Jsun Yui Wong
The computer program listed below seeks to solve the following problem based on the last problem in Table 2 of Gounaris and Floudas [9, p. 86]:
Minimize - (1 / 2) * ((X(1) ^ 4 - 16 * X(1) ^ 2 + 5 * X(1)) + (X(2) ^ 4 - 16 * X(2) ^ 2 + 5 * X(2)) + (X(3) ^ 4 - 16 * X(3) ^ 2 + 5 * X(3)) + (X(4) ^ 4 - 16 * X(4) ^ 2 + 5 *
X(4)) + (X(5) ^ 4 - 16 * X(5) ^ 2 + 5 * X(5))),
-5<= X(1), X(2), X(3), X(4), X(5)<=2.
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
22 FOR J55 = 1 TO 5
67 A(J55) = -5 + FIX(RND * 705) * .01
71 NEXT J55
128 FOR I = 1 TO 60000
129 FOR KKQQ = 1 TO 5
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 4))
181 J = 1 + FIX(RND * 5)
183 REM r = (1 - RND * 2) * A(J)
187 REM X(J) = A(J) + (RND ^ (RND * 10)) * r
189 X(J) = -5 + FIX(RND * 705) * .01
191 NEXT IPP
200 FOR J44 = 1 TO 5
201 IF X(J44) < -5 THEN 1670
203 IF X(J44) > 2 THEN 1670
255 NEXT J44
359 REM
365 POBA = (1 / 2) * ((X(1) ^ 4 - 16 * X(1) ^ 2 + 5 * X(1)) + (X(2) ^ 4 - 16 * X(2) ^ 2 + 5 * X(2)) + (X(3) ^ 4 - 16 * X(3) ^ 2 + 5 * X(3)) + (X(4) ^ 4 - 16 * X(4) ^ 2 + 5 * X(4)) + (X(5) ^ 4 - 16 * X(5) ^ 2 + 5 * 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 REM GOTO 128
1670 NEXT I
1889 REM IF M < -.7346 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4), A(5), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [26]. The complete output through JJJJ = -31999.97000000001 is shown below:
-5 -5 -5 -5 -5
500 -32000
-5 -5 -5 -5 -5
500 -31999.99
-5 -5 -5 -5 -5
500 -31999.98
-5 -5 -5 -5 -5
500 -31999.97000000001
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= -31999.97000000001 was 14 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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