Jsun Yui Wong
The present problem is based on the following multiple-objective nonlinear programming problem in Siwale [66, p. 3, Example 1]:
Minimize 1 - EXP(-SUM1), where SUM1 is defined by line 221 below
minimize 1 - EXP(-SUM2), where SUM2 is defined by line 225 below
subject to
-2 <=X(i) <=2, i=1, 2, 3,..., 8.
The above problem of 8 continuous variables has been modified to the following problem with 6 continuous variables (X(1) through X(6)) and 2 general integer variables (X(7) and X(8))--please see the computer program below.
Whereas line 128 of the earlier edition is 128 FOR I = 1 TO FIX(1 + RND * 100), here line 128 is 128 FOR I = 1 TO FIX(1 + RND * 75).
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), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)
81 FOR JJJJ = -32000 TO 32000
85 RANDOMIZE JJJJ
87 M = -3E+50
92 epsilon2 = RND
121 FOR J44 = 1 TO 8
122 A(J44) = -2 + INT(RND * 4)
123 NEXT J44
128 FOR I = 1 TO FIX(1 + RND * 75)
129 FOR KKQQ = 1 TO 8
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 3)
153 J = 1 + FIX(RND * 8)
154 IF J < 6.5 THEN GOTO 162 ELSE GOTO 156
156 R = (1 - RND * 2) * A(J)
158 X(J) = A(J) + (RND ^ (RND * 15)) * R
161 GOTO 169
162 IF RND < .5 THEN X(J) = A(J) - FIX(1 + RND * 2) ELSE X(J) = A(J) + FIX(1 + RND * 2)
169 NEXT IPP
170 FOR J44 = 1 TO 6
171 X(J44) = INT(X(J44))
175 NEXT J44
176 FOR J44 = 1 TO 8
177 IF X(J44) < -2## THEN 1670
187 IF X(J44) > 2## THEN 1670
191 NEXT J44
217 SUM1 = 0
219 FOR J44 = 1 TO 8
221 SUM1 = SUM1 + (X(J44) - 1 / 8 ^ .5##) ^ 2
222 NEXT J44
223 SUM2 = 0
224 FOR J44 = 1 TO 8
225 SUM2 = SUM2 + (X(J44) + 1 / 8 ^ .5##) ^ 2
226 NEXT J44
244 IF -1 + EXP(-SUM2) > epsilon2 THEN 1670
422 PDU = -1 + EXP(-SUM1)
466 P = PDU
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 8
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1522 g01star = -1 + EXP(-SUM1)
1524 g02star = -1 + EXP(-SUM2)
1557 GOTO 128
1670 NEXT I
1889 IF M < -.7 THEN 1999
1922 PRINT g01star, g02star, JJJJ
1924 PRINT A(1), A(2), A(3)
1926 PRINT A(4), A(5), A(6)
1928 PRINT A(7), A(8), M
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [73]. The complete output of a single run through JJJJ= -31987 is shown below:
-.6111392470888822 -.8375608937876204 -31997
0 0 0
0 0 0
.617246320182483 0 -.6111392470888822
-.6321205588285578 -.6321205588285578 -31987
0 0 0
0 0 0
0 0 -.6321205588285578
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 [73], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31987 was 2 seconds, not including the time for “Creating .EXE file" (15 seconds, total, including the time for “Creating .EXE file"). One can compare the computational results above with those in Siwale [66, pp. 4-7].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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