Jsun Yui Wong
The following computer program uses 16900000 and 7.477 in line 205 and line 569, respectively.
These two numbers are taken from Nema, Goulermas, Sparrow, and Cook [44, p. 1421].
Thus, in this paper line 205 and line 569 are as follows:
205 X(17)= 1- ( ( 745*X(4)/(X(2)*X(3)) )^2 + 16900000#) ^.5 / (110*X(6)^3 )
569 P= -.7854*X(1)*X(2)^2 *(3.3333*X(3)^2+14.9334*X(3)-43.0934 ) +1.508*X(1)*(X(6) ^2 +X(7)^2 ) -7.477*(X(6)^3 +X(7) ^3 ) -.7854*( X(4)*X(6)^2 +X(5)*X(7) ^2 ) +PTOTAL
One notes that line 193 of the followong computer program is
193 X(12)= 1.002467532# - ( 1.1*X(7) +1.9 ) /X(5). This 1.002467532 is based on 1.0025 of Sun, Zeng, and Pan [52, p. 3092]; for more details see Sun, Zeng, and Pan [52, p. 3092].
In contrast to the preceding paper, in the present paper all seven design variables are discrete; X(3) is an integer, as well.
0 DEFDBL A-Z
1 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)
4 REM DIM PE(35,35)
5 REM DIM SD(35,35)
88 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-3D+30
107 A(1)=2.6+ +FIX (RND*11) *.1
109 A(2)=.7+ FIX ( RND*2 ) *.1
111 A(3)=17+FIX( RND*12)
113 A(4)=7.3+ FIX( RND *11) *.1
114 A(5)=7.3+ FIX( RND *11) *.1
115 A(6)=2.9+ FIX(RND*101 ) *.01
116 A(7)=5+ FIX(RND*51 ) *.01
126 IMAR=10+FIX(RND*1500)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 7
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*7)
144 IF JJJJ<-32222 THEN 162 ELSE 145
145 IF B=3 GOTO 162
147 IF B=1 OR B=2 OR B=4 OR B=5 GOTO 150 ELSE IF B=6 OR B=7 GOTO 158
150 IF RND<.5 THEN X(B)=A(B)-FIX(1+RND*2)*.1 ELSE X(B)=A(B)+FIX(1+RND*2)*.1
152 GOTO 179
158 IF RND<.5 THEN X(B)=A(B)-FIX(1+RND*2)*.01 ELSE X(B)=A(B)+FIX(1+RND*2)*.01
161 GOTO 179
162 IF RND<.5 THEN X(B)=A(B)-FIX(1+RND*2) ELSE X(B)=A(B)+FIX(1+RND*2)
163 GOTO 179
164 FOR J44=1 TO 7
165 IF ABS(X(J44))>32000 THEN 1670
166 NEXT J44
176 IF RND<.9 THEN R=(1-RND*2)*A(B) ELSE IF RND<.5 THEN R=(1-RND*2)*(A(B) -.1) ELSE R=(1-RND*2)*(A(B) +.1)
177 IF RND<.1 THEN X(B)=CINT(A(B))-FIX(1+RND*3) ELSE IF RND<.1 THEN X(B)=CINT(A(B))+FIX(1+RND*3) ELSE X(B)=A(B)+(RND^(RND*10) )*R
178 REM IF RND<.1 THEN X(B)=INT(A(B))-FIX(1+RND*3) ELSE IF RND<.1 THEN X(B)=INT(A(B))+FIX(1+RND*3) ELSE X(B)=A(B)+(RND^(RND*10) )*R
179 NEXT IPP
181 IF ABS(X(2))<.0000001 THEN 1670
182 X(8)= 12 -X(1)/X(2)
185 X(9)= -5 +X(1)/X(2)
188 X(10)= 40 -X(2)*X(3)
190 IF ABS( X(4)) <.0000001 THEN 1670
191 X(11)= 1- ( 1.5*X(6) +1.9 ) /X(4)
192 IF ABS( X(5)) <.0000001 THEN 1670
193 X(12)= 1.002467532# - ( 1.1*X(7) +1.9 ) /X(5)
194 IF ABS(( X(1) * X(2)^2 * X(3) ) )<.0000001 THEN 1670
195 X(13)= 1- 27/( X(1) * X(2)^2 * X(3) )
196 IF ABS (( X(1) * X(2)^2 * X(3) ^2 ) )<.0000001 THEN 1670
197 X(14)= 1- 397.5 /( X(1) * X(2)^2 * X(3) ^2 )
198 IF ABS ( ( X(2) * X(3) * X(6) ^4 ) )<.0000001 THEN 1670
199 X(15)= 1- 1.93*X(4)^3 / ( X(2) * X(3) * X(6) ^4 )
200 IF ABS( ( X(2) * X(3) * X(7) ^4 ) )<.0000001 THEN 1670
201 X(16)= 1- 1.93*X(5)^3 / ( X(2) * X(3) * X(7) ^4 )
204 IF ABS( (110*X(6)^3 ) ) <.0000001 THEN 1670
205 X(17)= 1- ( ( 745*X(4)/(X(2)*X(3)) )^2 + 16900000#) ^.5 / (110*X(6)^3 )
