Jsun Yui Wong
The computer program listed below seeks to solve the following problem from Madic and Radovanovic [35, p. 230] of treating simultaneously two objectives (material removal rate (MRR) and surface roughness (SR)):
Maximize
MRR+1/SR= -.112931 + .0170470 * X(1) + .0002220059 * X(3) + .0190297 * X(2) - 7.23331D-05 * X(1) ^ 2 - 2.43026D-07 * (X(3)) ^ 2 - 3.03374D-04 * (X(2)) ^ 2 + 1.58294D-05 * (X(1)) * X(3) + .00148333 * X(1) * X(2) - 3.96310D-05 * X(3) * X(2) + (1 / (1.76966 + .882071 * X(1) + .00686577 * X(3) - .447132 * X(2) - .0373631 * X(1) ^ 2 - 9.89173D-06 * (X(3)) ^ 2 + .0221831 * (X(2)) ^ 2 + .000517857 * (X(1)) * X(3) + .0109375 * X(1) * X(2) - 2.76786D-04 * X(3) * X(2)))
where
6<= X(1) <=18
4<= X(2) <=12
50<= X(3) <= 750.
These three variables are treated as general integer variables in the following computer program.
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
89 RANDOMIZE JJJJ
90 M = -3E+30
96 A(1) = 6 + FIX(RND * 13)
98 A(2) = 4 + FIX(RND * 9)
99 A(3) = 50 + FIX(RND * 701)
128 FOR I = 1 TO 1000
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)
156 REM r = (1 - RND * 2) * A(J)
158 REM X(J) = A(J) + (RND ^ (RND * 10)) * r
162 IF RND < .5 THEN X(J) = A(J) - 1 ELSE X(J) = A(J) + 1
169 NEXT IPP
238 IF X(1) < 6## THEN 1670
239 IF X(1) > 18## THEN 1670
248 IF X(2) < 4## THEN 1670
249 IF X(2) > 12## THEN 1670
258 IF X(3) < 50## THEN 1670
259 IF X(3) > 750## THEN 1670
449 PDU = -.112931 + .0170470 * X(1) + .0002220059 * X(3) + .0190297 * X(2) - 7.23331D-05 * X(1) ^ 2 - 2.43026D-07 * (X(3)) ^ 2 - 3.03374D-04 * (X(2)) ^ 2 + 1.58294D-05 * (X(1)) * X(3) + .00148333 * X(1) * X(2) - 3.96310D-05 * X(3) * X(2) + (1 / (1.76966 + .882071 * X(1) + .00686577 * X(3) - .447132 * X(2) - .0373631 * X(1) ^ 2 - 9.89173D-06 * (X(3)) ^ 2 + .0221831 * (X(2)) ^ 2 + .000517857 * (X(1)) * X(3) + .0109375 * X(1) * X(2) - 2.76786D-04 * X(3) * X(2)))
466 P = PDU
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 3
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -5555555 THEN 1999
1904 PRINT A(1), A(2), A(3), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [53]. The complete output of a single run through JJJJ= -31998 is shown below:
18 12 50 .8339616646335211
-32000
18 12 50 .8339616646335211
-31999
18 12 50 .8339616646335211
-31998
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 [53], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31998 was 1 or 2 seconds, not including the time for “Creating .EXE file" (7 seconds, including the time for “Creating .EXE file"). One can compare the computational results above with those in Madic and Radovanovic [35, p. 230, Table 5].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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