(121),A(122),A(123),A(124),A(125)
1964  LPRINT A(126),A(127),A(128),A(129),A(130)
1965  LPRINT A(131),A(132),A(133),A(134),A(135)
1999 NEXT JJJJ

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  Its complete output through JJJJ=-31996 is presented below.  What immediately follows is a hand copy from the output on paper.

47.00003   12.99998   89.99999   30.55808   82.03843  
94.00001   89.00001   61.99999   50.00002   29.28149  
-389.0001   -31997
00010
00001
00010
00001
00100
00001
00100
00001
01000
10000
00100
00001
01000
00001
10000
10000
01000
01000
00010
01000
00100
10000
00010
10000
00100
90.00001   22.75834   47   84.33823   13.00004 
62   50.00001   94.00004   29.6707   89  
-390.0001   -31996
01000
00010
01000
00010
10000
00010
10000
00010
00001
00100
10000
00010
00001
00010
00100
00100
00001
00001
01000
00001
10000
00100
01000
00100
10000

Interpreted in accordance with line 1912 through line 1965, the output above was obtained in two minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter. 

References

[1] B. K.-S. Cheung, A. Langevin and H. Delmaire, Coupling Genetic Algorithm with a Grid Search Method To Solve Mixed Integer Nonlinear Programming Problems, Computers Math. Applic. Vol. 34, No. 12, pp.13-23, 1997. 

[2] Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

A Nonlinear Integer/Discrete/Continuous Solver Applied to an Oil Production Problem with 25 Oil Wells and 5 Oil Platforms, Third Edition

Jsun Yui Wong   

The following computer program tries to solve the problem in Cheung, Langevin, and Delmaire [1, page 17] of searching for locations for five platforms and allocating twenty-five wells to these platforms.  Rectangular distances are used in line 1371 below.

0 DEFSNG A-Z
3 DEFINT I,J,K,H
4 DIM X(155),A(155),L(590),K(33),PNEWM(555),ILO(55)
18 FOR IL=1 TO 50
19 READ L(IL)
20 NEXT IL
21 DATA 22,3,69,44,44,50,70,12,97,51,94,35,100,62,94,26,13,75,65,99
22 DATA 58,59,82,31,13,95,87,29,41,87,47,94,15,89,20,85,31,50,12,99,86,75,47,98,0,52,54,92,90,79
75 FOR JJJJ=-32000 TO 32000
76 RANDOMIZE JJJJ
77 M=-1.7E+38
88 FOR IAA=1 TO 10
89 A(IAA)=RND*100
90 NEXT IAA
111 FOR IBB= 11 TO 135 STEP 1
112 A(IBB)=0
113 NEXT IBB
121 FOR IBB= 11 TO 135 STEP 5
122 A(IBB)=1
123 NEXT IBB
126 REM   IMAR=10+FIX(RND*32700)
128 FOR I=1 TO 3270
129 FOR K=1 TO 135
131 X(K)=A(K)
132 NEXT K
141 IF RND<.5 THEN 181 ELSE 194
181 J=1+FIX(RND*10)
183 R=RND*(1-RND*2)*A(J)
191 IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
192 GOTO 1333
194 IF RND<1/25 THEN JJ=11 ELSE IF RND<1/24 THEN JJ=16 ELSE IF RND<1/23 THEN JJ=21 ELSE IF RND<1/22 THEN JJ=26 ELSE IF RND<1/21 THEN JJ=31 ELSE IF RND<1/20 THEN JJ=36 ELSE IF RND<1/19 THEN JJ=41 ELSE IF RND<1/18 THEN JJ=46 ELSE 196
195 GOTO 205
196 IF RND<1/17 THEN JJ=51 ELSE IF RND<1/16 THEN JJ=56 ELSE IF RND<1/15 THEN JJ=61 ELSE IF RND<1/14 THEN JJ=66 ELSE IF RND<1/13 THEN JJ=71 ELSE IF RND<1/12 THEN JJ=76 ELSE IF RND<1/11 THEN JJ=81 ELSE IF RND<1/10 THEN JJ=86 ELSE 198
197 GOTO 205
198 IF RND<1/9 THEN JJ=91 ELSE IF RND<1/8 THEN JJ=96 ELSE IF RND<1/7 THEN JJ=101 ELSE IF RND<1/6 THEN JJ=106 ELSE IF RND<1/5 THEN JJ=111 ELSE IF RND<1/4 THEN JJ=116 ELSE IF RND<1/3 THEN JJ=121 ELSE IF RND<1/2 THEN JJ=126 ELSE JJ=131
205 IF RND<.2 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=1 ELSE IF RND<.4 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=1:X(JJ+4)=0 ELSE IF RND<.6 THEN X(JJ)=0:X(JJ+1)=0:X(JJ+2)=1:X(JJ+3)=0:X(JJ+4)=0 ELSE 211
208 GOTO 1333
211 IF RND<.5 THEN X(JJ)=0:X(JJ+1)=1:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0 ELSE X(JJ)=1:X(JJ+1)=0:X(JJ+2)=0:X(JJ+3)=0:X(JJ+4)=0
1333 GOTO 1367
1367 FOR H=1 TO 25
1371 PNEWM(H)=-(ABS(L(H*2-1)-X(1))+ABS(L(H*2)-X(6)))*X(5*H+6)-(ABS(L(H*2-1)-X(2))+ABS(L(H*2)-X(7)))*X(5*H+7)-(ABS(L(H*2-1)-X(3))+ABS(L(H*2)-X(8)))*X(5*H+8)-(ABS(L(H*2-1)-X(4))+ABS(L(H*2)-X(9)))*X(5*H+9)-(ABS(L(H*2-1)-X(5))+ABS(L(H*2)-X(10)))*X(5*H+10)
1379 NEXT H
1389 PSUM=0
1391 FOR HH=1 TO 25
1393 PSUM=PSUM+PNEWM(HH)
1396 NEXT HH
1401 P=PSUM
1402 GOTO 1451
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 135
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-389.1 THEN 1912 ELSE 1999
1912 LPRINT A(1),A(2),A(3),A(4),A(5),A(6),A(7),A(8),A(9),A(10),M,JJJJ
1941  LPRINT A(11),A(12),A(13),A(14),A(15)
1942  LPRINT A(16),A(17),A(18),A(19),A(20)
1943  LPRINT A(21),A(22),A(23),A(24),A(25)
1944  LPRINT A(26),A(27),A(28),A(29),A(30)
1945  LPRINT A(31),A(32),A(33),A(34),A(35)
1946  LPRINT A(36),A(37),A(38),A(39),A(40)
1947  LPRINT A(41),A(42),A(43),A(44),A(45)
1948  LPRINT A(46),A(47),A(48),A(49),A(50)
1949  LPRINT A(51),A(52),A(53),A(54),A(55)
1950  LPRINT A(56),A(57),A(58),A(59),A(60)
1951  LPRINT A(61),A(62),A(63),A(64),A(65)
1952  LPRINT A(66),A(67),A(68),A(69),A(70)
1953  LPRINT A(71),A(72),A(73),A(74),A(75)
1954  LPRINT A(76),A(77),A(78),A(79),A(80)
1955  LPRINT A(81),A(82),A(83),A(84),A(85)
1956  LPRINT A(86),A(87),A(88),A(89),A(90)
1957  LPRINT A(91),A(92),A(93),A(94),A(95)
1958  LPRINT A(96),A(97),A(98),A(99),A(100)
1959  LPRINT A(101),A(102),A(103),A(104),A(105)
1960  LPRINT A(106),A(107),A(108),A(109),A(110)
1961  LPRINT A(111),A(112),A(113),A(114),A(115)
1962  LPRINT A(116),A(117),A(118),A(119),A(120)
1963  LPRINT A(121),A(122),A(123),A(124),A(125)
1964  LPRINT A(126),A(127),A(128),A(129),A(130)
1965  LPRINT A(131),A(132),A(133),A(134),A(135)
1999 NEXT JJJJ

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  Its complete output through JJJJ=-31996 is presented below.  What immediately follows is a hand copy from the output on paper.

