Jsun Yui Wong
The computer program listed below seeks to solve the following mixed-variable nonlinear program from Siwale [66, p. 10, Example 4]:
Minimize .6224 * (.0625 * X(1)) * X(3) * X(4) + 1.7781 * (.0625 * X(2)) * X(3) ^ 2 + 3.1661 * X(4) * (.0625 * X(1)) ^ 2 + 19.84 * X(3) * (.0625 * X(1)) ^ 2
subject to
X(4)-240<=0
-.0625 * X(1) + .0193 * X(3) <=0
-.0625 * X(2) + .00954 * X(3) <=0
-pie * X(3) ^ 2 * X(4) - 1.333333333333333333 * pie * X(3) ^ 3 + 1296000 <=0
X(i) epsilon [0.0625, 99] intersection {X(i) : X(i)=0.0625N, N epsilon Z}, i=1, 2;
X(i) epsilon [10.0, 200], i=3, 4.
.0625 * X(1) above is X(1) in Siwale [66, p. 10];
.0625 * X(1) above is X(2) in Siwale [66, p. 10].
One of the inequality constraints is expected to be binding. That makes the arrival of line 198, which is 198 X(3) = .0625 * X(1) / .0193.
Whereas line 128 of the earlier edition is 128 FOR I = 1 TO FIX(1 + RND * 10000), here line 128 is 128 FOR I = 1 TO FIX(1 + RND * 5000).
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
121 FOR J44 = 1 TO 2
122 A(J44) = FIX(1 + (RND * 200))
123 NEXT J44
124 A(3) = 10 + (RND * 190)
125 A(4) = 10 + (RND * 190)
128 FOR I = 1 TO FIX(1 + RND * 5000)
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)
154 IF J < 2.5 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 2
171 X(J44) = INT(X(J44))
175 NEXT J44
176 FOR J44 = 1 TO 2
177 IF X(J44) < 1## THEN 1670
187 IF X(J44) > 1584## THEN 1670
191 NEXT J44
193 IF X(3) < 10## THEN 1670
194 IF X(3) > 200## THEN 1670
196 IF X(4) < 10## THEN 1670
197 IF X(4) > 200## THEN 1670
198 X(3) = .0625 * X(1) / .0193
255 IF -.0625 * X(2) + .00954 * X(3) > 0 THEN 1670
259 IF -3.1415926535897932 * X(3) ^ 2 * X(4) - 1.333333333333333333 * 3.1415926535897932 * X(3) ^ 3 + 1296000 > 0 THEN 1670
428 PDU = -.6224 * (.0625 * X(1)) * X(3) * X(4) - 1.7781 * (.0625 * X(2)) * X(3) ^ 2 - 3.1661 * X(4) * (.0625 * X(1)) ^ 2 - 19.84 * X(3) * (.0625 * X(1)) ^ 2
466 P = PDU
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 < -6059.80 THEN 1999
1923 PRINT A(1), A(2), JJJJ
1924 PRINT A(3), A(4), M
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [73]. The complete output of a single run through JJJJ= -31973 is shown below:
13 7 -31989
42.09844559585492 176.6365958596064 -6059.714335449787
13 7 -31973
42.09844559585492 176.6365958711538 -6059.714335719758
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 = -31973 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 the last table on page 10 of Siwale [66].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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