Jsun Yui Wong

The computer program listed below seeks to solve the following integer nonlinear programming example in Luus [55], in Pant, Anand, Kishor, and Singh [71, p. 37, Table 2], and in Tambunan and Mauengkang [85, p. 5276]:

Minimize

(1 - .1 ^ X(1)) * (1 - .25 ^ X(2)) * (1 - .35 ^ X(3)) * (1 - .2 ^ X(4)) * (1 - .15 ^ X(5)) * (1 - .07 ^ X(6)) * (1 - .22 ^ X(7)) * (1 - .34 ^ X(8)) * (1 - .22 ^ X(9)) * (1 - .09 ^ X(10)) * (1 - .21 ^ X(11)) * (1 - .23 ^ X(12)) * (1 - .33 ^ X(13)) * (1 - .21 ^ X(14)) * (1 - .33 ^ X(15))

subject to

5 * X(1) + 4 * X(2) + 9 * X(3) + 7 * X(4) + 7 * X(5) + 5 * X(6) + 6 * X(7) + 9 * X(8) + 4 * X(9) + 5 * X(10) + 6 * X(11) + 7 * X(12) + 9 * X(13) + 8 * X(14) + 6 * X(15) <= 400

8 * X(1) + 9 * X(2) + 6 * X(3) + 7 * X(4) + 8 * X(5) + 8 * X(6) + 9 * X(7) + 6 * X(8) + 7 * X(9) + 8 * X(10) + 9 * X(11) + 7 * X(12) + 6 * X(13) + 5 * X(14) + 7 * X(15) <= 414.

One notes line 172, which is 172 IF X(J44) > 12 THEN 1670.

0 DEFDBL A-Z

1 REM DEFINT K

2 DIM N(99), A(45222), X(45012), D(111), P(111), PS(33), J44(45202), J(45211), AA(99), STIO(45303)

81 FOR JJJJ = -32000 TO 32000

85 RANDOMIZE JJJJ

87 M = -4E+250

121 FOR J44 = 1 TO 15

123 A(J44) = 1 + FIX(RND * 2)

124 NEXT J44

128 FOR I = 0 TO FIX(RND * 8000)

129 FOR KKQQ = 1 TO 15

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

135 FOR IPP = 1 TO FIX(1 + RND * 3.3)

143 j = 1 + FIX(RND * 15)

145 GOTO 162

154 IF j < 2.5 THEN GOTO 156 ELSE GOTO 162

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

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

161 GOTO 169

162 IF RND < .5 THEN X(j) = A(j) - FIX(1 + RND * 3.3) ELSE X(j) = A(j) + FIX(1 + RND * 3.3)

163 REM IF RND < .33 THEN X(j) = -1## ELSE IF RND < .5 THEN X(j) = 0## ELSE X(j) = 1##

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

169 NEXT IPP

171 FOR J44 = 1 TO 15

172 IF X(J44) > 12 THEN 1670

173 IF X(J44) < 1 THEN 1670

174 X(J44) = INT(X(J44))

175 NEXT J44

295 IF 8 * X(1) + 9 * X(2) + 6 * X(3) + 7 * X(4) + 8 * X(5) + 8 * X(6) + 9 * X(7) + 6 * X(8) + 7 * X(9) + 8 * X(10) + 9 * X(11) + 7 * X(12) + 6 * X(13) + 5 * X(14) + 7 * X(15) > 414 THEN 1670

296 IF 5 * X(1) + 4 * X(2) + 9 * X(3) + 7 * X(4) + 7 * X(5) + 5 * X(6) + 6 * X(7) + 9 * X(8) + 4 * X(9) + 5 * X(10) + 6 * X(11) + 7 * X(12) + 9 * X(13) + 8 * X(14) + 6 * X(15) > 400 THEN 1670

1107 P = (1 - .1 ^ X(1)) * (1 - .25 ^ X(2)) * (1 - .35 ^ X(3)) * (1 - .2 ^ X(4)) * (1 - .15 ^ X(5)) * (1 - .07 ^ X(6)) * (1 - .22 ^ X(7)) * (1 - .34 ^ X(8)) * (1 - .22 ^ X(9)) * (1 - .09 ^ X(10)) * (1 - .21 ^ X(11)) * (1 - .23 ^ X(12)) * (1 - .33 ^ X(13)) * (1 - .21 ^ X(14)) * (1 - .33 ^ X(15))

1111 IF P <= M THEN 1670

1420 M = P

1444 FOR KLX = 1 TO 15

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1557 GOTO 128

1670 NEXT I

1677 IF M < .94561 THEN 1999

1931 PRINT A(1), A(2), A(3), A(4), A(5), A(6)

1933 PRINT A(7), A(8), A(9), A(10), A(11), A(12), A(13), A(14), A(15), M, JJJJ

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [94]. The complete output of a single run through JJJJ= -31962 is shown below:**3 4 6 4 3****2****4 5 4 2 3****4 5 4 5 .9456133574581372****-31996**

3 4 6 4 3

2

4 5 4 2 3

4 5 4 5 .9456133574581372

-31988

3 4 6 4 3

2

4 5 4 2 3

4 5 4 5 .9456133574581372

-31980

3 4 6 4 3

2

4 5 4 2 3

4 5 4 5 .9456133574581372

-31962

.

.

.

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 [94], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31962 was 3 seconds, not including the time for “Creating .EXE file” (22 seconds, total, including the time for “Creating .EXE file”). One can compare the computational results above with those in Tambunan and Mawengkang [85, p. 5277, Table 1] and in Pant, Anand, Kishor, Singh [71, p. 40, Table 7], where one can see ( 3 4 6 4 3 2 4 5 4 2 3 4 5 4 5 ) and .945613. **Acknowledgment**

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

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