Jsun Yui Wong

The following correct information is about the computer used for the last three papers (posts):

Memory: 4.00 GB

Processor: Intel(R) Core(TM) i5 CPU M 430 @ 2.27 GHz.

« December 2019 | Main | February 2020 »

Jsun Yui Wong

The following correct information is about the computer used for the last three papers (posts):

Memory: 4.00 GB

Processor: Intel(R) Core(TM) i5 CPU M 430 @ 2.27 GHz.

Posted at 04:39 AM | Permalink | Comments (0)

Jsun Yui Wong

The computer program listed below seeks to solve the following mathematical formulation from Ghufran, Khowaja, and Ahsan [32, p. 143, the last formulation]:

Minimize

1377.5081 / X(1) + 2449.5358 / X(2) + 740.9373 / X(3) + 35.7884 / X(4) + 56.2973 / X(5)

subject to

X(1) + X(2) + 1.5 * X(3) + 1.5 * X(4) + 2 * X(5) + .5 * X(1) ^ .5 + .5 * X(2) ^ .5 + X(3) ^ .5 + X(4) ^ .5 + 1.5 * X(5) ^ .5 + 300 + 2.33 * (.25 * X(1) ^ 2 + .25 * X(2) ^ 2 + .35 * X(3) ^ 2 + .35 * X(4) ^ 2 + .45 * X(5) ^ 2 + .125 * X(1) + .125 * X(2) + .175 * X(3) + .175 * X(4) + .225 * X(5)) ^ .5 <=1500

2<= X(1) <= 1500

2<= X(2) <= 1920

2<= X(3) <= 1260

2<= X(4) <= 480

2<= X(5) <= 840

where X(1) through X(5) are integer variables.

0 DEFDBL A-Z

1 DEFINT K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)

81 FOR JJJJ = -32000 TO 32000

85 RANDOMIZE JJJJ

86 M = -3E+50

118 FOR J44 = 1 TO 5

119 A(J44) = 2 + (RND * 8)

120 NEXT J44

123 A(9) = RND

128 FOR I = 1 TO 90000

129 FOR KKQQ = 1 TO 5

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

151 FOR IPP = 1 TO FIX(1 + RND * 5)

153 J = 1 + FIX(RND * 5)

154 REM IF J > 8.5 THEN GOTO 156 ELSE GOTO 163

155 GOTO 162

156 r = (1 - RND * 2) * A(J)

158 X(J) = A(J) + (RND ^ (RND * 15)) * r

161 GOTO 169

162 REM IF RND < .5 THEN X(J) = A(J) - INT(RND * 15) ELSE X(J) = A(J) + INT(RND * 15)

163 IF RND < .5 THEN X(J) = A(J) - INT(RND * 5) ELSE X(J) = A(J) + INT(RND * 5)

164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0

169 NEXT IPP

215 FOR J44 = 1 TO 5

216 X(J44) = INT(X(J44))

218 IF X(J44) < 2 THEN 1670

219 NEXT J44

225 IF X(1) > 1500 THEN 1670

226 IF X(2) > 1920 THEN 1670

227 IF X(3) > 1260 THEN 1670

228 IF X(4) > 480 THEN 1670

230 IF X(5) > 840 THEN 1670

297 IF X(1) + X(2) + 1.5 * X(3) + 1.5 * X(4) + 2 * X(5) + .5 * X(1) ^ .5 + .5 * X(2) ^ .5 + X(3) ^ .5 + X(4) ^ .5 + 1.5 * X(5) ^ .5 + 300 + 2.33 * (.25 * X(1) ^ 2 + .25 * X(2) ^ 2 + .35 * X(3) ^ 2 + .35 * X(4) ^ 2 + .45 * X(5) ^ 2 + .125 * X(1) + .125 * X(2) + .175 * X(3) + .175 * X(4) + .225 * X(5)) ^ .5 > 1500 THEN 1670

