A Computer Program for Alkylation Process Optimization
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve the nonlinear programming formulation on page 42 of Bracken and McCormick [15, p. 42], which is briefly summarized as follows:
Maximize
( c1 * X(4) * X(7) - c2 * X(1) - c3 * X(2) - c4 * X(3) - c5 * X(5) )
subject to
X(j) LB <= X(j) <= X(j) UB, j=1, ..., 10,
(X(1) * (1.12 + .13167 * X(8) - .00667 * X(8) ^ 2)) - (99 / 100) * X(4) >= 0
-(X(1) * (1.12 + .13167 * X(8) - .00667 * X(8) ^ 2)) + (100 / 99) * X(4) >= 0
(86.35 + 1.098 * X(8) - .038 * X(8) ^ 2 + .325 * (X(6) - 89)) - (99 / 100) * X(7) >= 0
-(86.35 + 1.098 * X(8) - .038 * X(8) ^ 2 + .325 * (X(6) - 89)) + (100 / 99) * X(7) >= 0
(35.82 - .222 * X(10)) - (9 / 10) * X(9) >= 0
-(35.82 - .222 * X(10)) + (10 / 9) * X(9) >= 0
(-133 + 3 * X(7)) - (99 / 100) * X(10) >= 0
-(-133 + 3 * X(7)) + (100 / 99) * X(10) >= 0
1.22 * X(4) -X(1) - X(5) = 0
(98000 * X(3)) / (X(4) * X(9) + 1000 * X(3)) - X(6) = 0; this is correct, according to p. 40 of Reference 15
( (X(2) + X(5)) / X(1) ) - X(8) = 0.
The "final element" on p. 42 of Bracken an d McCormick [15] and four of the starting values (1745, 12000, 3048, and 1974) of Bracken and McCormick [15, p. 43, Table 4.2] help reduce the starting ranges of line 91, line 92, line 94, and line 95 below, which involve the four longest ranges, respectively.
0 REM DEFDBL A-Z
1 REM DEFINT I, J, K
2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(44), J44(44), PN(22), NN(22)
85 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3D+30
91 A(1) = 1700 + RND * 50
92 A(2) = 11900 + RND * 200
93 A(3) = 0 + RND * 120
94 A(4) = 3000 + RND * 50
95 A(5) = 1900 + RND * 50
96 A(6) = 85 + RND * 8
97 A(7) = 90 + RND * 5
98 A(8) = 3 + RND * 9
99 A(9) = 1.2 + RND * 2.8
100 A(10) = 145 + RND * 17
128 FOR i = 1 TO 100000
129 FOR KKQQ = 1 TO 10
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 10)
141 B = 1 + FIX(RND * 10)
144 IF RND < .9999 THEN 160 ELSE GOTO 167
160 r = (1 - RND * 2) * A(B)
164 X(B) = A(B) + (RND ^ (RND * 15)) * r
165 GOTO 168
167 REM IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)
168 NEXT IPP
181 X(5) = -X(1) + 1.22 * X(4)
184 X(8) = (X(2) + X(5)) / X(1)
187 REM X(6) = (98000 * X(3)) / (X(3) * X(9) + 1000 * X(3))
197 X(6) = (98000 * X(3)) / (X(4) * X(9) + 1000 * X(3))
210 IF (-133 + 3 * X(7)) - (99 / 100) * X(10) < 0 THEN 1670
214 IF -(-133 + 3 * X(7)) + (100 / 99) * X(10) < 0 THEN 1670
220 IF (35.82 - .222 * X(10)) - (9 / 10) * X(9) < 0 THEN 1670
224 IF -(35.82 - .222 * X(10)) + (10 / 9) * X(9) < 0 THEN 1670
230 IF (X(1) * (1.12 + .13167 * X(8) - .00667 * X(8) ^ 2)) - (99 / 100) * X(4) < 0 THEN 1670
235 IF -(X(1) * (1.12 + .13167 * X(8) - .00667 * X(8) ^ 2)) + (100 / 99) * X(4) < 0 THEN 1670
240 IF (86.35 + 1.098 * X(8) - .038 * X(8) ^ 2 + .325 * (X(6) - 89)) - (99 / 100) * X(7) < 0 THEN 1670
245 IF -(86.35 + 1.098 * X(8) - .038 * X(8) ^ 2 + .325 * (X(6) - 89)) + (100 / 99) * X(7) < 0 THEN 1670
324 IF X(1) > 2000 THEN 1670
325 IF X(1) < 0 THEN 1670
342 IF X(2) > 16000 THEN 1670
345 IF X(2) < 0 THEN 1670
351 IF X(3) > 120 THEN 1670
352 IF X(3) < 0 THEN 1670
353 IF X(4) > 5000 THEN 1670
354 IF X(4) < 0 THEN 1670
355 IF X(5) > 2000 THEN 1670
356 IF X(5) < 0 THEN 1670
361 IF X(6) > 93 THEN 1670
362 IF X(6) < 85 THEN 1670
363 IF X(7) > 95 THEN 1670
364 IF X(7) < 90 THEN 1670
365 IF X(8) > 12 THEN 1670
366 IF X(8) < 3 THEN 1670
367 IF X(9) > 4 THEN 1670
368 IF X(9) < 1.2 THEN 1670
369 IF X(10) > 162 THEN 1670
370 IF X(10) < 145 THEN 1670
468 PD1 = .063 * X(4) * X(7) - 5.04 * X(1) - .035 * X(2) - 10 * X(3) - 3.36 * X(5)
469 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 10
1455 A(KLX) = X(KLX)
1459 NEXT KLX
1670 NEXT i
1777 IF M < 1765 THEN 1999
1888 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), A(9), A(10), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -31834 is shown below:
1698.09 15711.85 54.65469 3031.221 2000
90.1657 94.99728 10.43046 1.566638 153.5229
1766.504 -31891
1698.208 15761.9595 54.46571 3031.318 2000
90.14706 95 10.45923 1.565209 153.5211
1767.145 -31834
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By using the following computer system and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31834 was 55 seconds, counting from "Starting program...". One can compare the computational results above with those in Bracken and McCormick [15, p. 44, Table 4.5] and in Babu and Angira [10, p. 997, Table 6].
The computational results presented above were obtained from the following computer system:
Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz
Installed memory (RAM): 4.00GB (3.87 GB usable)
System type: 64-bit Operating System.
Acknowledgement
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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