The computer program listed below seeks to solve the following extension of Gounaris and Floudas' [9, p. 86] last problem in Table 2 of 5 variables to 15 variables:
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(14) ^ 4 - 16 * X(14) ^ 2 + 5 * X(14)) + (X(15) ^ 4 - 16 * X(15) ^ 2 + 5 * X(15))),
-5<= X(1), X(2), X(3), ..., X(13), X(14), X(15) <=2.
One notes line 67, which is 67 A(J55) = -5 + FIX(RND * 705) * .01.
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 15
67 A(J55) = -5 + FIX(RND * 705) * .01
71 NEXT J55
128 FOR I = 1 TO 100000
129 FOR KKQQ = 1 TO 15
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 10))
181 J = 1 + FIX(RND * 15)
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 15
201 IF X(J44) < -5 THEN 1670
203 IF X(J44) > 2 THEN 1670
255 NEXT J44
301 ssuumm = 0
305 FOR J44 = 1 TO 15
308 ssuumm = ssuumm + X(J44) ^ 4 - 16 * X(J44) ^ 2 + 5 * X(J44)
311 NEXT J44
359 REM
361 REM
364 POBA = (1 / 2) * ssuumm
466 P = POBA
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 15
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1557 REM GOTO 128
1670 NEXT I
1889 IF M < 1495 THEN 1999
1900 PRINT A(1), A(2), A(3), A(4), A(5)
1911 PRINT A(6), A(7), A(8), A(9), A(10)
1915 PRINT A(11), A(12), A(13), A(14), A(15), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [26]. The complete output through JJJJ =-31999.75000000004 shown below:
-5 -5 -5 -5 -5
-5 -5 -5 -5 -5
-5 -4.98 -5 -5 -4.99
1495.008410085 -31999.95000000001
-5 -5 -5 -5 -5
-5 -5 -5 -5 -5
-5 -5 -5 -5 -5
1500 -31999.88000000002
-5 -5 -5 -5 -5
-5 -5 -4.99 -4.99 -5
-5 -5 -5 -5 -5
1496.66338001 -31999.82000000003
-5 -5 -5 -5 -5
-5 -5 -5 -5 -5
-5 -5 -5 -5 -5
1500 -31999.75000000004
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= -31999.75000000004 was 30 seconds, including the seconds for creating the .EXE file.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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