Jsun Yui Wong
The computer program listed below seeks to solve the following problem from Shen, Ma, and Chen [30, p. 453, Example 6].
Maximize -(-1.35) * ((X(1) ^ 2 * X(2) ^ .5 – 2 * X(1) * X(2) ^ -1 + X(2) ^ 2 – 2.8 * X(1) ^ -1 * X(2) + 7.5) / (X(1) * X(2) ^ 1.5 + 1)) – (12.99) * ((X(2) + .1) / (X(1) ^ 2 * X(2) ^ -1 – 3 * X(1) ^ -1 + 2 * X(1) * X(2) ^ 2 – 9 * X(2) ^ -1 + 12))
subject to
2 * X(1) ^ -1 + X(1) * X(2)<=4,
X(1) +3 * X(1) ^ -1 * X(2)<=5,
X(1) ^ 2 – 3 * X(2) ^ 3<=2,
1<=X(1) <= 3,
1<=X(2) <= 3.
X(3) through X(5) below are added slack variables.
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
72 A(1) = 1 + RND * 2
75 A(2) = 1 + RND * 2
128 FOR I = 1 TO 2000
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
133 FOR IPP = 1 TO (1 + FIX(RND * 2))
181 J = 1 + FIX(RND * 2)
183 r = (1 – RND * 2) * A(J)
187 X(J) = A(J) + (RND ^ (RND * 10)) * r
191 NEXT IPP
201 IF X(1) < 1 THEN 1670
203 IF X(1) > 3 THEN 1670
211 IF X(2) < 1 THEN 1670
213 IF X(2) > 3 THEN 1670
311 X(3) = 4 – 2 * X(1) ^ -1 – X(1) * X(2)
313 X(4) = 5 – X(1) – 3 * X(1) ^ -1 * X(2)
315 X(5) = 2 – X(1) ^ 2 + 3 * X(2) ^ 3
333 FOR J44 = 3 TO 5
336 IF X(J44) < 0 THEN X(J44) = X(J44) ELSE X(J44) = 0
339 NEXT J44
378 POBA = -(-1.35) * ((X(1) ^ 2 * X(2) ^ .5 – 2 * X(1) * X(2) ^ -1 + X(2) ^ 2 – 2.8 * X(1) ^ -1 * X(2) + 7.5) / (X(1) * X(2) ^ 1.5 + 1)) – (12.99) * ((X(2) + .1) / (X(1) ^ 2 * X(2) ^ -1 – 3 * X(1) ^ -1 + 2 * X(1) * X(2) ^ 2 – 9 * X(2) ^ -1 + 12)) + 1000000 * (X(3) + X(4) + 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 GOTO 128
1670 NEXT I
1889 IF M < -11111 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 [38]. The complete output through JJJJ = -31999.98 is shown below:
2.698672512963932 1.207578072004017 0
0 0 2.332207556891017 -32000
2.698682666462486 1.20758224763645 0
0 0 2.332213594166706 -31999.99
2.698690059295716 1.20758528793531 0
0 0 2.332217989915511 -31999.98
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 [38], the wall-clock time for obtaining the output through
JJJJ= -31999.98 was 1 or 2 seconds, not including the time for “Creating .EXE file.” One can compare the computational results above to the results in Shen, Ma, and Chen [30, p.452, Table 1].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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