208 IF ABS( (85*X(7)^3 ) )<.0000001 THEN 1670
209 X(18)= 1- ( ( 745*X(5)/(X(2)*X(3)) )^2 + 157500000#) ^.5 / (85*X(7)^3 )
221 IF X(1)<2.6 THEN 1670
222 IF X(2)<.7 THEN 1670
223 IF X(3)<17 THEN 1670
224 IF X(4)<7.3 THEN 1670
225 IF X(5)<7.3 THEN 1670
226 IF X(6)<2.9 THEN 1670
227 IF X(7)<5 THEN 1670
231 IF X(1)>3.6 THEN 1670
232 IF X(2)>.8 THEN 1670
233 IF X(3)>28 THEN 1670
234 IF X(4)>8.3 THEN 1670
235 IF X(5)>8.3 THEN 1670
236 IF X(6)>3.9 THEN 1670
237 IF X(7)>5.5 THEN 1670
421 FOR J44=8 TO 18
422 IF X(J44)<0 THEN P(J44)=9000000!*X(J44) ELSE P(J44)=0
423 NEXT J44
425 PTOTAL=P(8)+P(9)+P(10) +P(11)+P(12)+P(13)+P(14) +P(15)+P(16)+P(17)+P(18)
569 P= -.7854*X(1)*X(2)^2 *(3.3333*X(3)^2+14.9334*X(3)-43.0934 ) +1.508*X(1)*(X(6) ^2 +X(7)^2 ) -7.477*(X(6)^3 +X(7) ^3 ) -.7854*( X(4)*X(6)^2 +X(5)*X(7) ^2 ) +PTOTAL
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 18
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-2998.77 THEN 1999
1904 PRINT A(1),A(2),A(3)
1907 PRINT A(4),A(5),A(6)
1989 PRINT A(7),M,JJJJ
1990 PRINT A(8),A(9)
1991 PRINT A(10),A(11),A(12)
1992 PRINT A(13),A(14),A(15)
1993 PRINT A(16),A(17),A(18)
1999 NEXT JJJJ
This BASIC computer program was run via basica/D of Microsoft's GW-BASIC 3.11 interpreter for DOS. The complete output through JJJJ=-31999 is shown below. What follows is a hand copy from the computer-monitor screen; below there is no rounding by hand.
3.499999955296516 .6999999880790711 17
7.300000190734863 7.700000002980232 3.359999952837825
5.289999825879932 -2998.631502803308 -31982
6.999999978712627 2.12873735305763D-08
28.10000020265579 4.931510628957177D-02 1.151144091160461D-08
7.391523702726792D-02 .1979984895824379 .5049809955171642
.9054503581123036 8.711443202614813D-03 1.898909155188588D-03
3.5 .6999999880790711 17
7.300000369548798 7.700000375509262 3.359999960288405
5.290000092238188 -2998.631701402511 -31960
6.999999914850506 8.514949401128291D-08
28.10000020265579 4.931512804571248D-02 2.196003320853457D-08
7.391524885561507D-02 .1979984998259412 .504980963531294
.9054503634320382 8.711449500538024D-03 1.899059851030838D-03
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM, and the IBM basica/D interpreter, version GW BASIC 3.11, the wall-clock time for obtaining the output shown above was twelve seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[52] Chaoli Sun, Jianchao Zeng, Jeng-Shyang Pan (2011), A Modified Particle Swarm Optimization with Feasobo;oty-Based Rules for Mixed-Variables Optimization Problems. International Journal of Innovative Computing, Information and Control, Volume 7, Number 6, June 2011, 3081-3096.
[53] Jung-Fa Tsai (2010), Global Optimization for Signomial Discrete Programming Problems in Engineering Design. Engineering Optimization, 42:9, pp. 833-843.
[54] L.-W. Tsai, A. P. Morgan, Solving the Kinematics of the Most General Six- and Five-Degree-of Freedom Manipulators by Continuation Methods. Journal of Mechanisms, Transmissions, and Automation in Design, June 1985, Vol. 107, pp. 189-200.