326 FOR J44 = 1 TO 5

328 IF X(J44) < 2 THEN 1670

330 NEXT J44

1107 P = -1377.5081 / X(1) - 2449.5358 / X(2) - 740.9373 / X(3) - 35.7884 / X(4) - 56.2973 / X(5)

1111 IF P <= M THEN 1670

1450 M = P

1454 FOR KLX = 1 TO 5

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1536 dol = X(1) + X(2) + 1.5 * X(3) + 1.5 * X(4) + 2 * X(5) + .5 * X(1) ^ .5 + .5 * X(2) ^ .5 + X(3) ^ .5 + X(4) ^ .5 + 1.5 * X(5) ^ .5 + 300 + 2.33 * (.25 * X(1) ^ 2 + .25 * X(2) ^ 2 + .35 * X(3) ^ 2 + .35 * X(4) ^ 2 + .45 * X(5) ^ 2 + .125 * X(1) + .125 * X(2) + .175 * X(3) + .175 * X(4) + .225 * X(5)) ^ .5

1557 GOTO 128

1670 NEXT I

1889 REM

1933 PRINT A(1), A(2), A(3), A(4), A(5)

1936 PRINT M, JJJJ, dol

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [98]. The complete output of a single run through JJJJ= -31997 is shown below:**195 247 127 31 34****-25.6257125162278 -32000 1499.976988661132**

195 247 127 31 34

-25.6257125162278 -31999 1499.976988661132

195 247 127 31 34

-25.6257125162278 -31998 1499.976988661132

194 248 128 31 33

-25.62673366062364 -31997 1499.952155282742

.

.

.

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and QB64v1000-win [98], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31997 was 5 seconds, not including the time for “Creating .EXE file.” One can compare the computational results above with those in Ghufran, Khowaja, and Ahsan [32, pp. 143-144].

**Acknowledgment**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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Posted at 08:14 AM | Permalink | Comments (0)

Jsun Yui Wong

The computer program listed below seeks to solve the following mixed-integer nonlinear programming problem:

Minimize

X(9) + 746.921876 / X(1) + 329.7093584 / X(2) + 97.34568757 / X(3) + 270.4706345 / X(4) + 18.16836996 / X(5) + 3.470624826 / X(6) + 1.622428126 / X(7) + 5.700241329 / X(8)

subject to

- X(9) -(-443.0974013 / X(1) - 270.715638 / X(2) - 204.9419482 / X(3) - 240.6056485 / X(4) -10.7780449 / X(5) - 2.849638294 / X(6) - 3.415699137 / X(7) - 5.070828722 / X(8)) <= 4.121941

2.4 * X(1) + 3.4 * X(2) + 4 * X(3) + 4.6 * X(4) + 3 * X(5) + 4 * X(6) + 5 * X(7) + 6 * X(8) <= 5000

2<= X(1) <= 1214

2<= X(2) <= 822

2<= X(3) <= 1028

2<= X(4) <= 786

2<= X(5) <= 150

2<= X(6) <= 150

2<= X(7) <= 150

2<= X(8) <= 150

X(9)>=0

where X(1) through X(8) are integer variables and X(9) is a continuous variable.

The problem above is based on the second formulation of Example 1 in Varshney, Ahsan, and Khan [91, p. 399].

One notes line 243, which is 243 X(9) = -(-443.0974013 / X(1) - 270.715638 / X(2) - 204.9419482 / X(3) - 240.6056485 / X(4) - 10.7780449 / X(5) - 2.849638294 / X(6) - 3.415699137 / X(7) - 5.070828722 / X(8)) - 4.121941 from the first long inequality constraint above. That is a search for active constraint/s aiming towards optimality; please see Bernau [11].

