Jsun Yui Wong
The computer program listed below seeks to solve the following problem based on Chen [10, p. 1562, P3, Complex (Bridge) System] and on Liu and Qin [30, p. 2053, Problem 2, Complex (Bridge) System]:
Maximize O(1) * O(2) + O(3) * O(4) + O(1) * O(4) * O(5) + O(2) * O(3) * O(5) - O(1) * O(2) * O(3) * O(4) - O(1) * O(2) * O(3) * O(5) - O(1) * O(2) * O(4) * O(5) - O(1) * O(3) * O(4) * O(5) - O(2) * O(3) * O(4) * O(5) + 2 * O(1) * O(2) * O(3) * O(4) * O(5)
where O(J44) = 1 - ((1 - (X(J44 + 5)))) ^ X(J44)--see line 391 through line 394 below
subject to
1 * X(1) ^ 2 + 2 * X(2) ^ 2 + 3 * X(3) ^ 2 + 4 * X(4) ^ 2 + 2 * X(5) ^ 2<=110
(2.33 / 10 ^ 5) * ((-1000 / LOG(X(6))) ^ 1.5) * (X(1) + EXP(X(1) / 4)) + (1.45 / 10 ^ 5) * ((-1000 / LOG(X(7))) ^ 1.5) * (X(2) + EXP(X(2) / 4)) + (.541 / 10 ^ 5) * ((-1000 / LOG(X(8))) ^ 1.5) * (X(3) + EXP(X(3) / 4)) + (8.05 / 10 ^ 5) * ((-1000 / LOG(X(9))) ^ 1.5) * (X(4) + EXP(X(4) / 4)) + (1.95 / 10 ^ 5) * ((-1000 / LOG(X(10))) ^ 1.5) * (X(5) + EXP(X(5) / 4))<=175
7 * X(1) * EXP(X(1) / 4) + (8) * X(2) * EXP(X(2) / 4) + (8) * X(3) * EXP(X(3) / 4) + (6) * X(4) * EXP(X(4) / 4) + (9) * X(5) * EXP(X(5) / 4)<=200
.5<= X(i) <= 1, 6<=i<=10
where X(1) through X(5) are positive general integer variables with X(i)=1, 2, 3, ..., 10.
X(11) through X(13) below are slack variables added.
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 32000
89 RANDOMIZE JJJJ
90 M = -3E+30
95 FOR J44 = 1 TO 5
97 A(J44) = FIX(1 + RND * 10)
99 NEXT J44
115 FOR J44 = 6 TO 10
117 A(J44) = .5 + RND * .49999
119 NEXT J44
128 FOR I = 1 TO 100000
129 FOR KKQQ = 1 TO 10
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 3)
153 j = 1 + FIX(RND * 10)
155 IF j > 5.5 THEN GOTO 156 ELSE GOTO 164
156 r = (1 - RND * 2) * A(j)
158 X(j) = A(j) + (RND ^ (RND * 10)) * r
161 GOTO 169
164 IF RND < .5 THEN X(j) = A(j) - 1 ELSE X(j) = A(j) + 1
169 NEXT IPP
326 FOR J44 = 1 TO 5
327 X(J44) = CINT(X(J44))
328 IF X(J44) < 1 THEN 1670
329 IF X(J44) > 10 THEN 1670
331 NEXT J44
336 FOR J44 = 6 TO 10
338 IF X(J44) < .5## THEN 1670
339 IF X(J44) > .999999## THEN 1670
340 NEXT J44
341 X(11) = 110 - 1 * X(1) ^ 2 - 2 * X(2) ^ 2 - 3 * X(3) ^ 2 - 4 * X(4) ^ 2 - 2 * X(5) ^ 2
343 X(12) = 200 - 7 * X(1) * EXP(X(1) / 4) - (8) * X(2) * EXP(X(2) / 4) - (8) * X(3) * EXP(X(3) / 4) - (6) * X(4) * EXP(X(4) / 4) - (9) * X(5) * EXP(X(5) / 4)
346 X(13) = 175 - (2.33 / 10 ^ 5) * ((-1000 / LOG(X(6))) ^ 1.5) * (X(1) + EXP(X(1) / 4)) - (1.45 / 10 ^ 5) * ((-1000 / LOG(X(7))) ^ 1.5) * (X(2) + EXP(X(2) / 4)) - (.541 / 10 ^ 5) * ((-1000 / LOG(X(8))) ^ 1.5) * (X(3) + EXP(X(3) / 4)) - (8.05 / 10 ^ 5) * ((-1000 / LOG(X(9))) ^ 1.5) * (X(4) + EXP(X(4) / 4)) - (1.95 / 10 ^ 5) * ((-1000 / LOG(X(10))) ^ 1.5) * (X(5) + EXP(X(5) / 4))
355 FOR J44 = 11 TO 13
357 IF X(J44) < 0 THEN X(J44) = X(J44) ELSE X(J44) = 0
359 NEXT J44
391 FOR J44 = 1 TO 5
393 O(J44) = 1 - ((1 - (X(J44 + 5)))) ^ X(J44)
394 NEXT J44
401 PDU = O(1) * O(2) + O(3) * O(4) + O(1) * O(4) * O(5) + O(2) * O(3) * O(5) - O(1) * O(2) * O(3) * O(4) - O(1) * O(2) * O(3) * O(5) - O(1) * O(2) * O(4) * O(5) - O(1) * O(3) * O(4) * O(5) - O(2) * O(3) * O(4) * O(5) + 2 * O(1) * O(2) * O(3) * O(4) * O(5) + 1000000 * (X(11) + X(12) + X(13))
466 P = PDU
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 13
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < .99988961 THEN 1999
1904 PRINT A(1), A(2), A(3)
1905 PRINT A(4), A(5), A(6)
1906 PRINT A(7), A(8), A(9)
1907 PRINT A(10), A(11), A(12), A(13)
1909 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [45]. The complete output of a single run through JJJJ= -31917 is shown below:
3 3 2
4 1 .8271828129627745
.8584470687531135 .9146456241665405 .6473915423816696
.7083633509542693
.9998896175115296 -31982
3 3 2
4 1 .8275566506233765
.8585263665874964 .914785253366289 .6470983072525923
.7044017880815086
.9998896208547377 -31917
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 [45], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31917 was 5 minutes, total, including the time for “Creating .EXE file." One can compare the computational results above with those in Chen [10, p. 1565, Table 6] and in Liu and Qin [30, p. 2054, Table VIII].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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