Jsun Yui Wong
The computer program listed below seeks to solve the following mixed-integer nonlinear programming problem from Dhingra [13, pp. 577-578], Deep et al. [12, p. 517, Problem 18], and Liu and Qin [27, p. 2054, Problem 3]:
Maximize (1 - (1 - X(5)) ^ X(1)) * (1 - (1 - X(6)) ^ X(2)) * (1 - (1 - X(7)) ^ X(3)) * (1 - (1 - X(8)) ^ X(4))
subject to
1 * X(1) ^ 2 + 2 * X(2) ^ 2 + 3 * X(3) ^ 2 + 2 * X(4) ^ 2<=250
(1 / 10 ^ 5) * (-1000 / LOG(X(5))) ^ 1.5 * (X(1) + EXP(X(1) / 4)) + (2.3 / 10 ^ 5) * (-1000 / LOG(X(6))) ^ 1.5 * (X(2) + EXP(X(2) / 4)) + (.3 / 10 ^ 5) * (-1000 / LOG(X(7))) ^ 1.5 * (X(3) + EXP(X(3) / 4)) + (2.3 / 10 ^ 5) * (-1000 / LOG(X(8))) ^ 1.5 * (X(4) + EXP(X(4) / 4))<=400
6 * X(1) * EXP(X(1) / 4) + (6) * X(2) * EXP(X(2) / 4) + (8) * X(3) * EXP(X(3) / 4) + (7) * X(4) * EXP(X(4) / 4)<=500
1<= X(i) <= 10, i=1, 2, 3, 4
X(1) through X(4) are integer variables
.5<= X(5), X(6), X(7), X(8)<=.999999.
X(9) through X(11) below are slack variables added.
The sequence of line 341 through line 346 aims to get domino effect.
The formulation above has the operating time = 1000 hours (see above and see line 346 below), which comes from Dhingra [13, p. 578, Table 1], whereas the operating time (T) of the preceding paper is 100 hours; this 100 hours comes from Deep et al. [12, p. 517].
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)
81 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3E+30
95 FOR J44 = 1 TO 4
97 A(J44) = FIX(1 + RND * 10)
99 NEXT J44
115 FOR J44 = 5 TO 8
117 A(J44) = .5 + RND * .499999
119 NEXT J44
128 FOR I = 1 TO 20000
129 FOR KKQQ = 1 TO 8
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 3)
153 j = 1 + FIX(RND * 8)
154 REM GOTO 164
155 REM IF j > 4.5 THEN GOTO 156 ELSE GOTO 164
156 r = (1 - RND * 2) * A(j)
158 X(j) = A(j) + (RND ^ (RND * 10)) * r
161 GOTO 169
164 IF RND < .5 THEN X(j) = A(j) - 1 ELSE X(j) = A(j) + 1
169 NEXT IPP
326 FOR J44 = 1 TO 4
327 X(J44) = INT(X(J44))
328 IF X(J44) < 1 THEN 1670
329 IF X(J44) > 10 THEN 1670
331 NEXT J44
336 FOR J44 = 5 TO 8
338 IF X(J44) < .5## THEN 1670
339 IF X(J44) > .999999## THEN 1670
340 NEXT J44
341 X(9) = 250 - 1 * X(1) ^ 2 - 2 * X(2) ^ 2 - 3 * X(3) ^ 2 - 2 * X(4) ^ 2
343 X(10) = 500 - 6 * X(1) * EXP(X(1) / 4) - (6) * X(2) * EXP(X(2) / 4) - (8) * X(3) * EXP(X(3) / 4) - (7) * X(4) * EXP(X(4) / 4)
346 X(11) = 400 - (1 / 10 ^ 5) * (-1000 / LOG(X(5))) ^ 1.5 * (X(1) + EXP(X(1) / 4)) - (2.3 / 10 ^ 5) * (-1000 / LOG(X(6))) ^ 1.5 * (X(2) + EXP(X(2) / 4)) - (.3 / 10 ^ 5) * (-1000 / LOG(X(7))) ^ 1.5 * (X(3) + EXP(X(3) / 4)) - (2.3 / 10 ^ 5) * (-1000 / LOG(X(8))) ^ 1.5 * (X(4) + EXP(X(4) / 4))
355 FOR J44 = 9 TO 11
357 IF X(J44) < 0 THEN X(J44) = X(J44) ELSE X(J44) = 0
359 NEXT J44
393 PDU = (1 - (1 - X(5)) ^ X(1)) * (1 - (1 - X(6)) ^ X(2)) * (1 - (1 - X(7)) ^ X(3)) * (1 - (1 - X(8)) ^ X(4)) + 1000000 * (X(9) + X(10) + X(11))
466 P = PDU
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 11
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < .9999545 THEN 1999
1904 PRINT A(1), A(2), A(3)
1905 PRINT A(4), A(5), A(6)
1906 PRINT A(7), A(8), A(9)
1907 PRINT A(10), A(11)
1909 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [39]. The complete output through JJJJ= -31931 is shown below:
5 5 4
6 .9028407381597928 .8878405733015752
.9485972637679766 .8487191793558045 0
0 0
.999954625226262 -31997
5 5 4
6 .8995776108129475 .8884690670098343
.9479772095053202 .851707452609658 0
0 0
.9999545713940635 -31931
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 [39], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31931 was 54 seconds, not including the time for “Creating .EXE file” (62 seconds, total, including the time for “Creating .EXE file” ). One can compare the computational results above with those in Dhingra [13, p. 578, Table 2], in Deep et al. [12, p. 517, Problem-18], and in Liu and Qin [27, p. 2054, Table IX]:
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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[40] Jsun Yui Wong (2009, July 18). An Integer Programming Computer Program Applied to One-Dimensional Space Allocation. Retrieved from http://wongsllllblog.blogspot.com/2009/07/
[41] Jsun Yui Wong (2009, December 18). A Heuristic Nonlinear Integer Solver Applied to a Problem of Assignment of Facilities to Locations. Retrieved from http://wongsnewnewblog.blogspot.ca/2009/12/
[42] Jsun Yui Wong (2011, July 23). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to Three Instances of the Haverly Pooling Problem. Retrieved from http://myblogsubstance.typepad.com/substance/2011/07/
[43] Jsun Yui Wong (2011 July 27). A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to an Alkylation-Process Model, Sixth Edition. Retrieved from http://computationalresultsfromcomputerprograms.wordpress.com/2011/07/27/
[44] Jsun Yui Wong (2012, April 24). The Domino Method of General Integer Nonlinear Programming Applied to Problem 10 of Lawler and Bell. Retrieved from http://computationalresultsfromcomputerprograms.wordpress.com/2012/4/24/
[45] Jsun Yui Wong (2012, September 27). A Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a Linear Ordering Problem with 22 Facilities. Retrieved from http://computationalresultsfromcomputerprograms.wordpress.com/2012/9/27/
[46] Jsun Yui Wong (2013 January 10). The Domino Method of General Integer Nonlinear Programming Applied to Alkylation Process Optimization. http://myblogsubstance.typepad.com/substance/2013/01/
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