Jsun Yui Wong
The computer program listed below seeks to solve Example 2 of Lu et al. [11, p. 153]:
Minimize X(1) ^ -2 * X(2) ^ -1.5 * X(3) ^ 1.2 * X(4) ^ 3 - 3 * X(3) ^ .5 + X(2) - 4 * X(4)
subject to 0.01<= X(1), X(2), X(3), X(4)<=10.
One notes that here line 128 is 128 FOR I = 1 TO 30000.
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 -31999.96999 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
22 FOR J55 = 1 TO 4
67 A(J55) = .01 + FIX(RND * 1005) * .01
71 NEXT J55
128 FOR I = 1 TO 30000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 4))
181 J = 1 + FIX(RND * 4)
183 REM r = (1 - RND * 2) * A(J)
187 REM X(J) = A(J) + (RND ^ (RND * 10)) * r
189 X(J) = .01 + FIX(RND * 1005) * .01
191 NEXT IPP
200 FOR J44 = 1 TO 4
201 IF X(J44) < .01 THEN 1670
203 IF X(J44) > 10 THEN 1670
255 NEXT J44
359 POBA = -X(1) ^ -2 * X(2) ^ -1.5 * X(3) ^ 1.2 * X(4) ^ 3 + 3 * X(3) ^ .5 - X(2) + 4 * X(4)
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 4
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 REM GOTO 128
1670 NEXT I
1889 REM IF M < -.7346 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [24]. The complete output through JJJJ = -31999.97000000001 is shown below:
10 .32 .01 10 39.76007478129893
-32000
10 .32 .01 9.98 39.68139169526792
-31999.99
10 .32 .01 10 39.76007478129893
-31999.98
10 .32 .01 10 39.76007478129893
-31999.97000000001
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. One can compare the computational results above to the results in Lu et al. [11, Table 1, p. 153].
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and qb64v1000-win [24], the wall-clock time for obtaining the output through JJJJ=-31999.97000000001 was 13 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.
References
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