The computer program listed below seeks to solve the following problem based on/modified from Example 5 on page 50 of Tsai and Lin [24].
Minimize X(1) ^ 2 * X(2) ^ .816 * X(3) ^ 1.2 - X(1) ^ .8 - X(2) ^ .5 - X(3) ^ 1.2
subject to
X(1) ^ .8 + X(2) ^ .9 + X(3) ^ .5>=16
X(1) ^ -1.5 + X(2) ^ 1.7+ X(3) ^ 1.2<=500
where X(1), X(2), X(3) Epsilon { 1.1, 1.2, 1.3,..., 52.0}.
X(1), X(2), and X(3) are discrete variables.
The added variables X(4) and X(5) below are slack variables. One takes note of line 330, which is 330 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0.
0 DEFDBL A-Z
2 DEFINT K
3 DIM B(99), N(99), A(99), H(99), L(99), U(99), X(1111), D(111), P(111), PS(33)
12 FOR JJJJ = -32000 TO 32000 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
71 FOR J44 = 1 TO 3
75 A(J44) = 1.1 + (INT(RND * 510)) * .1
79 NEXT J44
128 FOR I = 1 TO 50
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 2))
181 J = 1 + FIX(RND * 3)
182 X(J) = 1.1 + (INT(RND * 510)) * .1
183 REM r = (1 - RND * 2) * A(J)
187 REM X(J) = A(J) + (RND ^ (RND * 10)) * r
191 NEXT IPP
211 IF X(1) < 1.1 THEN 1670
212 IF X(1) > 52 THEN 1670
213 IF X(2) < 1.1 THEN 1670
214 IF X(2) > 52 THEN 1670
215 IF X(3) < 1.1 THEN 1670
216 IF X(3) > 52 THEN 1670
301 X(4) = -16 + X(1) ^ .8 + X(2) ^ .9 + X(3) ^ .5
303 X(5) = 500 - X(1) ^ -1.5 - X(2) ^ 1.7 - X(3) ^ 1.2
325 FOR J99 = 4 TO 5
330 IF X(J99) < 0 THEN X(J99) = X(J99) ELSE X(J99) = 0
331 NEXT J99
357 POBA = -X(1) ^ 2 * X(2) ^ .816 * X(3) ^ 1.2 + X(1) ^ .8 + X(2) ^ .5 + X(3) ^ 1.2 + 1000000 * (X(4) + X(5))
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 5
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -8.33 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4)
1901 PRINT A(5), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [25]. The complete output through JJJJ =-31974.60000000407
is shown below:
1.1 18.6 1.1 0
0 -8.222813024242807 -31988.67000000181
1.1 18.6 1.1 0
0 -8.222813024242807 -31981.340000003
1.1 18.7 1.1 0
0 -8.275851373759423 -31974.60000000407
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 [25], the wall-clock time for obtaining the output through JJJJ=-31974.60000000407 was 10 seconds--most of these seconds were for creating the .EXE file.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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