Optimizing an Equality-Constrained Nonlinear Function, an Optimization Test Problem, Second Edition
Jsun Yui Wong
The optimization test problem here is from Yang [123, p. 3 of 6, one can view this directly on Google]:
Minimize - ((238 ^ .5)) ^ 238 * PROD
where PROD = pi X(J44), J44=1 through 238
subject to sigma X(J44) ^ 2 =1, 0<= X(J44)<=1 for J=1, 2, ..., 238.
One notes line 219, which is 219 X(1) = (1 - SUMM) ^ .5.
While the earlier edition has 235 dimensions, the edition here has 238 dimensions.
0 DEFDBL A-Z
2 REM DEFINT K
3 DIM B(99), N(99), A(200111), H(99), L(200111), U(99), X(200111), D(111), P(511), PS(33), J(200111), J44(200111), KKQQ(200111), KLX(200111), W(200111), LSUM(200111)
12 FOR JJJJ = -32000 TO 32000 STEP .01
13 RANDOMIZE JJJJ
16 M = -1D+37
18 FOR J44 = 1 TO 238
19 A(J44) = RND * .1
25 NEXT J44
128 FOR I = 1 TO 50000
129 FOR KKQQ = 1 TO 238
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO (1 + FIX(RND * 5))
148 J = 1 + FIX(RND * 240)
154 IF RND < .5 THEN GOTO 157 ELSE GOTO 164
157 R = (1 - RND * 2) * (A(J))
160 X(J) = A(J) + (RND ^ (RND * 30)) * R
161 GOTO 174
164 IF RND < .5 THEN X(J) = A(J) - FIX(1 + RND * .3) ELSE X(J) = A(J) + FIX(1 + RND * .3)
174 NEXT IPP
201 FOR J44 = 1 TO 238
205 IF X(J44) < 0 THEN 1670
207 IF X(J44) > 1 THEN 1670
208 NEXT J44
210 SUMM = 0
211 FOR J44 = 2 TO 238
213 REM PROD = PROD* X(J44) ...16 * X(J44) ^ 2 + 5 * X(J44))
214 SUMM = SUMM + X(J44) ^ 2
215 NEXT J44
217 IF (1 - SUMM) < 0## THEN 1670
219 X(1) = (1 - SUMM) ^ .5
220 PROD = 1
221 FOR J44 = 1 TO 238
223 REM PROD = PROD* X(J44) ...16 * X(J44) ^ 2 + 5 * X(J44))
224 PROD = PROD * X(J44)
227 NEXT J44
1118 P = ((238 ^ .5)) ^ 238 * PROD
1119 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 238
1459 A(KLX) = X(KLX)
1460 NEXT KLX
1555 REM PRINT A(1), A(2), A(5000), M, JJJJ
1557 GOTO 128
1670 NEXT I
1910 IF M < .1 THEN GOTO 1999
1922 PRINT A(1), A(2), A(238), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [120]. The complete output of one run through JJJJ=-31997.910000000034 is shown below:
6.482037135137717D-02 6.482036974432712D-02 6.482036621246243D-02
1.000000000000578 -31999.17000000013
6.482037256411673D-02 .0648203706088149 6.482036603305502D-02
1.000000000000443 -31998.33000000027
6.482037076188071D-02 6.482037196126396D-02 6.482036621329226D-02
1.000000000000503 -31997.91000000034
One notes that only 3 values of the 238 values of A(1) through A(238) are shown above, in accordance with line 1922, which is 1922 PRINT A(1), A(2), A(238), M, JJJJ.
The system properties of the computer system used include Intel Core 2 Duo CPU E8400 @ 3.00GHz 3.00GHz, 4.00GB of RAM, and qb64v1000-win [120]. The wall-clock time (not CPU time) for obtaining the output shown above was 7 minutes, counting from “Starting program…”. The results presented above are compatible with those presented in Yang [123, p. 3 of 6].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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