Jsun Yui Wong
The computer program listed below seeks to solve the following problem from Li and Tsai [25, p. 11, Example 2]:
Minimize 400 * X(1) ^ .9 + 1000 - 22 * (X(2) + 14.7) ^ 1.2 + X(4)
subject to
X(2) = EXP(-3950 / (X(3) + 460) + 11.86)
144*( 80 - X(3) =X(1)*X(4)
0<=X(1) <=15.1
14.7<=X(2) <=94.2
-459.67<=X(3) <=80
0<=X(4).
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 -31980 STEP .01
14 RANDOMIZE JJJJ
16 M = -1D+37
66 REM GOTO 111
71 unitsize(1) = .001
73 unitsize(2) = .001
75 unitsize(3) = .001
77 unitsize(4) = .001
81 A(1) = 0 + FIX(RND * 1000) * unitsize(1)
83 A(2) = 14.7 + FIX(RND * 1000) * unitsize(2)
85 A(3) = -459.67 + FIX(RND * 1000) * unitsize(3)
86 A(4) = 0 + FIX(RND * 1000) * unitsize(4)
87 REM A(4) = 0 + FIX(RND * 15.1)
89 GOTO 128
111 A(1) = 0 + (RND * 15)
112 A(2) = 14.7 + (RND * 79.5)
113 A(3) = -459.67 + (RND * 539.67)
114 A(4) = 0 + (RND * 10)
128 FOR I = 1 TO 3000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 3))
181 j = 1 + FIX(RND * 4)
201 REM r = (1 - RND * 2) * A(j)
205 REM X(j) = A(j) + (RND ^ (RND * 10)) * r
187 IF RND < .5 THEN X(j) = A(j) - FIX(RND * 10) * unitsize(j) ELSE X(j) = A(j) + FIX(RND * 10) * unitsize(j)
222 NEXT IPP
225 X(3) = (144 * 80 - X(1) * X(4)) / 144
227 IF (-3950 / (X(3) + 460) + 11.86) > 85 THEN GOTO 1670
233 X(2) = EXP(-3950 / (X(3) + 460) + 11.86)
268 IF X(1) < 0## THEN 1670
269 IF X(1) > 15## THEN 1670
278 IF X(2) < 14.7## THEN 1670
289 IF X(2) > 94.2## THEN 1670
291 IF X(3) < -459.67## THEN 1670
293 IF X(3) > 80## THEN 1670
295 IF X(4) < 0## THEN 1670
443 POBA = -400 * X(1) ^ .9 - 1000 - 22 * (X(2) - 14.7) ^ 1.2 - X(4)
466 P = POBA
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 4
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -5194.867## THEN 1999
1907 PRINT A(1), A(2), A(3), A(4), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [51]. The complete output through JJJJ = -31980.59000000311 is shown below:
3.469446951953614D-18 94.1778659402041 80
0 -5194.866244203784 -31990.85000000147
1.734723475976807D-18 94.1778659402041 80
8.673617379884036D-18 -5194.866244203783 -31985.74000000228
8.673617379884036D-19 94.1778659402041 80
0 -5194.866244203783 -31980.77000000308
1.734723475976807D-18 94.1778659402041 80
0 -5194.866244203783 -31980.59000000311
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 [51], the wall-clock time (not CPU time) for obtaining the output through
JJJJ = -31980.59000000311 was 11 seconds, not including the time for “Creating .EXE file” (19 seconds, total, including the time for “Creating .EXE file”). One can compare the computational results above with those on p. 11 of Li and Tsai [25, Example 2].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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