0 DEFDBL A-Z

1 DEFINT K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)

81 FOR JJJJ = -32000 TO 32000

85 RANDOMIZE JJJJ

86 M = -3E+50

118 FOR J44 = 1 TO 8

119 A(J44) = 2 + (RND * 8)

120 NEXT J44

123 A(9) = RND

128 FOR I = 1 TO 90000

129 FOR KKQQ = 1 TO 9

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

151 FOR IPP = 1 TO FIX(1 + RND * 5)

153 J = 1 + FIX(RND * 9)

154 IF J > 8.5 THEN GOTO 156 ELSE GOTO 163

155 GOTO 162

156 r = (1 - RND * 2) * A(J)

158 X(J) = A(J) + (RND ^ (RND * 15)) * r

161 GOTO 169

162 REM IF RND < .5 THEN X(J) = A(J) - INT(RND * 15) ELSE X(J) = A(J) + INT(RND * 15)

163 IF RND < .5 THEN X(J) = A(J) - INT(RND * 5) ELSE X(J) = A(J) + INT(RND * 5)

164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0

169 NEXT IPP

215 FOR J44 = 1 TO 8

216 X(J44) = INT(X(J44))

218 IF X(J44) < 2 THEN 1670

219 NEXT J44

225 IF X(1) > 1214 THEN 1670

226 IF X(2) > 822 THEN 1670

227 IF X(3) > 1028 THEN 1670

228 IF X(4) > 786 THEN 1670

230 IF X(5) > 150 THEN 1670

233 IF X(6) > 150 THEN 1670

234 IF X(7) > 150 THEN 1670

235 IF X(8) > 150 THEN 1670

243 X(9) = -(-443.0974013 / X(1) - 270.715638 / X(2) - 204.9419482 / X(3) - 240.6056485 / X(4) - 10.7780449 / X(5) - 2.849638294 / X(6) - 3.415699137 / X(7) - 5.070828722 / X(8)) - 4.121941

245 IF X(9) < 0## THEN 1670

297 IF 2.4 * X(1) + 3.4 * X(2) + 4 * X(3) + 4.6 * X(4) + 3 * X(5) + 4 * X(6) + 5 * X(7) + 6 * X(8) > 5000 THEN 1670

326 FOR J44 = 1 TO 8

328 IF X(J44) < 2 THEN 1670

330 NEXT J44

1105 P = -X(9) - 746.921876 / X(1) - 329.7093584 / X(2) - 97.34568757 / X(3) - 270.4706345 / X(4) - 18.16836996 / X(5) - 3.470624826 / X(6) - 1.622428126 / X(7) - 5.700241329 / X(8)

1111 IF P <= M THEN 1670

1450 M = P

1454 FOR KLX = 1 TO 9

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1535 dol = 2.4 * X(1) + 3.4 * X(2) + 4 * X(3) + 4.6 * X(4) + 3 * X(5) + 4 * X(6) + 5 * X(7) + 6 * X(8)

1557 GOTO 128

1670 NEXT I

1889 IF M < -4.6385 THEN 1999

1933 PRINT A(1), A(2), A(3), A(4), A(5)

1936 PRINT A(6), A(7), A(8), A(9), M, JJJJ, dol

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [96]. The complete output of a single run through JJJJ= -31979 is shown below:

534 317 208 251 74

30 24 32 .0471294257120855

-4.638472226772392 -32000 5000

534 317 208 251 74

30 24 32 .0471294257120855

-4.638472226772392 -31993 5000

534 317 208 251 74

30 24 32 .0471294257120855

-4.638472226772392 -31979 5000

.

.

.

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and QB64v1000-win [96], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31979 was 15 seconds, not including the time for “Creating .EXE file.” One can compare the computational results above with those in Varshney, Ahsan, and Khan [91, p. 400], where one can see the following numbers: 534, 317, 208, 251, 74, 30, 24, 32, 0.04712943, 5000.

**Acknowledgment**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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The two computer programs listed below seek to solve the two formulations in Khan, Maiti, and Ahsan [49, p. 705].

1. Example 1 in Khan, Maiti, and Ahsan [49]

Minimize

.5 * X(5) + .5 * X(6)

subject to

-(-14566711.59 / X(1) - 221179342.00 / X(2) - 607364036.51 / X(3) - 88587552.79 / X(4)) -X(5) <= 96754589.11

-(-1580.89 / X(1) - 123578.82 / X(2) - 190094.68 / X(3) - 4727.52 / X(4)) - x(6)<=27061.62

15 * X(1) + 7 * X(2) + 5 * X(3) + 9 * X(4) <= 200

2<=X(1)<=8

2<=X(2)<=34

2<=X(3)<=45

2<=X(4)<=12

X(5)>=0

X(6)>=0

where X(1) through X(4) are integer variables, and X(5) and X(6) are continuous variables.

