Jsun Yui Wong
The computer program listed below seeks to solve the following multi-objective preemptive (lexicographic) goal program from Baykasoglu, Owen, and Gindy [12, p. 971, Test problem A-2]:
Lexmin
{ z1=(X(3)), z2=(X(10)), z3=(5 * X(5)), z4=(3 * X(7)), z5=(X(4)) }
subject to
X(3) – X(4) + X(1) + X(2)=80
X(5) + X(1)=70
X(7) + X(2)=45
X(9) – X(10)+ X(1) + X(2)=90
X(1), X(2), X(3), …, X(10)>=0.
One notes that line 1302, which is 1302 P = -100000000000000 * X(3) – 10000000000 * X(10) – 10000000000 * 5 * X(5) – 1000000 * 3 * X(7) – X(4), is a use of Hillier and Lieberman’s streamlined procedure [40, pp. 289-291] for preemptive goal programming.
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
121 FOR J44 = 1 TO 10
122 A(J44) = FIX(RND * 50)
123 NEXT J44
128 FOR I = 0 TO FIX(RND * 800000)
129 FOR KKQQ = 1 TO 10
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
135 FOR IPP = 1 TO FIX(1 + RND * 3.3)
143 j = 1 + FIX(RND * 10)
144 IF RND < .5 THEN GOTO 156 ELSE GOTO 162
145 REM GOTO 162
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 * 2.3) ELSE X(j) = A(j) + FIX(1 + RND * 2.3)
169 NEXT IPP
291 X(3) = 80 + X(4) – X(1) – X(2)
296 X(5) = 70 – X(1)
298 X(7) = 45 – X(2)
299 X(9) = 90 + X(10) – X(1) – X(2)
331 FOR J44 = 1 TO 10
332 IF X(J44) < 0 THEN 1670
334 NEXT J44
1302 P = -100000000000000 * X(3) – 10000000000 * X(10) – 10000000000 * 5 * X(5) – 1000000 * 3 * X(7) – X(4)
1311 IF P <= M THEN 1670
1420 M = P
1442 FOR KLX = 1 TO 10
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1677 IF M < -75111111 GOTO 1999
1931 PRINT A(1), A(2), A(3), A(4), A(5)
1939 PRINT A(6), A(7), A(8), A(9), A(10), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [97]. The complete output of a single run through JJJJ= -31062 is shown below:
70 20 0 10 0
10.95891032498612 25 3.489204533175562
0 7.00201049957276D-19 -75000010 -31548
70 20 0 9.9999999999999998
0
41.99957990943607 25 .1944046351790445
0 5.86148583170695D-19 -75000010 -31062
.
.
.
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 [97], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31062 was 13 minutes, total, including the time for “Creating .EXE file.” One can compare the computational results above with those in Baykasoglu, Owen, and Gindy [12, p. 971].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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