47.00003   12.99998   89.99999   30.55808   82.03843  
94.00001   89.00001   61.99999   50.00002   29.28149  
-389.0001   -31997
00010
00001
00010
00001
00100
00001
00100
00001
01000
10000
00100
00001
01000
00001
10000
10000
01000
01000
00010
01000
00100
10000
00010
10000
00100
90.00001   22.75834   47   84.33823   13.00004 
62   50.00001   94.00004   29.6707   89  
-390.0001   -31996
01000
00010
01000
00010
10000
00010
10000
00010
00001
00100
10000
00010
00001
00010
00100
00100
00001
00001
01000
00001
10000
00100
01000
00100
10000

Interpreted in accordance with line 1912 through line 1965, the output above was obtained in two minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter. 

References

[1] B. K.-S. Cheung, A. Langevin and H. Delmaire, Coupling Genetic Algorithm with a Grid Search Method To Solve Mixed Integer Nonlinear Programming Problems, Computers Math. Applic. Vol. 34, No. 12, pp.13-23, 1997. 

[2] Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

A Nonlinear Integer/Discrete/Continuous Solver Applied to an Oil Production Problem with 25 Oil Wells and 5 Oil Platforms, Second Edition

Jsun Yui Wong   

The following computer program tries to solve the problem in Cheung, Langevin, and Delmaire [1, page 17] of searching for locations for five platforms and allocating twenty-five wells to these platforms.  Rectangular distances are used in lines 1333-1357 below.

While line 183 of the previous edition is 183 R=RND*3*(1-RND*2)*A(J), line 183 of the present edition is 183 R=RND*(1-RND*2)*A(J).