One notes and line 243 line 244, which are 243 X(5) = -(-14566711.59 / X(1) - 221179342.00 / X(2) - 607364036.51 / X(3) - 88587552.79 / X(4)) - 96754589.11 and 244 X(6) = -(-1580.89 / X(1) - 123578.82 / X(2) - 190094.68 / X(3) - 4727.52 / X(4)) - 27061.62 from the long inequality constraints above. That is a search for active constraint/s aiming towards optimality; please see Bernau [11].

0 DEFDBL A-Z

1 DEFINT K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)

81 FOR JJJJ = -32000 TO 32000

85 RANDOMIZE JJJJ

86 M = -3E+50

118 FOR J44 = 1 TO 4

119 A(J44) = 2 + (RND * 5)

120 NEXT J44

123 A(5) = RND * 1000

125 A(6) = RND * 10

128 FOR I = 1 TO 9000

129 FOR KKQQ = 1 TO 6

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

151 FOR IPP = 1 TO FIX(1 + RND * 5)

153 J = 1 + FIX(RND * 6)

154 IF J < 4.5 THEN GOTO 163 ELSE GOTO 156

155 REM GOTO 162

156 r = (1 - RND * 2) * A(J)

158 X(J) = A(J) + (RND ^ (RND * 15)) * r

161 GOTO 169

162 REM IF RND < .5 THEN X(J) = A(J) - INT(RND * 15) ELSE X(J) = A(J) + INT(RND * 15)

163 IF RND < .5 THEN X(J) = A(J) - INT(RND * 5) ELSE X(J) = A(J) + INT(RND * 5)

164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0

169 NEXT IPP

215 FOR J44 = 1 TO 4

216 X(J44) = INT(X(J44))

217 REM X(4) = INT(X(4))

218 IF X(J44) < 2 THEN 1670

219 NEXT J44

222 REM IF X(9) < 0## THEN 1670

225 IF X(1) > 8 THEN 1670

226 IF X(2) > 34 THEN 1670

227 IF X(3) > 45 THEN 1670

228 IF X(4) > 12 THEN 1670

229 IF X(5) < 0## THEN 1670

230 IF X(6) < 0## THEN 1670

243 X(5) = -(-14566711.59 / X(1) - 221179342.00 / X(2) - 607364036.51 / X(3) - 88587552.79 / X(4)) - 96754589.11

244 X(6) = -(-1580.89 / X(1) - 123578.82 / X(2) - 190094.68 / X(3) - 4727.52 / X(4)) - 27061.62

245 IF X(5) < 0## THEN 1670

246 IF X(6) < 0## THEN 1670

297 IF 15 * X(1) + 7 * X(2) + 5 * X(3) + 9 * X(4) > 200 THEN 1670

1108 P = -.5 * X(5) - .5 * X(6)

1111 IF P <= M THEN 1670

1450 M = P

1454 FOR KLX = 1 TO 6

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1533 dol = 15 * X(1) + 7 * X(2) + 5 * X(3) + 9 * X(4)

1557 GOTO 128

1670 NEXT I

1889 IF M < -999999999 THEN 1999

1933 PRINT A(1), A(2), A(3), A(4)

1936 PRINT A(5), A(6), M, JJJJ, dol

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [95]. The complete output of a single run through JJJJ= -31996 is shown below:

**2 7 17 4****4.936974495649338D-03 3746.862142857145 -1873.43353991582****-32000 200**

2 7 17 4

4.936974495649338D-03 3746.862142857145 -1873.43353991582

-31999 200

2 7 17 4

4.936974495649338D-03 3746.862142857145 -1873.43353991582

-31998 200

2 7 17 4

4.936974495649338D-03 3746.862142857145 -1873.43353991582

-31997 200

2 7 17 4

4.936974495649338D-03 3746.862142857145 -1873.43353991582

-31996 200

.

