Jsun Yui Wong
The computer program listed below seeks to solve the following problem from Varshney, Najmussehar, and Ahsan [88, p. 1003]:
Minimize
X(1) + X(2)
subject to
54.81089 / X(3) + 29.74633 / X(4) + 28.93946 / X(5) + 33.67489 / X(6) - X(1) <= 7.138824
73.45820 / X(3) + 33.47274 / X(4) + 15.13047 / X(5) + 43.04568 / X(6) - X(2) <= 7.486473
3 * X(3) + 4 * X(4) + 5 * X(5) + 6 * X(6) <= 350
X(1) >= 0
X(2) >= 0
2<= X(3) <= 73
2<= X(4) <= 28
2<= X(5) <= 23
2<= X(6) <= 29
X(3) through X(6) are integer variables.
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 6
123 A(J44) = RND * 20
126 NEXT J44
128 FOR I = 0 TO FIX(RND * 10000)
129 FOR KKQQ = 1 TO 6
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 2.3)
143 j = 1 + FIX(RND * 6)
145 REM 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 * 1.3) ELSE X(j) = A(j) + FIX(1 + RND * 1.3)
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 = 3 TO 6
173 IF X(J44) < 2 THEN 1670
174 X(J44) = INT(X(J44))
175 NEXT J44
179 IF X(3) > 73 THEN 1670
184 IF X(4) > 28 THEN 1670
188 IF X(5) > 23 THEN 1670
189 IF X(6) > 29 THEN 1670
190 IF X(1) <0 THEN 1670
191 IF X(2) <0 THEN 1670
192 IF 54.81089 / X(3) + 29.74633 / X(4) + 28.93946 / X(5) + 33.67489 / X(6) - X(1) > 7.138824 THEN 1670
194 IF 73.45820 / X(3) + 33.47274 / X(4) + 15.13047 / X(5) + 43.04568 / X(6) - X(2) > 7.486473 THEN 1670
196 IF 3 * X(3) + 4 * X(4) + 5 * X(5) + 6 * X(6) > 350 THEN 1670
999 P = -X(1) - X(2)
1111 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 6
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -.121 THEN 1999
1931 PRINT A(1), A(2), A(3), A(4), A(5), A(6), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [93]. The complete output of a single run through JJJJ= -31862 is shown below:
7.754391177101408D-02 4.299311091301682D-02 32
19 14 18 -.120537022684031
-31862
.
.
.
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 [93], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31862 was 3 seconds, not including the time for “Creating .EXE file” (20 seconds, total, including the time for “Creating .EXE file”). One can compare the computational results above with those in Varshney, Najmussehar, and Ahsan [88, p. 1003].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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