0 DEFSNG A-Z
3 DEFINT I,J,K
4 DIM X(155),A(155),L(33),K(33)
75 FOR JJJJ=-32000 TO 32000
84 RANDOMIZE JJJJ
87 M=-1.7E+38
88 FOR IAA=1 TO 10
89 A(IAA)=RND*100
90 NEXT IAA
91 A(11)=0:A(12)=0:A(13)=0:A(14)=0:A(15)=1:                                        A(16)=0:A(17)=0:A(18)=0:A(19)=0:A(20)=1
92 A(21)=0:A(22)=0:A(23)=0:A(24)=0:A(25)=1:                                        A(26)=0:A(27)=0:A(28)=0:A(29)=0:A(30)=1
93 A(31)=0:A(32)=0:A(33)=0:A(34)=0:A(35)=1:                                        A(36)=0:A(37)=0:A(38)=0:A(39)=0:A(40)=1
94 A(41)=0:A(42)=0:A(43)=0:A(44)=0:A(45)=1:                                        A(46)=0:A(47)=0:A(48)=0:A(49)=0:A(50)=1
95 A(51)=0:A(52)=0:A(53)=0:A(54)=0:A(55)=1:                                        A(56)=0:A(57)=0:A(58)=0:A(59)=0:A(60)=1
96 A(61)=0:A(62)=0:A(63)=0:A(64)=0:A(65)=1:                                        A(66)=0:A(67)=0:A(68)=0:A(69)=0:A(70)=1
97 A(71)=0:A(72)=0:A(73)=0:A(74)=0:A(75)=1:                                        A(76)=0:A(77)=0:A(78)=0:A(79)=0:A(80)=1
98 A(81)=0:A(82)=0:A(83)=0:A(84)=0:A(85)=1:                                        A(86)=0:A(87)=0:A(88)=0:A(89)=0:A(90)=1
99 A(91)=0:A(92)=0:A(93)=0:A(94)=0:A(95)=1:                                        A(96)=0:A(97)=0:A(98)=0:A(99)=0:A(100)=1
100 A(101)=0:A(102)=0:A(103)=0:A(104)=0:A(105)=1:                                        A(106)=0:A(107)=0:A(108)=0:A(109)=0:A(110)=1
101 A(111)=0:A(112)=0:A(113)=0:A(114)=0:A(115)=1:                                        A(116)=0:A(117)=0:A(118)=0:A(119)=0:A(120)=1
102 A(121)=0:A(122)=0:A(123)=0:A(124)=0:A(125)=1:                                        A(126)=0:A(127)=0:A(128)=0:A(129)=0:A(130)=1
103 A(131)=0:A(132)=0:A(133)=0:A(134)=0:A(135)=1
126 REM   IMAR=10+FIX(RND*32700)
128 FOR I=1 TO 3270
129 FOR K=1 TO 135
131 X(K)=A(K)
132 NEXT K
141 IF RND<.5 THEN 181 ELSE 298
181 J=1+FIX(RND*10)
183 R=RND*(1-RND*2)*A(J)
191 IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
198    GOTO 1333
298 IF RND<1/25 THEN 401 ELSE IF RND<1/24 THEN 411 ELSE IF RND<1/23 THEN 421 ELSE IF RND<1/22 THEN 431 ELSE IF RND<1/21 THEN 441 ELSE IF RND<1/20 THEN 451 ELSE IF RND<1/19 THEN 461 ELSE IF RND<1/18 THEN 471 ELSE IF RND<1/17 THEN 481 ELSE 299
299 IF RND<1/16 THEN 491 ELSE IF RND<1/15 THEN 501 ELSE IF RND<1/14 THEN 511 ELSE IF RND<1/13 THEN 521 ELSE IF RND<1/12 THEN 531 ELSE IF RND<1/11 THEN 541 ELSE IF RND<1/10 THEN 551 ELSE IF RND<1/9 THEN 561 ELSE IF RND<1/8 THEN 571 ELSE 300
300 IF RND<1/7 THEN 581 ELSE IF RND<1/6 THEN 591 ELSE IF RND<1/5 THEN 601 ELSE IF RND<1/4 THEN 611 ELSE IF RND<1/3 THEN 621 ELSE IF RND<1/2 THEN 631 ELSE 641
401 IF RND<.2 THEN X(11)=0:X(12)=0:X(13)=0:X(14)=0:X(15)=1 ELSE IF RND<.4 THEN X(11)=0:X(12)=0:X(13)=0:X(14)=1:X(15)=0 ELSE IF RND<.6 THEN X(11)=0:X(12)=0:X(13)=1:X(14)=0:X(15)=0 ELSE IF RND<.8 THEN X(11)=0:X(12)=1:X(13)=0:X(14)=0:X(15)=0 ELSE 405
403 GOTO 1333
405 X(11)=1:X(12)=0:X(13)=0:X(14)=0:X(15)=0
408 GOTO 1333
411 IF RND<.2 THEN X(16)=0:X(17)=0:X(18)=0:X(19)=0:X(20)=1 ELSE IF RND<.4 THEN X(16)=0:X(17)=0:X(18)=0:X(19)=1:X(20)=0 ELSE IF RND<.6 THEN X(16)=0:X(17)=0:X(18)=1:X(19)=0:X(20)=0 ELSE IF RND<.8 THEN X(16)=0:X(17)=1:X(18)=0:X(19)=0:X(20)=0 ELSE 415
413 GOTO 1333
415 X(16)=1:X(17)=0:X(18)=0:X(19)=0:X(20)=0
418 GOTO 1333
421 IF RND<.2 THEN X(21)=0:X(22)=0:X(23)=0:X(24)=0:X(25)=1 ELSE IF RND<.4 THEN X(21)=0:X(22)=0:X(23)=0:X(24)=1:X(25)=0 ELSE IF RND<.6 THEN X(21)=0:X(22)=0:X(23)=1:X(24)=0:X(25)=0 ELSE IF RND<.8 THEN X(21)=0:X(22)=1:X(23)=0:X(24)=0:X(25)=0 ELSE 425
423 GOTO 1333
425 X(21)=1:X(22)=0:X(23)=0:X(24)=0:X(25)=0
428 GOTO 1333
431 IF RND<.2 THEN X(26)=0:X(27)=0:X(28)=0:X(29)=0:X(30)=1 ELSE IF RND<.4 THEN X(26)=0:X(27)=0:X(28)=0:X(29)=1:X(30)=0 ELSE IF RND<.6 THEN X(26)=0:X(27)=0:X(28)=1:X(29)=0:X(30)=0 ELSE IF RND<.8 THEN X(26)=0:X(27)=1:X(28)=0:X(29)=0:X(30)=0 ELSE 435
433 GOTO 1333
435 X(26)=1:X(27)=0:X(28)=0:X(29)=0:X(30)=0
438 GOTO 1333
441 IF RND<.2 THEN X(31)=0:X(32)=0:X(33)=0:X(34)=0:X(35)=1 ELSE IF RND<.4 THEN X(31)=0:X(32)=0:X(33)=0:X(34)=1:X(35)=0 ELSE IF RND<.6 THEN X(31)=0:X(32)=0:X(33)=1:X(34)=0:X(35)=0 ELSE IF RND<.8 THEN X(31)=0:X(32)=1:X(33)=0:X(34)=0:X(35)=0 ELSE 445
443 GOTO 1333
445 X(31)=1:X(32)=0:X(33)=0:X(34)=0:X(35)=0
448 GOTO 1333
451 IF RND<.2 THEN X(36)=0:X(37)=0:X(38)=0:X(39)=0:X(40)=1 ELSE IF RND<.4 THEN X(36)=0:X(37)=0:X(38)=0:X(39)=1:X(40)=0 ELSE IF RND<.6 THEN X(36)=0:X(37)=0:X(38)=1:X(39)=0:X(40)=0 ELSE IF RND<.8 THEN X(36)=0:X(37)=1:X(38)=0:X(39)=0:X(40)=0 ELSE 455
453 GOTO 1333
455 X(36)=1:X(37)=0:X(38)=0:X(39)=0:X(40)=0
458 GOTO 1333
461 IF RND<.2 THEN X(41)=0:X(42)=0:X(43)=0:X(44)=0:X(45)=1 ELSE IF RND<.4 THEN X(41)=0:X(42)=0:X(43)=0:X(44)=1:X(45)=0 ELSE IF RND<.6 THEN X(41)=0:X(42)=0:X(43)=1:X(44)=0:X(45)=0 ELSE IF RND<.8 THEN X(41)=0:X(42)=1:X(43)=0:X(44)=0:X(45)=0 ELSE 465
463 GOTO 1333
465 X(41)=1:X(42)=0:X(43)=0:X(44)=0:X(45)=0
468 GOTO 1333
471 IF RND<.2 THEN X(46)=0:X(47)=0:X(48)=0:X(49)=0:X(50)=1 ELSE IF RND<.4 THEN X(46)=0:X(47)=0:X(48)=0:X(49)=1:X(50)=0 ELSE IF RND<.6 THEN X(46)=0:X(47)=0:X(48)=1:X(49)=0:X(50)=0 ELSE IF RND<.8 THEN X(46)=0:X(47)=1:X(48)=0:X(49)=0:X(50)=0 ELSE 475
473 GOTO 1333
475 X(46)=1:X(47)=0:X(48)=0:X(49)=0:X(50)=0
478 GOTO 1333
481 IF RND<.2 THEN X(51)=0:X(52)=0:X(53)=0:X(54)=0:X(55)=1 ELSE IF RND<.4 THEN X(51)=0:X(52)=0:X(53)=0:X(54)=1:X(55)=0 ELSE IF RND<.6 THEN X(51)=0:X(52)=0:X(53)=1:X(54)=0:X(55)=0 ELSE IF RND<.8 THEN X(51)=0:X(52)=1:X(53)=0:X(54)=0:X(55)=0 ELSE 485
483 GOTO 1333
485 X(51)=1:X(52)=0:X(53)=0:X(54)=0:X(55)=0
488 GOTO 1333
491 IF RND<.2 THEN X(56)=0:X(57)=0:X(58)=0:X(59)=0:X(60)=1 ELSE IF RND<.4 THEN X(56)=0:X(57)=0:X(58)=0:X(59)=1:X(60)=0 ELSE IF RND<.6 THEN X(56)=0:X(57)=0:X(58)=1:X(59)=0:X(60)=0 ELSE IF RND<.8 THEN X(56)=0:X(57)=1:X(58)=0:X(59)=0:X(60)=0 ELSE 495
493 GOTO 1333
495 X(56)=1:X(57)=0:X(58)=0:X(59)=0:X(60)=0
498 GOTO 1333
