A Computer Program for a Chemical Equilibrium Problem
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the following nonlinear programming problem from Bracken and McCormick [15, p. 48]:
Minimize
T1+ … + T10
where T1 = X(1) * (-6.089 + LOG(X(1) / S)), . .., T10 = X(10) * (-22.179 + LOG(X(10) / S)),
where S = X(1) + X(2) + X(3) + X(4) + X(5) + X(6) + X(7) + X(8) + X(9) + X(10)
subject to
X(1) + 2 * X(2) + 2 * X(3) + X(6) + X(10) =2
X(4) + 2 * X(5) + X(6) + X(7) =1
X(3) + X(7) + X(8) + 2 * X(9) + X(10) =1
X(1)>=0,…, X(10)>=0.
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
92 FOR J44 = 1 TO 10
93 A(J44) = .0001 + RND
94 NEXT J44
128 FOR i = 1 TO 30000
129 FOR KKQQ = 1 TO 10
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 7)
141 B = 1 + FIX(RND * 10)
144 IF RND < .5 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
281 X(7) = 1 - X(4) - 2 * X(5) - X(6)
284 X(1) = 2 - 2 * X(2) - 2 * X(3) - X(6) - X(10)
288 X(8) = 1 - X(3) - X(7) - 2 * X(9) - X(10)
311 FOR J44 = 1 TO 10
321 IF X(J44) < 0 THEN 1670
322 IF X(J44) > 10 THEN 1670
331 NEXT J44
447 S = X(1) + X(2) + X(3) + X(4) + X(5) + X(6) + X(7) + X(8) + X(9) + X(10)
451 T1 = X(1) * (-6.089 + LOG(X(1) / S))
452 T2 = X(2) * (-17.164 + LOG(X(2) / S))
453 T3 = X(3) * (-34.054 + LOG(X(3) / S))
454 T4 = X(4) * (-5.914 + LOG(X(4) / S))
455 T5 = X(5) * (-24.721 + LOG(X(5) / S))
456 T6 = X(6) * (-14.986 + LOG(X(6) / S))
457 T7 = X(7) * (-24.100 + LOG(X(7) / S))
458 T8 = X(8) * (-10.708 + LOG(X(8) / S))
459 T9 = X(9) * (-26.662 + LOG(X(9) / S))
460 T10 = X(10) * (-22.179 + LOG(X(10) / S))
464 PD1 = -T1 - T2 - T3 - T4 - T5 - T6 - T7 - T8 - T9 - T10
466 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 0 TO 10
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1670 NEXT i
1777 IF M < -47.77 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= -31972 is shown below:
4.083138E-02 .1497418 .7803211 1.408125E-03
.4850834 6.988918E-04 2.772626E-02
1.817354E-02 3.771763E-02 9.834383E-02
47.76106 -31990
4.079816E-02 .1529855 .7762265 1.414638E-03
.4849713 7.259846E-04 2.791685E-02
.0182576 3.877413E-02 .1000517 47.76088
-31972
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 = -31972 was 3 seconds, counting from “Starting program…”. One can compare the computational results above with those in Bracken and McCormick [15, p. 49, Table 5.2].
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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computerprogramsandresults 