Jsun Yui Wong
The computer program listed below seeks to solve the following problem from Mellal and Zio [34, p. 217, Life-Support System in a Space Capsule]:
Minimize K(1) * (TAN(3.141592654 * X(1) / 2)) ^alpha(1)+ K(2) * (TAN(3.141592654 * X(2) / 2))^alpha(2) + K(3) * (TAN(3.141592654 * X(3) / 2))^alpha(3) + K(4)* (TAN(3.141592654 * X(4) / 2)) ^alph(4)
subject to
.5<= X(i) <=1, for i=1, 2, 3, 4
RS = 1 - X(3) * ((1 - X(1)) * (1 - X(4))) ^ 2 - (1 - X(3)) * (1 - X(2) * (1 - (1 - X(1)) * (1 - X(4)))) ^ 2
0.99 <= RS <=1
alpha(1) through alpha(4) =1, 1, 1, 1, respectively; K(1) through K(4)= 25, 25, 50, 37.5, respectively.
X(5) and X(6) below are slack variables added.
Whereas line 128 of thr earlier edition is 128 FOR I = 1 TO 20000 , here line 128 is 128 FOR I = 1 TO 10000.
0 DEFDBL A-Z
1 DEFINT K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20)
81 FOR JJJJ = -32000 TO 31500
89 RANDOMIZE JJJJ
90 M = -3E+30
95 FOR J44 = 1 TO 4
97 A(J44) = .5 + RND * .5
99 NEXT J44
128 FOR I = 1 TO 10000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 3)
153 j = 1 + FIX(RND * 4)
156 r = (1 - RND * 2) * A(j)
158 X(j) = A(j) + (RND ^ (RND * 10)) * r
169 NEXT IPP
326 FOR J44 = 1 TO 4
327 IF X(J44) < .5 THEN 1670
328 IF X(J44) > 1 THEN 1670
331 NEXT J44
333 RS = 1 - X(3) * ((1 - X(1)) * (1 - X(4))) ^ 2 - (1 - X(3)) * (1 - X(2) * (1 - (1 - X(1)) * (1 - X(4)))) ^ 2
334 IF RS < .99## THEN 1670
335 IF RS > 1## THEN 1670
336 X(5) = 1 - RS
337 X(6) = -.99 + RS
355 FOR J44 = 5 TO 6
357 IF X(J44) < 0## THEN X(J44) = X(J44) ELSE X(J44) = 0
359 NEXT J44
411 PDU = -25 * (TAN(3.141592654 * X(1) / 2)) - 25 * (TAN(3.141592654 * X(2) / 2)) - 50 * (TAN(3.141592654 * X(3) / 2)) - 37.5 * (TAN(3.141592654 * X(4) / 2)) + 1000000 * (X(5) + X(6))
466 P = PDU
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 6
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -390.572 THEN 1999
1904 PRINT A(1), A(2), A(3)
1905 PRINT A(4), A(5), A(6), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [46]. The top-two candidate solutions of a single run through JJJJ= -31266 are shown below:
.8257483241377608 .8901250489112406 .6275694761976304
.7287752110739787 0 0 -390.5708320895516
-31308
.8254927914020735 .8902662534407841 .627177540172993
.7289195985628147 0 0 -390.5709136319074
-31266
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 [46], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31266 was 155 seconds, total, including the time for “Creating .EXE file." One can compare the computational results above with those in Mellal and Zio [34, p. 224, Table 13].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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