501 IF RND<.2 THEN X(61)=0:X(62)=0:X(63)=0:X(64)=0:X(65)=1 ELSE IF RND<.4 THEN X(61)=0:X(62)=0:X(63)=0:X(64)=1:X(65)=0 ELSE IF RND<.6 THEN X(61)=0:X(62)=0:X(63)=1:X(64)=0:X(65)=0 ELSE IF RND<.8 THEN X(61)=0:X(62)=1:X(63)=0:X(64)=0:X(65)=0 ELSE 505
503 GOTO 1333
505 X(61)=1:X(62)=0:X(63)=0:X(64)=0:X(65)=0
508 GOTO 1333
511 IF RND<.2 THEN X(66)=0:X(67)=0:X(68)=0:X(69)=0:X(70)=1 ELSE IF RND<.4 THEN X(66)=0:X(67)=0:X(68)=0:X(69)=1:X(70)=0 ELSE IF RND<.6 THEN X(66)=0:X(67)=0:X(68)=1:X(69)=0:X(70)=0 ELSE IF RND<.8 THEN X(66)=0:X(67)=1:X(68)=0:X(69)=0:X(70)=0 ELSE 515
513 GOTO 1333
515 X(66)=1:X(67)=0:X(68)=0:X(69)=0:X(70)=0
518 GOTO 1333
521 IF RND<.2 THEN X(71)=0:X(72)=0:X(73)=0:X(74)=0:X(75)=1 ELSE IF RND<.4 THEN X(71)=0:X(72)=0:X(73)=0:X(74)=1:X(75)=0 ELSE IF RND<.6 THEN X(71)=0:X(72)=0:X(73)=1:X(74)=0:X(75)=0 ELSE IF RND<.8 THEN X(71)=0:X(72)=1:X(73)=0:X(74)=0:X(75)=0 ELSE 525
523 GOTO 1333
525 X(71)=1:X(72)=0:X(73)=0:X(74)=0:X(75)=0
528 GOTO 1333
531 IF RND<.2 THEN X(76)=0:X(77)=0:X(78)=0:X(79)=0:X(80)=1 ELSE IF RND<.4 THEN X(76)=0:X(77)=0:X(78)=0:X(79)=1:X(80)=0 ELSE IF RND<.6 THEN X(76)=0:X(77)=0:X(78)=1:X(79)=0:X(80)=0 ELSE IF RND<.8 THEN X(76)=0:X(77)=1:X(78)=0:X(79)=0:X(80)=0 ELSE 535
533 GOTO 1333
535 X(76)=1:X(77)=0:X(78)=0:X(79)=0:X(80)=0
538 GOTO 1333
541 IF RND<.2 THEN X(81)=0:X(82)=0:X(83)=0:X(84)=0:X(85)=1 ELSE IF RND<.4 THEN X(81)=0:X(82)=0:X(83)=0:X(84)=1:X(85)=0 ELSE IF RND<.6 THEN X(81)=0:X(82)=0:X(83)=1:X(84)=0:X(85)=0 ELSE IF RND<.8 THEN X(81)=0:X(82)=1:X(83)=0:X(84)=0:X(85)=0 ELSE 545
543 GOTO 1333
545 X(81)=1:X(82)=0:X(83)=0:X(84)=0:X(85)=0
548 GOTO 1333
551 IF RND<.2 THEN X(86)=0:X(87)=0:X(88)=0:X(89)=0:X(90)=1 ELSE IF RND<.4 THEN X(86)=0:X(87)=0:X(88)=0:X(89)=1:X(90)=0 ELSE IF RND<.6 THEN X(86)=0:X(87)=0:X(88)=1:X(89)=0:X(90)=0 ELSE IF RND<.8 THEN X(86)=0:X(87)=1:X(88)=0:X(89)=0:X(90)=0 ELSE 555
553 GOTO 1333
555 X(86)=1:X(87)=0:X(88)=0:X(89)=0:X(90)=0
558 GOTO 1333
561 IF RND<.2 THEN X(91)=0:X(92)=0:X(93)=0:X(94)=0:X(95)=1 ELSE IF RND<.4 THEN X(91)=0:X(92)=0:X(93)=0:X(94)=1:X(95)=0 ELSE IF RND<.6 THEN X(91)=0:X(92)=0:X(93)=1:X(94)=0:X(95)=0 ELSE IF RND<.8 THEN X(91)=0:X(92)=1:X(93)=0:X(94)=0:X(95)=0 ELSE 565
563 GOTO 1333
565 X(91)=1:X(92)=0:X(93)=0:X(94)=0:X(95)=0
568 GOTO 1333
571 IF RND<.2 THEN X(96)=0:X(97)=0:X(98)=0:X(99)=0:X(100)=1 ELSE IF RND<.4 THEN X(96)=0:X(97)=0:X(98)=0:X(99)=1:X(100)=0 ELSE IF RND<.6 THEN X(96)=0:X(97)=0:X(98)=1:X(99)=0:X(100)=0 ELSE IF RND<.8 THEN X(96)=0:X(97)=1:X(98)=0:X(99)=0:X(100)=0 ELSE 575
573 GOTO 1333
575 X(96)=1:X(97)=0:X(98)=0:X(99)=0:X(100)=0
578 GOTO 1333
581 IF RND<.2 THEN X(101)=0:X(102)=0:X(103)=0:X(104)=0:X(105)=1 ELSE IF RND<.4 THEN X(101)=0:X(102)=0:X(103)=0:X(104)=1:X(105)=0 ELSE IF RND<.6 THEN X(101)=0:X(102)=0:X(103)=1:X(104)=0:X(105)=0 ELSE 585
583 GOTO 1333
585 IF RND<.5 THEN X(101)=0:X(102)=1:X(103)=0:X(104)=0:X(105)=0 ELSE X(101)=1:X(102)=0:X(103)=0:X(104)=0:X(105)=0
588 GOTO 1333
591 IF RND<.2 THEN X(106)=0:X(107)=0:X(108)=0:X(109)=0:X(110)=1 ELSE IF RND<.4 THEN X(106)=0:X(107)=0:X(108)=0:X(109)=1:X(110)=0 ELSE IF RND<.6 THEN X(106)=0:X(107)=0:X(108)=1:X(109)=0:X(110)=0 ELSE 595
593 GOTO 1333
595 IF RND<.5 THEN X(106)=0:X(107)=1:X(108)=0:X(109)=0:X(110)=0 ELSE X(106)=1:X(107)=0:X(108)=0:X(109)=0:X(110)=0
598 GOTO 1333
601 IF RND<.2 THEN X(111)=0:X(112)=0:X(113)=0:X(114)=0:X(115)=1 ELSE IF RND<.4 THEN X(111)=0:X(112)=0:X(113)=0:X(114)=1:X(115)=0 ELSE IF RND<.6 THEN X(111)=0:X(112)=0:X(113)=1:X(114)=0:X(115)=0 ELSE 605
603 GOTO 1333
605 IF RND<.5 THEN X(111)=0:X(112)=1:X(113)=0:X(114)=0:X(115)=0 ELSE X(111)=1:X(112)=0:X(113)=0:X(114)=0:X(115)=0
608 GOTO 1333
611 IF RND<.2 THEN X(116)=0:X(117)=0:X(118)=0:X(119)=0:X(120)=1 ELSE IF RND<.4 THEN X(116)=0:X(117)=0:X(118)=0:X(119)=1:X(120)=0 ELSE IF RND<.6 THEN X(116)=0:X(117)=0:X(118)=1:X(119)=0:X(120)=0 ELSE 615
613 GOTO 1333
615 IF RND<.5 THEN X(116)=0:X(117)=1:X(118)=0:X(119)=0:X(120)=0 ELSE X(116)=1:X(117)=0:X(118)=0:X(119)=0:X(120)=0
618 GOTO 1333
621 IF RND<.2 THEN X(121)=0:X(122)=0:X(123)=0:X(124)=0:X(125)=1 ELSE IF RND<.4 THEN X(121)=0:X(122)=0:X(123)=0:X(124)=1:X(125)=0 ELSE IF RND<.6 THEN X(121)=0:X(122)=0:X(123)=1:X(124)=0:X(125)=0 ELSE 625
623 GOTO 1333
625 IF RND<.5 THEN X(121)=0:X(122)=1:X(123)=0:X(124)=0:X(125)=0 ELSE X(121)=1:X(122)=0:X(123)=0:X(124)=0:X(125)=0
628 GOTO 1333
631 IF RND<.2 THEN X(126)=0:X(127)=0:X(128)=0:X(129)=0:X(130)=1 ELSE IF RND<.4 THEN X(126)=0:X(127)=0:X(128)=0:X(129)=1:X(130)=0 ELSE IF RND<.6 THEN X(126)=0:X(127)=0:X(128)=1:X(129)=0:X(130)=0 ELSE 635
633 GOTO 1333
635 IF RND<.5 THEN X(126)=0:X(127)=1:X(128)=0:X(129)=0:X(130)=0 ELSE X(126)=1:X(127)=0:X(128)=0:X(129)=0:X(130)=0
638 GOTO 1333
641 IF RND<.2 THEN X(131)=0:X(132)=0:X(133)=0:X(134)=0:X(135)=1 ELSE IF RND<.4 THEN X(131)=0:X(132)=0:X(133)=0:X(134)=1:X(135)=0 ELSE IF RND<.6 THEN X(131)=0:X(132)=0:X(133)=1:X(134)=0:X(135)=0 ELSE 645
643 GOTO 1333
645 IF RND<.5 THEN X(131)=0:X(132)=1:X(133)=0:X(134)=0:X(135)=0 ELSE X(131)=1:X(132)=0:X(133)=0:X(134)=0:X(135)=0
648 GOTO 1333
653 GOTO 1333
658 GOTO 1333
663 GOTO 1333
668 GOTO 1333
673 GOTO 1333
678 GOTO 1333
683 GOTO 1333
693 GOTO 1333
1333 PNEWMA1=      -(ABS(22-X(1))+ABS(3-X(6)))*X(11)-(ABS(22-X(2))+ABS(3-X(7)))*X(12)     -(ABS(22-X(3))+ABS(3-X(8)))*X(13)   - (ABS(22-X(4))+ABS(3-X(9)))*X(14)-(ABS(22-X(5))+ABS(3-X(10)))*X(15)
1334 PNEWMA2=      -(ABS(69-X(1))+ABS(44-X(6)))*X(16)-(ABS(69-X(2))+ABS(44-X(7)))*X(17)     -(ABS(69-X(3))+ABS(44-X(8)))*X(18)   - (ABS(69-X(4))+ABS(44-X(9)))*X(19)-(ABS(69-X(5))+ABS(44-X(10)))*X(20)
1335 PNEWMA3=      -(ABS(44-X(1))+ABS(50-X(6)))*X(21)-(ABS(44-X(2))+ABS(50-X(7)))*X(22)     -(ABS(44-X(3))+ABS(50-X(8)))*X(23)   - (ABS(44-X(4))+ABS(50-X(9)))*X(24)-(ABS(44-X(5))+ABS(50-X(10)))*X(25)
1336 PNEWMA4=      -(ABS(70-X(1))+ABS(12-X(6)))*X(26)-(ABS(70-X(2))+ABS(12-X(7)))*X(27)     -(ABS(70-X(3))+ABS(12-X(8)))*X(28)   - (ABS(70-X(4))+ABS(12-X(9)))*X(29)-(ABS(70-X(5))+ABS(12-X(10)))*X(30)
