Jsun Yui Wong
The computer program listed below seeks to solve the following problem from page 711 of Li and Lu [9, Program 8].
Minimize X(1) ^ 2 * X(2) ^ .816 - 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<=31,
where
X(1) Epsilon { 1.1, 3.2, 5.3, 7.4, 9.5, 12.6, 14.7, 16.8},
X(2), X(3) Epsilon { 1.1, 1.2, 1.3, 1.4, 1.5, 2.0, 2.6, 2.7, 2.8, 2.9, 3.1, 3.2, 3.3, 3.4, 3.5, 4.0, 4.6, 4.7, 4.8, 4.9,
.
.
.
23.1, 23.2, 23.3, 23.4, 23.5, 24.0, 24.6, 24.7, 24.8, 24.9, 25.1, 25.2, 25.3, 25.4, 25.5, 26.0, 26.6, 26.7}.
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
51 IF RND < .125 THEN A(1) = 1.1 ELSE IF RND < .143 THEN A(1) = 3.2 ELSE IF RND < .167 THEN A(1) = 5.3 ELSE IF RND < .2 THEN A(1) = 7.4 ELSE IF RND < .25 THEN A(1) = 9.5 ELSE IF RND < .333 THEN A(1) = 12.6 ELSE IF RND < .5 THEN A(1) = 14.7 ELSE A(1) = 16.8
71 FOR J44 = 2 TO 3
73 J99 = 2 * INT(RND * 12)
89 IF RND < .1 THEN A(J44) = 1.1 + J99 ELSE IF RND < .111 THEN A(J44) = 1.2 + J99 ELSE IF RND < .125 THEN A(J44) = 1.3 + J99 ELSE IF RND < .143 THEN A(J44) = 1.4 + J99 ELSE IF RND < .167 THEN A(J44) = 1.5 + J99 ELSE IF RND < .2 THEN A(J44) = 2.0 + J99 ELSE IF RND < .25 THEN A(J44) = 2.6 + J99 ELSE IF RND < .333 THEN A(J44) = 2.7 + J99 ELSE IF RND < .5 THEN A(J) = 2.8 + J99 ELSE A(J) = 2.9 + J99
99 NEXT J44
128 FOR I = 1 TO 20000
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 1))
151 J99 = 2 * INT(RND * 12)
161 J = 2 + FIX(RND * 2)
169 IF RND < .1 THEN X(J) = 1.1 + J99 ELSE IF RND < .111 THEN X(J) = 1.2 + J99 ELSE IF RND < .125 THEN X(J) = 1.3 + J99 ELSE IF RND < .143 + J99 THEN X(J) = 1.4 + J99 ELSE IF RND < .167 THEN X(J) = 1.5 + J99 ELSE IF RND < .2 THEN X(J) = 2.0 + J99 ELSE IF RND < .25 THEN X(J) = 2.6 + J99 ELSE IF RND < .333 THEN X(J) = 2.7 + J99 ELSE IF RND < .5 THEN X(J) = 2.8 + J99 ELSE X(J) = 2.9 + J99
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) > 16.8 THEN 1670
213 IF X(2) < 1.1 THEN 1670
214 IF X(2) > 26.7 THEN 1670
215 IF X(3) < 1.1 THEN 1670
216 IF X(3) > 26.7 THEN 1670
301 X(4) = -16 + X(1) ^ .8 + X(2) ^ .9 + X(3) ^ .5
303 X(5) = 31 - 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(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 < -685.5 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 [26]. The complete output through JJJJ = -31890.48000001753 is shown below:
16.8 3.1 14 0
0 -685.0154632676962 -31988.7500000018
16.8 3.1 14 0
0 -685.0154632676962 -31974.990000004
16.8 3.1 14 0
0 -685.0154632676962 -31890.48000001753
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 [26], the wall-clock time for obtaining the output through JJJJ= -31890.48000001753 was 8 minutes.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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