Jsun Yui Wong
The computer program listed
below seeks to solve the following test problem in Parsopoulos and Vrahatis
[85, Test Problem 3]:
minimize f =
- (P0 + P1 + P2 + P3 + P4 + P5)
where P0 through P5 are
defined by the following lines 1020 through 1025, respectively.
The best solutions are
x*=(0 11 22
16 6) and x*=(0 12
23 17 6) for f(x*)= -737, Parsopoulos
and Vrahatis [85, Test Problem 3].
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 5
21 A(J44) = -10 + FIX(RND * 21)
22 NEXT J44
128 FOR I = 1 TO 20000
129 FOR KKQQ = 1 TO 5
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND ^ 5 * 5)
143 J = 1 + FIX(RND * 5)
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 5
167 X(J44) = INT(X(J44))
168 NEXT J44
182 FOR J44 = 1 TO 5
183 IF X(J44) < -100 THEN 1670
184 IF X(J44) > 100 THEN 1670
185 NEXT J44
1020 P0 = 15 * X(1) + 27 * X(2) + 36 *
X(3) + 18 * X(4) + 12 * X(5)
1021 P1 = -(35 * X(1) - 20 * X(2)
- 10 * X(3) + 32 * X(4) - 10 * X(5) ) * X(1)
1022 P2 = -(-20 * X(1) + 40 * X(2) - 6
* X(3) - 31 * X(4) + 32 * X(5) ) * X(2)
1023 P3 = -(-10 * X(1) - 6 * X(2) + 11 * X(3) - 6 * X(4) - 10 * X(5) ) * X(3)
1024 P4 = -(32 * X(1) - 31 * X(2) - 6 * X(3) + 38 * X(4) - 20 * X(5)) * X(4)
1025 P5 = -(-10 * X(1) + 32 * X(2) - 10
* X(3) - 20 * X(4) + 31 * X(5)) * X(5)
1041 P = P0 + P1 + P2 + P3 + P4 + P5
1111 IF P <= M THEN 1670
1420 M = P
1444 FOR KLX = 1 TO 5
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1890 REM
IF M<-9999 THEN 1999
1926 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 [120]. The
output of one run through JJJJ = -31998.87 is summarized below:
0 11
22 16 6
737 -32000
0 11
22 16 6
737 -31999.99
.
.
.
0 12
23 17 6
737 -31999.43
.
.
.
0 12
23 17 6
737 -31998.87
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 = -31998.87 was 14 seconds,
counting from "Starting program...".
One
can compare the computational results above with those in Parsopoulos and
Vrahatis [85, Test Problem 3].
Acknowledgement
I would like to acknowledge
the encouragement of Roberta Clark and Tom Clark.
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