1337 PNEWMA5=      -(ABS(97-X(1))+ABS(51-X(6)))*X(31)-(ABS(97-X(2))+ABS(51-X(7)))*X(32)     -(ABS(97-X(3))+ABS(51-X(8)))*X(33)   - (ABS(97-X(4))+ABS(51-X(9)))*X(34)-(ABS(97-X(5))+ABS(51-X(10)))*X(35)
1338 PNEWMA6=      -(ABS(94-X(1))+ABS(35-X(6)))*X(36)-(ABS(94-X(2))+ABS(35-X(7)))*X(37)     -(ABS(94-X(3))+ABS(35-X(8)))*X(38)   - (ABS(94-X(4))+ABS(35-X(9)))*X(39)-(ABS(94-X(5))+ABS(35-X(10)))*X(40)
1339 PNEWMA7=      -(ABS(100-X(1))+ABS(62-X(6)))*X(41)-(ABS(100-X(2))+ABS(62-X(7)))*X(42)     -(ABS(100-X(3))+ABS(62-X(8)))*X(43)   - (ABS(100-X(4))+ABS(62-X(9)))*X(44)-(ABS(100-X(5))+ABS(62-X(10)))*X(45)
1340 PNEWMA8=      -(ABS(94-X(1))+ABS(26-X(6)))*X(46)-(ABS(94-X(2))+ABS(26-X(7)))*X(47)     -(ABS(94-X(3))+ABS(26-X(8)))*X(48)   - (ABS(94-X(4))+ABS(26-X(9)))*X(49)-(ABS(94-X(5))+ABS(26-X(10)))*X(50)
1341 PNEWMA9=      -(ABS(13-X(1))+ABS(75-X(6)))*X(51)-(ABS(13-X(2))+ABS(75-X(7)))*X(52)     -(ABS(13-X(3))+ABS(75-X(8)))*X(53)   - (ABS(13-X(4))+ABS(75-X(9)))*X(54)-(ABS(13-X(5))+ABS(75-X(10)))*X(55)
1342 PNEWMA10=      -(ABS(65-X(1))+ABS(99-X(6)))*X(56)-(ABS(65-X(2))+ABS(99-X(7)))*X(57)     -(ABS(65-X(3))+ABS(99-X(8)))*X(58)   - (ABS(65-X(4))+ABS(99-X(9)))*X(59)-(ABS(65-X(5))+ABS(99-X(10)))*X(60)
1343 PNEWMA11=      -(ABS(58-X(1))+ABS(59-X(6)))*X(61)-(ABS(58-X(2))+ABS(59-X(7)))*X(62)     -(ABS(58-X(3))+ABS(59-X(8)))*X(63)   - (ABS(58-X(4))+ABS(59-X(9)))*X(64)-(ABS(58-X(5))+ABS(59-X(10)))*X(65)
1344 PNEWMA12=      -(ABS(82-X(1))+ABS(31-X(6)))*X(66)-(ABS(82-X(2))+ABS(31-X(7)))*X(67)     -(ABS(82-X(3))+ABS(31-X(8)))*X(68)   - (ABS(82-X(4))+ABS(31-X(9)))*X(69)-(ABS(82-X(5))+ABS(31-X(10)))*X(70)
1345 PNEWMA13=      -(ABS(13-X(1))+ABS(95-X(6)))*X(71)-(ABS(13-X(2))+ABS(95-X(7)))*X(72)     -(ABS(13-X(3))+ABS(95-X(8)))*X(73)   - (ABS(13-X(4))+ABS(95-X(9)))*X(74)-(ABS(13-X(5))+ABS(95-X(10)))*X(75)
1346 PNEWMA14=      -(ABS(87-X(1))+ABS(29-X(6)))*X(76)-(ABS(87-X(2))+ABS(29-X(7)))*X(77)     -(ABS(87-X(3))+ABS(29-X(8)))*X(78)   - (ABS(87-X(4))+ABS(29-X(9)))*X(79)-(ABS(87-X(5))+ABS(29-X(10)))*X(80)
1347 PNEWMA15=      -(ABS(41-X(1))+ABS(87-X(6)))*X(81)-(ABS(41-X(2))+ABS(87-X(7)))*X(82)     -(ABS(41-X(3))+ABS(87-X(8)))*X(83)   - (ABS(41-X(4))+ABS(87-X(9)))*X(84)-(ABS(41-X(5))+ABS(87-X(10)))*X(85)
1348 PNEWMA16=      -(ABS(47-X(1))+ABS(94-X(6)))*X(86)-(ABS(47-X(2))+ABS(94-X(7)))*X(87)     -(ABS(47-X(3))+ABS(94-X(8)))*X(88)   - (ABS(47-X(4))+ABS(94-X(9)))*X(89)-(ABS(47-X(5))+ABS(94-X(10)))*X(90)
1349 PNEWMA17=      -(ABS(15-X(1))+ABS(89-X(6)))*X(91)-(ABS(15-X(2))+ABS(89-X(7)))*X(92)     -(ABS(15-X(3))+ABS(89-X(8)))*X(93)   - (ABS(15-X(4))+ABS(89-X(9)))*X(94)-(ABS(15-X(5))+ABS(89-X(10)))*X(95)
1350 PNEWMA18=      -(ABS(20-X(1))+ABS(85-X(6)))*X(96)-(ABS(20-X(2))+ABS(85-X(7)))*X(97)     -(ABS(20-X(3))+ABS(85-X(8)))*X(98)   - (ABS(20-X(4))+ABS(85-X(9)))*X(99)-(ABS(20-X(5))+ABS(85-X(10)))*X(100)
1351 PNEWMA19=      -(ABS(31-X(1))+ABS(50-X(6)))*X(101)-(ABS(31-X(2))+ABS(50-X(7)))*X(102)     -(ABS(31-X(3))+ABS(50-X(8)))*X(103)   - (ABS(31-X(4))+ABS(50-X(9)))*X(104)-(ABS(31-X(5))+ABS(50-X(10)))*X(105)
1352 PNEWMA20=      -(ABS(12-X(1))+ABS(99-X(6)))*X(106)-(ABS(12-X(2))+ABS(99-X(7)))*X(107)     -(ABS(12-X(3))+ABS(99-X(8)))*X(108)   - (ABS(12-X(4))+ABS(99-X(9)))*X(109)-(ABS(12-X(5))+ABS(99-X(10)))*X(110)
1353 PNEWMA21=      -(ABS(86-X(1))+ABS(75-X(6)))*X(111)-(ABS(86-X(2))+ABS(75-X(7)))*X(112)     -(ABS(86-X(3))+ABS(75-X(8)))*X(113)   - (ABS(86-X(4))+ABS(75-X(9)))*X(114)-(ABS(86-X(5))+ABS(75-X(10)))*X(115)
1354 PNEWMA22=      -(ABS(47-X(1))+ABS(98-X(6)))*X(116)-(ABS(47-X(2))+ABS(98-X(7)))*X(117)     -(ABS(47-X(3))+ABS(98-X(8)))*X(118)   - (ABS(47-X(4))+ABS(98-X(9)))*X(119)-(ABS(47-X(5))+ABS(98-X(10)))*X(120)
1355 PNEWMA23=      -(ABS(0-X(1))+ABS(52-X(6)))*X(121)-(ABS(0-X(2))+ABS(52-X(7)))*X(122)     -(ABS(0-X(3))+ABS(52-X(8)))*X(123)   - (ABS(0-X(4))+ABS(52-X(9)))*X(124)-(ABS(0-X(5))+ABS(52-X(10)))*X(125)
1356 PNEWMA24=      -(ABS(54-X(1))+ABS(92-X(6)))*X(126)-(ABS(54-X(2))+ABS(92-X(7)))*X(127)     -(ABS(54-X(3))+ABS(92-X(8)))*X(128)   - (ABS(54-X(4))+ABS(92-X(9)))*X(129)-(ABS(54-X(5))+ABS(92-X(10)))*X(130)
1357 PNEWMA25=      -(ABS(90-X(1))+ABS(79-X(6)))*X(131)-(ABS(90-X(2))+ABS(79-X(7)))*X(132)     -(ABS(90-X(3))+ABS(79-X(8)))*X(133)   - (ABS(90-X(4))+ABS(79-X(9)))*X(134)-(ABS(90-X(5))+ABS(79-X(10)))*X(135)
1437 P1NEWONE= PNEWMA1+PNEWMA2+PNEWMA3+PNEWMA4+PNEWMA5
1438 P1NEWTWO= PNEWMA6+PNEWMA7+PNEWMA8+PNEWMA9+PNEWMA10
1439 P1NEWTHR= PNEWMA11+PNEWMA12+PNEWMA13+PNEWMA14+PNEWMA15
1440 P1NEWFOU= PNEWMA16+PNEWMA17+PNEWMA18+PNEWMA19+PNEWMA20
1441 P1NEWFIV= PNEWMA21+PNEWMA22+PNEWMA23+PNEWMA24+PNEWMA25
1448 P=+P1NEWONE+P1NEWTWO+P1NEWTHR+P1NEWFOU+P1NEWFIV
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 135
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-390.1 THEN 1912 ELSE 1999
1912 LPRINT A(1),A(2),A(3),A(4),A(5),A(6),A(7),A(8),A(9),A(10),M,JJJJ
1941  LPRINT A(11),A(12),A(13),A(14),A(15)
1942  LPRINT A(16),A(17),A(18),A(19),A(20)
1943  LPRINT A(21),A(22),A(23),A(24),A(25)
1944  LPRINT A(26),A(27),A(28),A(29),A(30)
1945  LPRINT A(31),A(32),A(33),A(34),A(35)
1946  LPRINT A(36),A(37),A(38),A(39),A(40)
1947  LPRINT A(41),A(42),A(43),A(44),A(45)
1948  LPRINT A(46),A(47),A(48),A(49),A(50)
1949  LPRINT A(51),A(52),A(53),A(54),A(55)
1950  LPRINT A(56),A(57),A(58),A(59),A(60)
1951  LPRINT A(61),A(62),A(63),A(64),A(65)
1952  LPRINT A(66),A(67),A(68),A(69),A(70)
1953  LPRINT A(71),A(72),A(73),A(74),A(75)
1954  LPRINT A(76),A(77),A(78),A(79),A(80)
1955  LPRINT A(81),A(82),A(83),A(84),A(85)
1956  LPRINT A(86),A(87),A(88),A(89),A(90)
1957  LPRINT A(91),A(92),A(93),A(94),A(95)
1958  LPRINT A(96),A(97),A(98),A(99),A(100)
1959  LPRINT A(101),A(102),A(103),A(104),A(105)
1960  LPRINT A(106),A(107),A(108),A(109),A(110)
1961  LPRINT A(111),A(112),A(113),A(114),A(115)
1962  LPRINT A(116),A(117),A(118),A(119),A(120)
1963  LPRINT A(121),A(122),A(123),A(124),A(125)
1964  LPRINT A(126),A(127),A(128),A(129),A(130)
1965  LPRINT A(131),A(132),A(133),A(134),A(135)
1999 NEXT JJJJ