.

.

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and QB64v1000-win [95], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31996 was 3 seconds, not including the time for “Creating .EXE file.” One can compare the computational results above with those in Khan, Maiti, and Ahsan [49, p. 704, Table 3], where one can see the following numbers: 2, 7, 17, 4, 200.

2. Example 2 in Khan, Maiti, and Ahsan [49]

Only the four different measurement costs in Example 1 are changed to 7.5; please see the following line 297 and line 1533.

0 DEFDBL A-Z

1 DEFINT K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)

81 FOR JJJJ = -32000 TO 32000

85 RANDOMIZE JJJJ

86 M = -3E+50

118 FOR J44 = 1 TO 4

119 A(J44) = 2 + (RND * 5)

120 NEXT J44

123 A(5) = RND * 1000

125 A(6) = RND * 10

128 FOR I = 1 TO 9000

129 FOR KKQQ = 1 TO 6

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

151 FOR IPP = 1 TO FIX(1 + RND * 5)

153 J = 1 + FIX(RND * 6)

154 IF J < 4.5 THEN GOTO 163 ELSE GOTO 156

155 REM GOTO 162

156 r = (1 - RND * 2) * A(J)

158 X(J) = A(J) + (RND ^ (RND * 15)) * r

161 GOTO 169

163 IF RND < .5 THEN X(J) = A(J) - INT(RND * 5) ELSE X(J) = A(J) + INT(RND * 5)

164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0

169 NEXT IPP

215 FOR J44 = 1 TO 4

216 X(J44) = INT(X(J44))

217 REM X(4) = INT(X(4))

218 IF X(J44) < 2 THEN 1670

219 NEXT J44

222 REM IF X(9) < 0## THEN 1670

225 IF X(1) > 8 THEN 1670

226 IF X(2) > 34 THEN 1670

227 IF X(3) > 45 THEN 1670

228 IF X(4) > 12 THEN 1670

229 IF X(5) < 0## THEN 1670

230 IF X(6) < 0## THEN 1670

243 X(5) = -(-14566711.59 / X(1) - 221179342.00 / X(2) - 607364036.51 / X(3) - 88587552.79 / X(4)) - 96754589.11

244 X(6) = -(-1580.89 / X(1) - 123578.82 / X(2) - 190094.68 / X(3) - 4727.52 / X(4)) - 27061.62

245 IF X(5) < 0## THEN 1670

246 IF X(6) < 0## THEN 1670

297 IF 7.5 *( X(1) + X(2) + X(3) + X(4) ) > 200 THEN 1670

1108 P = -.5 * X(5) - .5 * X(6)

1111 IF P <= M THEN 1670

1450 M = P

1454 FOR KLX = 1 TO 6

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1533 dol = 7.5 *( X(1) + X(2) + X(3) + X(4) )

1557 GOTO 128

1670 NEXT I

1889 IF M < -999999999 THEN 1999

1933 PRINT A(1), A(2), A(3), A(4)

1936 PRINT A(5), A(6), M, JJJJ, dol

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [95]. The complete output of a single run through JJJJ= -31996 is shown below:

**2 7 12 5****10456995.80930953 8169.669476190476 -5232582.739392861****-32000 195**

2 7 12 5

10456995.80930953 8169.669476190476 -5232582.739392861

-31999 195

2 7 12 5

10456995.80930953 8169.669476190476 -5232582.739392861

-31998 195

2 7 12 5

10456995.80930953 8169.669476190476 -5232582.739392861

-31997 195

2 7 12 5

10456995.80930953 8169.669476190476 -5232582.739392861

-31996 195

.

.

.

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and QB64v1000-win [95], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31996 was 3 seconds, not including the time for “Creating .EXE file.” One can compare the computational results above with those in Khan, Maiti, and Ahsan [49, p. 706, Table 4], where one can see the following numbers: 2, 7, 12, 5, 195.

**Acknowledgment**

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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