Jsun Yui Wong
The computer program listed below seeks to solve the following test problem in Parsopoulos and Vrahatis [85, Test Problem 4]:
minimize f = (9 * X(1) ^ 2 + 2 * X(2) ^ 2 – 11) ^ 2 + (3 * X(1) + 4 * X(2) ^ 2 – 7) ^ 2
with solution at x*=(1, 1) and f(x*)=0, Parsopoulos and Vrahatis [85, Test Problem 4].
.
0 REM DEFDBL A-Z
1 REM 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)
12 FOR JJJJ = -32000 TO 32000 STEP .01
13 RANDOMIZE JJJJ
16 M = -1D+37
19 FOR J44 = 1 TO 2
21 A(J44) = -10 + FIX(RND * 21)
22 NEXT J44
128 FOR I = 1 TO 100
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND ^ 5 * 5)
143 J = 1 + FIX(RND * 4)
154 IF RND < .5 THEN GOTO 156 ELSE GOTO 162
156 R = (1 – RND * 2) * A(J)
158 X(J) = A(J) + (RND ^ (RND * 30)) * R
161 GOTO 165
162 REM IF RND < .16666 THEN X(J) = A(J) – FIX(1 + RND * 2.3) ELSE IF RND < .33333 THEN X(J) = A(J) + FIX(1 + RND * 2.3) ELSE IF RND < .5 THEN X(J) = A(J) – FIX(1 + RND * 20.3) ELSE IF RND < .66666 THEN X(J) = A(J) + FIX(1 + RND * 20.3) ELSE IF RND < .83333 THEN X(J) = A(J) – FIX(1 + RND * 200.3) ELSE X(J) = A(J) + FIX(1 + RND * 200.3)
164 IF RND < .5 THEN X(J) = A(J) – FIX(1 + RND * .3) ELSE X(J) = A(J) + FIX(1 + RND * .3)
165 NEXT IPP
166 FOR J44 = 1 TO 2
167 X(J44) = INT(X(J44))
168 NEXT J44
182 FOR J44 = 1 TO 2
183 IF X(J44) < -100 THEN 1670
184 IF X(J44) > 100 THEN 1670
185 NEXT J44
1020 P = -(9 * X(1) ^ 2 + 2 * X(2) ^ 2 – 11) ^ 2 – (3 * X(1) + 4 * X(2) ^ 2 – 7) ^ 2
1111 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 2
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1890 REM IF M < 30665 THEN 1999
1926 PRINT A(1), A(2), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with qb64v1000-win [120]. The complete output of one run through JJJJ = -31999.84 is shown below:
1 -1 0 -32000
-1 1 -36 -31999.99
-1 1 -36 -31999.98
-1 1 -36 -31999.97
1 -1 0 -31999.96
-1 1 -36 -31999.95
1 -1 0 -31999.94
-1 -1 -36 -31999.93
-1 1 -36 -31999.92
-1 -1 -36 -31999.91
-1 -1 -36 -31999.9
1 -1 0 -31999.89
-1 1 -36 -31999.88
-1 1 -36 -31999.87
-1 -1 -36 -31999.86
-1 1 -36 -31999.85
1 1 0 -31999.84
Two distinct solutions are shown above at x*=(1, -1) and x*=(1, 1).
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen.
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 through JJJJ = -31999.84 was 2 seconds, counting from “Starting program…”. One can compare the computational results above with those in Parsopoulos and Vrahatis [85, Test Problem 4].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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