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  Its complete output through JJJJ=-31998 is presented below.  What immediately follows is a hand copy from the output on paper.

26.65677   46.99999   89.99997   13   86.72194  
50   93.99998   62.00001   88.99994   29.45179  
-389.0001   -32000
10000
00001
10000
00001
00100
00001
00100
00001
00010
01000
00100
00001
00010
00001
01000
01000
00010
00010
10000
00010
00100
01000
10000
01000
00100
93.56821   30.99998   47   82.7294   13 
71.64384     49.99999   94.00001   29.88918   89.00001  
-390.0001   -31999
01000
00010
01000
00010
10000
00010
10000
00010
00001
00100
01000
00010
00001
00010
00100
00100
00001
00001
01000
00001
10000
00100
01000
00100
10000
13   84.48901   90.00002   47   22.30278   
88.99994   29.28982   62   94   50  
-389   -31998
00001
01000
00001
01000
00100
01000
00100
01000
10000
00010
00100
01000
10000
01000
00010
00010
10000
10000
00001
10000
00100
00010
00001
00010
00100

Interpreted in accordance with line 1912 through line 1965, the output above was obtained in one minute on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter. 

References

[1] B. K.-S. Cheung, A. Langevin and H. Delmaire, Coupling Genetic Algorithm with a Grid Search Method To Solve Mixed Integer Nonlinear Programming Problems, Computers Math. Applic. Vol. 34, No. 12, pp.13-23, 1997. 

[2] Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

Testing a Nonlinear Integer/Discrete/Continuous Programming Solver with a Transformer Design Model Involving Continuous Variables, Fourth Edition

Jsun Yui Wong

The following computer program tries to solve a problem considered by Ballard, Jelinek, and Schinzinger [1, p. 265], by Bartholomew-Biggs [2, p. 307], by Hock and Schittkowski [3, p. 108], and by Price [4, p. 340].  For more details, see Schinzinger [5], page 192 and page 193 in particular.

Firstly, from among the given inequality constraints one chooses an inequality constraint that will be changed to an equality constraint.  That leads to line 231 of the following computer program.  In general, the worst case scenario is that one may have to choose each inequality constraint, one at a time.

Line 75 and line 128 are noteworthy.

This post is similar to the October 23 post with the title "A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a Transformer Design Model with Integer Variables and Continuous Variables" of the present blog.

