Jsun Yui Wong
The computer program listed below seeks to solve the immediately following 2-objective nonlinear integer goal programming problem:
Minimize P1* X(4)
Minmize P2* X(6)
where P1>>P2
subject to
X(1) ^ 2 + 4 * X(2) +X(3)-X(4)=4
X(1) + X(2) ^ 2 + X(5) - X(6)= 10
X(1), X(2)>=0 and are integers
X(3) * X(4) = 0
X(5) * X(6) =0
X(3) through X(6)>=0.
The problem above is based on a problem in Malhotra and Arora [62, p. 48, Auxiliary Problem (P2)].
0 DEFDBL A-Z
1 REM DEFINT X, A
2 DIM N(99), A(45222), X(45012), D(111), P(111), PS(33), J44(45202), J(45211), AA(99), STIO(45303)
81 FOR JJJJ = -32000 TO 32000
85 RANDOMIZE JJJJ
87 M = -4E+250
120 FOR J44 = 1 TO 6
121 A(J44) = FIX(RND * 3)
123 NEXT J44
128 FOR I = 0 TO FIX(RND * 90000)
129 FOR KKQQ = 1 TO 6
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 3.3)
143 j = 1 + FIX(RND * 6)
144 IF RND < .5 THEN GOTO 156 ELSE GOTO 162
145 GOTO 162
154 REM IF j > 3.5 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 * 3.3) ELSE X(j) = A(j) + FIX(1 + RND * 3.3)
169 NEXT IPP
201 FOR J44 = 1 TO 6
205 IF X(J44) < 0 THEN 1670
206 NEXT J44
214 X(1) = INT(X(1))
215 X(2) = INT(X(2))
221 IF X(3) * X(4) > 0## THEN 1670
224 IF X(5) * X(6) > 0## THEN 1670
236 GOTO 1244
1244 X(3) = 4 + X(4) - X(1) ^ 2 - 4 * X(2)
1250 X(5) = 10 + X(6) - X(1) - X(2) ^ 2
1267 FOR J44 = 1 TO 6
1268 REM X(J44) = INT(X(J44))
1269 IF X(J44) < 0 THEN 1670
1270 NEXT J44
1275 X(1) = INT(X(1))
1277 X(2) = INT(X(2))
1296 IF X(3) * X(4) > 0## THEN 1670
1298 IF X(5) * X(6) > 0## THEN 1670
1305 P = -10 ^ 40 * X(4) - X(6)
1418 IF P <= M THEN 1670
1420 M = P
1442 FOR KLX = 1 TO 6
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1931 PRINT A(1), A(2), A(3), A(4), A(5), A(6), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [103]. The complete output of a single run through JJJJ=-31996 is shown below:
0 1 0 0 9
0 0 -32000
2 2 2 1 0
2 -4D+250 -31999
1 2 0 5 5
0 -5D+40 -31998
1 0 3 0 9
0 0 -31997
0 1 0 0 9
0 0 -31996
.
.
.
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 [103], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31996 was 2 seconds, not including the time for “Creating .EXE file.” One can compare the computational results above with those in Malhotra and Arora [62, p. 50].
Remark 3 and remark 4 on page 198 of Winston and Venkataramanan are noteworthy [104].
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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