Jsun Yui Wong
The computer program listed below seeks to solve the following problem from page 32 of Raghav, Ali, and Bari [61; the second problem on p. 32]:
Minimize ((.8316 + (X(5) – 1) * .06) / X(1) + (.3358 + (X(6) – 1) * .02) / X(2) + (.1062 + (X(7) – 1) * .01) / X(3) + (.2791 + (X(8) – 1) * .02) / X(4))
subject to
((2.4 + (.9 / X(5))) * X(1) + (3.4 + (.8 / X(6))) * X(2) + (4 + (1.25 / X(7))) * X(3) + (4.6 + (1.68 / X(8))) * X(4)) <= 5000
2<= X(1) <= 1214
2<= X(2) <= 822
2<= X(3) <= 1028
2<= X(4) <= 786.
X(1) through X(4) are integer variables, and X(5) through X(8) are continuous and >1.
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
120 A(1) = 2 + ((RND * 500))
121 A(2) = 2 + ((RND * 500))
122 A(3) = 2 + ((RND * 500))
123 A(4) = 2 + ((RND * 500))
124 A(5) = 1 + ((RND * 3))
125 A(6) = 1 + ((RND * 3))
126 A(7) = 1 + ((RND * 3))
127 A(8) = 1 + ((RND * 3))
128 FOR I = 1 TO FIX(120000 + RND * 120000)
129 FOR KKQQ = 1 TO 8
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 4)
153 J = 1 + FIX(RND * 8)
154 IF RND < .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 * 2) ELSE X(J) = A(J) + FIX(1 + RND * 2)
169 NEXT IPP
170 FOR J44 = 1 TO 4
171 X(J44) = INT(X(J44))
172 IF X(J44) < 2 THEN 1670
173 NEXT J44
174 IF X(1) > 1214 THEN 1670
175 IF X(2) > 822 THEN 1670
176 IF X(3) > 1028 THEN 1670
177 IF X(4) > 786 THEN 1670
190 FOR J44 = 5 TO 8
192 IF X(J44) <= 1 THEN 1670
193 NEXT J44
423 IF ((2.4 + (.9 / X(5))) * X(1) + (3.4 + (.8 / X(6))) * X(2) + (4 + (1.25 / X(7))) * X(3) + (4.6 + (1.68 / X(8))) * X(4)) > 5000 THEN 1670
444 PDU = -((.8316 + (X(5) – 1) * .06) / X(1) + (.3358 + (X(6) – 1) * .02) / X(2) + (.1062 + (X(7) – 1) * .01) / X(3) + (.2791 + (X(8) – 1) * .02) / X(4))
466 P = PDU
1111 IF P <= M THEN 1670
1450 M = P
1454 FOR KLX = 1 TO 8
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < -.007 THEN 1999
1923 PRINT A(1), A(2), A(3), A(4)
1924 PRINT A(5), A(6), A(7), A(8), M, JJJJ
1999 NEXT JJJJ
.
This BASIC computer program was run with QB64v1000-win [76]. The output of a single run through JJJJ= -31997 is summarized below:
.
.
.
593 321 163 249
2.177165922925384 1.926564694447423 1.744560694620744
2.169946237545697 -4.537370279648064D-03 -31998
595 321 163 249
2.208299520140577 1.943336232570953 1.729004715705757
2.19337853751922 -4.53736834068757D-03 -31997
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 [76], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31997 was 7 seconds, not including the time for “Creating .EXE file” (20 seconds, total, including the time for “Creating .EXE file”). One can compare the computational results above with those on page 32 of Raghav, Ali, and Bari [61].
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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