The computer program listed below seeks to solve the following multi-objective geometric programming problem from Das and Roy [15, p. 8, Expression (5)]:
Minimize
(40 / (X(1) * X(2) * X(3)) + 40 * X(2) * X(3))
minimize
(800 / (X(1) * X(2) * X(3)))
subject to
X(1) * X(2) + 2 * X(1) * X(3) <= 4
where X(1), X(2), X(3) > 0.
One notes line 89, which is 89 IF RND < 1 / 9 THEN w1 = .1 ELSE IF RND < 1 / 8 THEN w1 = .2 ELSE IF RND < 1 / 7 THEN w1 = .3 ELSE IF RND < 1 / 6 THEN w1 = .4 ELSE IF RND < 1 / 5 THEN w1 = .5 ELSE IF RND < 1 / 4 THEN w1 = .6 ELSE IF RND < 1 / 3 THEN w1 = .7 ELSE IF RND < 1 / 2 THEN w1 = .8 ELSE w1 = .9.
0 DEFDBL A-Z
1 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)
81 FOR JJJJ = -32000 TO 32000
85 RANDOMIZE JJJJ
87 M = -3E+50
89 IF RND < 1 / 9 THEN w1 = .1 ELSE IF RND < 1 / 8 THEN w1 = .2 ELSE IF RND < 1 / 7 THEN w1 = .3 ELSE IF RND < 1 / 6 THEN w1 = .4 ELSE IF RND < 1 / 5 THEN w1 = .5 ELSE IF RND < 1 / 4 THEN w1 = .6 ELSE IF RND < 1 / 3 THEN w1 = .7 ELSE IF RND < 1 / 2 THEN w1 = .8 ELSE w1 = .9
90 w2 = 1 - w1
92 A(1) = .0000001 + (RND * 14)
93 A(2) = .0000001 + (RND * 14)
95 A(3) = .0000001 + (RND * 14)
98 REM A(4) = .0001 + (RND * 14)
128 FOR I = 1 TO 100000
129 FOR KKQQ = 1 TO 3
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 2)
153 J = 1 + FIX(RND * 3)
154 REM GOTO 162
156 r = (1 - RND * 2) * A(J)
158 X(J) = A(J) + (RND ^ (RND * 15)) * r
161 REM GOTO 169
162 REM IF RND < .5 THEN X(J) = A(J) - 1 ELSE X(J) = A(J) + 1
169 NEXT IPP
177 IF X(1) < .0000001## THEN 1670
187 IF X(2) < .0000001## THEN 1670
188 IF X(3) < .0000001## THEN 1670
222 IF X(1) * X(2) + 2 * X(1) * X(3) > 4## THEN 1670
411 PDU = w1 * (-40 / (X(1) * X(2) * X(3)) - 40 * X(2) * X(3)) + (1 - w1) * (-800 / (X(1) * X(2) * X(3)))
466 P = PDU
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 3
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1458 g01star = (-40 / (X(1) * X(2) * X(3)) - 40 * X(2) * X(3))
1459 g02star = (-800 / (X(1) * X(2) * X(3)))
1557 GOTO 128
1670 NEXT I
1889 IF M < -99999 THEN 1999
1924 PRINT M, A(1), A(2), A(3), w1, w2, JJJJ, g01star, g02star
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [59]. Selected candidate solutions of a single run through JJJJ= -31962 are shown below:
-189.3378586403213 .9403202707443356 2.135488016906122
1.0591908904584 .7 .3 -31994
-109.2822877083477 -376.1341908149261
-117.8052601537484 1.354028933490705 1.480071993439512
.7370373142943388 .9 9.999999999999998D-02
-31993 -70.71542176355258 -541.6138056655108
-158.4928060252262 1.099662725187852 1.81544857119669
.9110151825948194 .8 .2 -31992
-88.14937497459734 -439.866530227742
-212.4239707161775 .8218050685224012 2.441177438901182
1.213078431807047 .6 .4 -31987
-134.8898458728574 -328.7251579811579
-228.3506663050602 .7250664455975634 2.749548974482393
1.383593400479356 .5 .5 -31983
-166.6717897581436 -290.0295428519767
-224.6495666190694 .4616664502330952 4.325660765870922
2.169301611907041 .2 .8 -31970
-384.5798644862868 -184.666992152265
-236.6397950135448 .5523106823612127 3.600565003291208
1.820867810801176 .3 .7 -31967
-273.2926872391645 -220.9314126311364
-191.986886467252 .3533301904818593 5.645004496367646
2.837925459033808 .1 .9 -31964
-647.8707353381623 -141.3331254815954
-236.8389463004006 .6371852618920043 3.13323632825863
1.572186387095502 .4 .6 -31962
-209.7850054567928 -254.874906862806
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 [59], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31962 was 16 seconds, not including the time for “Creating .EXE file" (23 seconds, total, including the time for “Creating .EXE file"). One can compare the computational results above with those in Das and Roy [15, Table 1, pp. 8-9].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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