0 REM    DEFINT A-Z
1 REM    DEFSNG L,S,P,M,R,Q
2 DEFSNG A-Z
3 DEFINT J,K
4 DIM X(42),A(42),L(33),K(33)
75 FOR FFFF=-32000 TO 32000 STEP .1
84 RANDOMIZE FFFF
87 M=-1.7E+38
91 FOR KK=1 TO 6
94 A(KK)=RND*30
95 NEXT KK
126 IMAR=10+FIX(RND*25)
128 FOR I=1 TO IMAR STEP .1
129 FOR K=1 TO 6
131 X(K)=A(K)
132 NEXT K
181 J=1+FIX(RND*6)
183 R=(1-RND*2)*A(J)
191 IF RND<1/10 THEN X(J)=A(J)+RND^9*R ELSE IF RND<1/9 THEN X(J)=A(J)+RND^8*R ELSE IF RND<1/8 THEN X(J)=A(J)+RND^7*R ELSE IF RND<1/7 THEN X(J)=A(J)+RND^6*R ELSE IF RND<1/6 THEN X(J)=A(J)+RND^5*R ELSE IF RND<1/5 THEN X(J)=A(J)+RND^4*R ELSE 193
192 GOTO 222
193 IF RND<1/4 THEN X(J)=A(J)+RND^3*R ELSE IF RND<1/3 THEN X(J)=A(J)+RND^2*R ELSE IF RND<1/2 THEN X(J)=A(J)+RND^1*R ELSE X(J)=A(J)+RND^0*R
194 REM  IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
222 XUP=1-.00058*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))
226 XDO=.00062*X(1)*X(4)*(X(1)+X(2)+X(3))
227 IF XUP<.00001 THEN 1670
228 IF XDO<.00001 THEN 1670
231 X(5)=(      XUP/XDO       )^.5
351 L1=-.001*X(1)*X(2)*X(3)*X(4)*X(5)*X(6)+2.07
352 REM  L2=.00062*X(1)*X(4)*X(5)^2*(X(1)+X(2)+X(3))+.00058*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))-1.2
511 IF L1>0 THEN L1=-1000000! ELSE L1=0
512 REM     IF L2>0 THEN L2=-1000000! ELSE L2=0
1311     SS=L1
1333 P1NEWMAY=-.0204*X(1)*X(4)*(X(1)+X(2)+X(3))-.0187*X(2)*X(3)*(X(1)+1.57*X(2)+X(4))-.0607*X(1)*X(4)*X(5)^2*(X(1)+X(2)+X(3))-.0437*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))+SS
1448 P=P1NEWMAY
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 6
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-135.4 THEN 1912 ELSE 1999
1912 PRINT A(1),A(2),A(3),A(4),A(5),A(6),M,FFFF,I
1999 REM
2000 NEXT FFFF

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  Only the top-three solutions among the seven candidate solutions produced are presented below.    What immediately follows is a manual copy from the computer screen.

5.266829   4.659148   10.35624   12.29814   .7557036
.8764388   -135.087   -8398.455   20.00004

5.434915   4.798931   10.51272   11.44078   .7722216
.8657278   -135.1721   -3880.058   15.00002

5.289292   4.71823   10.73957   11.86368   .74216
.8771828   -135.2053   15442.78   30.00008

Interpreted in accordance with line 1912, the solution at FFFF=-8398.455 is the best among the seven candidate solutions produced.  One notes that 135.087 presented above to 135.075961 of Bartholomew-Biggs as presented in Hock and Schittkowski [3] is 1.000081724 to 1; 135.087 to 135.1023 of Ballard, Jelinet, and Schinzinger [1] is 0.999886752 to 1.  This complete run through the whole computer program took three hours on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter. 

References

[1]  Ballard, D.H., Jelinet, C. A., and Schinzinger, R., An Algorithm for the Solution of Constrained Generalized Polynomial Programming Problems, The Computer Journal: Vol. 17, Number 3, pp. 261-266, 1974.

[2]  Bartholomew-Biggs, M. C., A Numerical Comparison between Two Approaches to the Nonlinear Programming Problem, Toward Global Optimization 2, Edited by L. C. W. Dixon and G. P. Szego, North-Hollad Publishing Company, Amsterdam, Holland, pp. 293-312, 1978.

[3]  Hock, W., and K. Schittkowski, 1981.  Test Examples for Nonlinear Programming Codes.  Lecture Notes in Economics and Mathematical Systems, No. 187.  Springer-Verlag, New York.

[4]  Price, W. L., Global Optimization by Controlled Random Search, Journal of Optimization Theory and Applications: Vol. 40, No. 3, July 1983.

[5]  Schinzinger, R. (1965).  Optimization in Electromagnetic System Design, in Recent Advances in Optimization Techniques, edited by A. Lavi and T. P. Vogl, New York: Wiley, pp. 163-213.

[6]  Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

Testing a Nonlinear Integer/Discrete/Continuous Programming Solver with a Transformer Design Model Involving Continuous Variables, Third Edition

Jsun Yui Wong

The following computer program tries to solve a problem considered by Ballard, Jelinek, and Schinzinger [1, p. 265], by Bartholomew-Biggs [2, p. 307], Hock and Schittkowski [3, p. 108], and by Price [4, p. 340].  For more details, see Schinzinger [5], page 192 and page 193 in particular.

Firstly, from among the given inequality constraints one chooses an inequality constraint that will be changed to an equality constraint.  That leads to line 231 of the following computer program.  In general, the worst case scenario is that one may have to choose each inequality constraint, one at a time.

Line 191 and line 193 are noteworthy.

This post is similar to the October 23 post with the title "A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a Transformer Design Model with Integer Variables and Continuous Variables" of the present blog.

0 REM    DEFINT A-Z
1 REM    DEFSNG L,S,P,M,R,Q
2 DEFSNG A-Z
3 DEFINT I,J,K
4 DIM X(42),A(42),L(33),K(33)
75 FOR JJJJ=-32000 TO 32000
84 RANDOMIZE JJJJ
87 M=-1.7E+38
91 FOR KK=1 TO 6
94 A(KK)=RND*30
95 NEXT KK
126 REM   IMAR=10+FIX(RND*32700)
128 FOR I=1 TO 1000
129 FOR K=1 TO 6
131 X(K)=A(K)
132 NEXT K
181 J=1+FIX(RND*6)
183 R=(1-RND*2)*A(J)
191 IF RND<1/10 THEN X(J)=A(J)+RND^9*R ELSE IF RND<1/9 THEN X(J)=A(J)+RND^8*R ELSE IF RND<1/8 THEN X(J)=A(J)+RND^7*R ELSE IF RND<1/7 THEN X(J)=A(J)+RND^6*R ELSE IF RND<1/6 THEN X(J)=A(J)+RND^5*R ELSE IF RND<1/5 THEN X(J)=A(J)+RND^4*R ELSE 193
192 GOTO 222
193 IF RND<1/4 THEN X(J)=A(J)+RND^3*R ELSE IF RND<1/3 THEN X(J)=A(J)+RND^2*R ELSE IF RND<1/2 THEN X(J)=A(J)+RND^1*R ELSE X(J)=A(J)+RND^0*R
194 REM  IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
222 XUP=1-.00058*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))
226 XDO=.00062*X(1)*X(4)*(X(1)+X(2)+X(3))
227 IF XUP<.00001 THEN 1670
228 IF XDO<.00001 THEN 1670
231 X(5)=(      XUP/XDO       )^.5
351 L1=-.001*X(1)*X(2)*X(3)*X(4)*X(5)*X(6)+2.07
352 REM  L2=.00062*X(1)*X(4)*X(5)^2*(X(1)+X(2)+X(3))+.00058*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))-1.2
511 IF L1>0 THEN L1=-1000000! ELSE L1=0
512 REM     IF L2>0 THEN L2=-1000000! ELSE L2=0
1311     SS=L1
1333 P1NEWMAY=-.0204*X(1)*X(4)*(X(1)+X(2)+X(3))-.0187*X(2)*X(3)*(X(1)+1.57*X(2)+X(4))-.0607*X(1)*X(4)*X(5)^2*(X(1)+X(2)+X(3))-.0437*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))+SS
1448 P=P1NEWMAY
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 6
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-135.4 THEN 1912 ELSE 1999
1912 PRINT A(1),A(2),A(3),A(4),A(5),A(6),M,JJJJ
1999 NEXT JJJJ

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  The complete printout is shown below.  What immediately follows is a manual copy from the computer screen.

