Jsun Yui Wong
The computer program listed below seeks to solve the following "optimization problem of minimization of the surface roughness in machining AI Alloy SIC," Mellal and Williams [36, p. 46]:
Minimize .72412 + .00325 * X(1) - .19694 * X(2) + 4.19915 * X(3) - .18753 * X(4) - .000018 * X(1) ^ 2 - 3.42419 * X(3) ^ 2 + 3.33125 * X(2) * X(3) - .56484 * X(3) * X(4)
subject to
90<= X(1) <=210
.15<= X(2) <=.25
.20<= X(3) <=.60
.40<= X(4) <=1.20.
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)
81 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3E+30
122 A(1) = 90 + RND * 120
124 A(2) = .15 + RND * .10
126 A(3) = .20 + RND * .40
127 A(4) = .40 + RND * .80
128 FOR I = 1 TO 1000
129 FOR KKQQ = 1 TO 4
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 2)
153 J = 1 + FIX(RND * 4)
156 r = (1 - RND * 2) * A(J)
158 X(J) = A(J) + (RND ^ (RND * 10)) * r
169 NEXT IPP
233 IF X(1) < 90## THEN 1670
234 IF X(1) > 210## THEN 1670
236 IF X(2) < .15## THEN 1670
237 IF X(2) > .25## THEN 1670
241 IF X(3) < .20## THEN 1670
242 IF X(3) > .60## THEN 1670
245 IF X(4) < .4## THEN 1670
246 IF X(4) > 1.20## THEN 1670
447 PDU = -.72412 - .00325 * X(1) + .19694 * X(2) - 4.19915 * X(3) + .18753 * X(4) + .000018 * X(1) ^ 2 + 3.42419 * X(3) ^ 2 - 3.33125 * X(2) * X(3) + .56484 * X(3) * X(4)
466 P = PDU
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 4
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -33333333 THEN 1999
1904 PRINT A(1), A(2), A(3), A(4), M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [49]. The complete output of a single run through JJJJ= -31999 is shown below:
209.9999999991342 .1500000000000166 .2000000000000256
1.19999999999999 -1.025481300003811 -32000
209.999999998173 .1500000000000021 .2000000000000246
1.199999999999485 -1.025481300008095 -31999
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 [49], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31999 was 1 or 2 seconds, not including the time for “Creating .EXE file." One can compare the computational results above with those in Mellal and Williams [36, p. 46, Table 5].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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