Jsun Yui Wong
The computer program listed below seeks to solve the following problem based on the system reliability problem in Luus [25] and in Tambunen and Mawengkang [32]:
Maximize
15
product (1 - (1 - reliability(i)) ^ X(i))
i=1
subject to
15
sum cost(i) * X(i) <=400
i=1
15
sum weight(i) * X(i) <=414
i=1
X(i) =1, 2, 3,..., 10, i=1,..., 15.
X(1) through X(15) are general integer variables.
X(16) and X(17) below are slack variables added.
One notes line 107, which is 107 A(J44) = 1 + FIX(RND * 10).
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)
11 RR(1) = .90: RR(2) = .75: RR(3) = .65: RR(4) = .80: RR(5) = .85: RR(6) = .93: RR(7) = .78: RR(8) = .66: RR(9) = .78: RR(10) = .91: RR(11) = .79: RR(12) = .77: RR(13) = .67: RR(14) = .79: RR(15) = .67
31 CC(1) = 5: CC(2) = 4: CC(3) = 9: CC(4) = 7: CC(5) = 7: CC(6) = 5: CC(7) = 6: CC(8) = 9: CC(9) = 4: CC(10) = 5: CC(11) = 6: CC(12) = 7: CC(13) = 9: CC(14) = 8: CC(15) = 6
51 WW(1) = 8: WW(2) = 9: WW(3) = 6: WW(4) = 7: WW(5) = 8: WW(6) = 8: WW(7) = 9: WW(8) = 6: WW(9) = 7: WW(10) = 8: WW(11) = 9: WW(12) = 7: WW(13) = 6: WW(14) = 5: WW(15) = 7
88 FOR JJJJ = -32000 TO 32000
89 RANDOMIZE JJJJ
90 M = -3E+30
106 FOR J44 = 1 TO 15
107 A(J44) = 1 + FIX(RND * 10)
109 NEXT J44
128 FOR I = 1 TO 40000
129 FOR KKQQ = 1 TO 15
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
151 FOR IPP = 1 TO FIX(1 + RND * 3)
153 j = 1 + FIX(RND * 15)
154 r = (1 - RND * 2) * A(j)
155 X(j) = A(j) + (RND ^ (RND * 10)) * r
159 NEXT IPP
311 FOR J44 = 1 TO 15
312 X(J44) = INT(X(J44))
313 IF X(J44) < 1 THEN 1670
314 IF X(J44) > 10 THEN 1670
317 NEXT J44
371 SUMCON = 0
374 FOR J44 = 1 TO 15
376 SUMCON = SUMCON + CC(J44) * X(J44)
377 NEXT J44
378 X(16) = 400 - SUMCON
379 IF X(16) < 0 THEN X(16) = X(16) ELSE X(16) = 0
380 SUMWW = 0
381 FOR J44 = 1 TO 15
382 SUMWW = SUMWW + WW(J44) * X(J44)
383 NEXT J44
384 X(17) = 414 - SUMWW
385 IF X(17) < 0 THEN X(17) = X(17) ELSE X(17) = 0
386 SUMOBJ = 1
387 FOR J44 = 1 TO 15
388 SUMOBJ = SUMOBJ * (1 - (1 - RR(J44)) ^ X(J44))
389 NEXT J44
438 PDU = SUMOBJ + 1000000 * (X(16) + X(17))
466 P = PDU
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 17
1455 A(KLX) = X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M < .94 THEN 1999
1904 PRINT A(1), A(2), A(3), A(4)
1905 PRINT A(5), A(6), A(7), A(8)
1906 PRINT A(9), A(10), A(11), A(12)
1907 PRINT A(13), A(14), A(15), A(16), A(17)
1915 PRINT M, JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with QB64v1000-win [33]. The complete output through JJJJ = -31619 is shown below:
3 4 6 4
3 2 4 5
4 2 3 4
5 4 5 0 0
.9456133574581372 -31980
3 4 6 4
3 2 4 5
4 2 3 4
5 4 5 0 0
.9456133574581372 -31619
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 [33], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31619 was 100 seconds, not including the time for “Creating .EXE file” (110 seconds, total, including the time for “Creating .EXE file” ).
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[33] Wikipedia, QB64, https://en.wikipedia.org/wiki/QB64.
[34] 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/
[35] 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/
[36] 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/
[37] 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/
[38] 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/
[39] 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/
[40] 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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