5.483327   4.637876   10.19847   12.03633   .7474994
.8870888   -135.1197   -13561

5.205195   4.342032   10.74569   12.92793   .7378702
.8935049   -135.3699   -9631

5.629148   4.620409   10.87343   11.17092   .7418716
.8832078   -135.2645   3983

5.344272   4.817055   9.63476   12.58506   .7545975
.8787974   -135.2342   6462

Interpreted in accordance with line 1912, the solution at JJJJ=-13561is the best among the candidate solutions shown above.  One notes that 135.1197 presented above to 135.075961 of Bartholomew-Biggs as presented in Hock and Schittkowski [3] is 1.00032381 to 1; 135.1197 to 135.1023 of Ballard, Jelinet, and Schinzinger [1] is 1.000128791 to 1.  This complete run through JJJJ=32000 took eighty-six minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter. 

References

[1]  Ballard, D.H., Jelinet, C. A., and Schinzinger, R., An Algorithm for the Solution of Constrained Generalized Polynomial Programming Problems, The Computer Journal: Vol. 17, Number 3, pp. 261-266, 1974.

[2]  Bartholomew-Biggs, M. C., A Numerical Comparison between Two Approaches to the Nonlinear Programming Problem, Toward Global Optimization 2, Edited by L. C. W. Dixon and G. P. Szego, North-Hollad Publishing Company, Amsterdam, Holland, pp. 293-312, 1978.

[3]  Hock, W., and K. Schittkowski, 1981.  Test Examples for Nonlinear Programming Codes.  Lecture Notes in Economics and Mathematical Systems, No. 187.  Springer-Verlag, New York.

[4]  Price, W. L., Global Optimization by Controlled Random Search, Journal of Optimization Theory and Applications: Vol. 40, No. 3, July 1983.

[5]  Schinzinger, R. (1965).  Optimization in Electromagnetic System Design, in Recent Advances in Optimization Techniques, edited by A. Lavi and T. P. Vogl, New York: Wiley, pp. 163-213.

[6]  Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.

Testing a Nonlinear Integer/Discrete/Continuous Programming Solver with a Transformer Design Model Involving Continuous Variables, Second Edition

Jsun Yui Wong

The following computer program tries to solve a problem considered by Ballard, Jelinek, and Schinzinger [1, p. 265], by Bartholomew-Biggs [2, p. 307], Hock and Schittkowski [3, p. 108], and by Price [4, p. 340].  For more details, see Schinzinger [5], page 192 and page 193 in particular.

Firstly, from among the given inequality constraints one chooses an inequality constraint that will be changed to an equality constraint.  For example, that leads to line 231 of the following computer program.  In general, the worst case scenario is that one may have to choose each inequality constraint, one at a time.

While line 128 of the preceding post is 128 FOR I=1 TO 3270, line 128 of the present post is 128 FOR I=1 TO 500.

This post is similar to the October 23 post with the title "A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a Transformer Design Model with Integer Variables and Continuous Variables" of the present blog.

0 REM    DEFINT A-Z
1 REM    DEFSNG L,S,P,M,R,Q
2 DEFSNG A-Z
3 DEFINT I,J,K
4 DIM X(42),A(42),L(33),K(33)
75 FOR JJJJ=-32000 TO 32000
84 RANDOMIZE JJJJ
87 M=-1.7E+38
91 FOR KK=1 TO 6
94 A(KK)=RND*30
95 NEXT KK
126 REM   IMAR=10+FIX(RND*32700)
128 FOR I=1 TO 500
129 FOR K=1 TO 6
131 X(K)=A(K)
132 NEXT K
181 J=1+FIX(RND*6)
183 R=(1-RND*2)*A(J)
191 IF RND<.14 THEN X(J)=A(J)+RND^5*R ELSE IF RND<.17 THEN X(J)=A(J)+R ELSE IF RND<.2 THEN X(J)=A(J)+RND*R ELSE IF RND<.25 THEN X(J)=A(J)+RND^2*R ELSE IF RND<.33 THEN X(J)=A(J)+RND^3*R ELSE IF RND<.5 THEN X(J)=A(J)+RND^4*R ELSE X(J)=A(J)+RND^6*R
222 XUP=1-.00058*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))
226 XDO=.00062*X(1)*X(4)*(X(1)+X(2)+X(3))
227 IF XUP<.00001 THEN 1670
228 IF XDO<.00001 THEN 1670
231 X(5)=(      XUP/XDO       )^.5
351 L1=-.001*X(1)*X(2)*X(3)*X(4)*X(5)*X(6)+2.07
352 REM  L2=.00062*X(1)*X(4)*X(5)^2*(X(1)+X(2)+X(3))+.00058*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))-1.2
511 IF L1>0 THEN L1=-1000000! ELSE L1=0
512 REM     IF L2>0 THEN L2=-1000000! ELSE L2=0
1311     SS=L1
1333 P1NEWMAY=-.0204*X(1)*X(4)*(X(1)+X(2)+X(3))-.0187*X(2)*X(3)*(X(1)+1.57*X(2)+X(4))-.0607*X(1)*X(4)*X(5)^2*(X(1)+X(2)+X(3))-.0437*X(2)*X(3)*X(6)^2*(X(1)+1.57*X(2)+X(4))+SS
1448 P=P1NEWMAY
1451 IF P<=M THEN 1670
1657 FOR KEW=1 TO 6
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1666 GOTO 128
1670 NEXT I
1890 IF M>-135.4 THEN 1912 ELSE 1999
1912 PRINT A(1),A(2),A(3),A(4),A(5),A(6),M,JJJJ
1917 REM   PRINT M,JJJJ
1999 NEXT JJJJ

The BASIC computer program above was run with Microsoft's GW BASIC 3.11 interpreter, which is not a compiler.  The complete printout is shown below.  What immediately follows is a manual copy from the computer screen.

5.305737   4.676226   11.40576   11.08196   .7803025
.8459121   -135.3753   -1331

5.05612   4.526118   10.89219   12.65925   .7500547
.8746034   -135.2733   4088

Interpreted in accordance with line 1912, the solution at JJJJ=4088 is the better between the two candidate solutions shown above.  One notes that 135.2733 presented  above to 135.075961 of Bartholomew-Biggs as presented in Hock and Schittkowski [3] is 1.001460948 to 1.  This complete run through JJJJ=32000 took forty-five minutes on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter. 

References

[1]  Ballard, D.H., Jelinet, C. A., and Schinzinger, R., An Algorithm for the Solution of Constrained Generalized Polynomial Programming Problems, The Computer Journal: Vol. 17, Number 3, pp. 261-266, 1974.

[2]  Bartholomew-Biggs, M. C., A Numerical Comparison between Two Approaches to the Nonlinear Programming Problem, Toward Global Optimization 2, Edited by L. C. W. Dixon and G. P. Szego, North-Hollad Publishing Company, Amsterdam, Holland, pp. 293-312, 1978.

[3]  Hock, W., and K. Schittkowski, 1981.  Test Examples for Nonlinear Programming Codes.  Lecture Notes in Economics and Mathematical Systems, No. 187.  Springer-Verlag, New York.

[4]  Price, W. L., Global Optimization by Controlled Random Search, Journal of Optimization Theory and Applications: Vol. 40, No. 3, July 1983.

[5]  Schinzinger, R. (1965).  Optimization in Electromagnetic System Design, in Recent Advances in Optimization Techniques, edited by A. Lavi and T. P. Vogl, New York: Wiley, pp. 163-213.

[6]  Microsoft Corp. BASIC, second edition (May 1982), Version 1.10. Boca Raton, Florida: IBM Corp., Personal Computer, P. O. Box 1328-C, Boca Raton, Florida 33432, 1981.