[55] 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/
[56] 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/
[57] Jsun Yui Wong (2011, May 15). The Domino Method Applied to Solving a Nonlinear System of Ten Equations of a Model of Propane-in-Air Combustion, Fourth Edition. Retrieved from http://computationalresultsfromcomputerprograms.wordpress.com/2011/05/15/
[58] Jsun Yui Wong (2011, May 5). The Domino Method Applied to Solving a Nonlinear System of Five Equations, Third Edition. Retrieved from http://computationalresultsfromcomputerprograms.wordpress.com/2011/05/05/
[59] 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/
[60] Jsun Yui Wong (2012, April 10). The Domino Method of General Integer Nonlinear Programming Applied to a Coil Compression Spring Design. Retrieved from http://myblogsubstance.typepad.com/substance/2012/04/
[61] Jsun Yui Wong (2012, April 21). The Domino Method of General Integer Nonlinear Programming Applied to a Five-Step Cantilever Beam Design. Retrieved from http://computationalresultsfromcomputerprograms.wordpress.com/2012/04/21/
[62] 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/
[63] Jsun Yui Wong (2013, January 14). The Domino Method of General Integer Nonlinear Programming Applied to a Nonlinear Programming Problem with Integer Variables and Continuous Variables, Revised Edition. Retrieved from http://myblogsubstance.typepad.com/substance/2013/01/
[64] Jsun Yui Wong (2013, January 24). The Domino Method of General Integer Nonlinear Programming Applied to a Nonlinear Programming Problem with Eight 0-1 Variables and Nine Continuous Variables. Retrieved from http://computationalresultsfromcomputerprograms.wordpress.com/2013/01/24/
The following computer program uses 16900000 and 7.477 in line 205 and line 569, respectively.
These two numbers are taken from Nema, Goulermas, Sparrow, and Cook [44, p. 1421].
Thus, in this paper line 205 and line 569 are as follows:
205 X(17)= 1- ( ( 745*X(4)/(X(2)*X(3)) )^2 + 16900000#) ^.5 / (110*X(6)^3 )
569 P= -.7854*X(1)*X(2)^2 *(3.3333*X(3)^2+14.9334*X(3)-43.0934 ) +1.508*X(1)*(X(6) ^2 +X(7)^2 ) -7.477*(X(6)^3 +X(7) ^3 ) -.7854*( X(4)*X(6)^2 +X(5)*X(7) ^2 ) +PTOTAL
One notes that line 193 of the followong computer program is
193 X(12)= 1.002467532# - ( 1.1*X(7) +1.9 ) /X(5). This 1.002467532 is based on 1.0025 of Sun, Zeng, and Pan [52, p. 3092]; for more details see Sun, Zeng, and Pan [52, p. 3092].
In contrast to the preceding paper, in the present paper all seven design variables are discrete; X(3) is an integer, as well.
0 DEFDBL A-Z
1 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)
4 REM DIM PE(35,35)
5 REM DIM SD(35,35)
88 FOR JJJJ=-32000 TO 32000
89 RANDOMIZE JJJJ
90 M=-3D+30
107 A(1)=2.6+ +FIX (RND*11) *.1
109 A(2)=.7+ FIX ( RND*2 ) *.1
111 A(3)=17+FIX( RND*12)
113 A(4)=7.3+ FIX( RND *11) *.1
114 A(5)=7.3+ FIX( RND *11) *.1
115 A(6)=2.9+ FIX(RND*101 ) *.01
116 A(7)=5+ FIX(RND*51 ) *.01
126 IMAR=10+FIX(RND*1500)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 7
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*7)
144 IF JJJJ<-32222 THEN 162 ELSE 145
145 IF B=3 GOTO 162
147 IF B=1 OR B=2 OR B=4 OR B=5 GOTO 150 ELSE IF B=6 OR B=7 GOTO 158
150 IF RND<.5 THEN X(B)=A(B)-FIX(1+RND*2)*.1 ELSE X(B)=A(B)+FIX(1+RND*2)*.1
152 GOTO 179
158 IF RND<.5 THEN X(B)=A(B)-FIX(1+RND*2)*.01 ELSE X(B)=A(B)+FIX(1+RND*2)*.01
161 GOTO 179
162 IF RND<.5 THEN X(B)=A(B)-FIX(1+RND*2) ELSE X(B)=A(B)+FIX(1+RND*2)
163 GOTO 179
164 FOR J44=1 TO 7
165 IF ABS(X(J44))>32000 THEN 1670
166 NEXT J44
176 IF RND<.9 THEN R=(1-RND*2)*A(B) ELSE IF RND<.5 THEN R=(1-RND*2)*(A(B) -.1) ELSE R=(1-RND*2)*(A(B) +.1)
177 IF RND<.1 THEN X(B)=CINT(A(B))-FIX(1+RND*3) ELSE IF RND<.1 THEN X(B)=CINT(A(B))+FIX(1+RND*3) ELSE X(B)=A(B)+(RND^(RND*10) )*R
178 REM IF RND<.1 THEN X(B)=INT(A(B))-FIX(1+RND*3) ELSE IF RND<.1 THEN X(B)=INT(A(B))+FIX(1+RND*3) ELSE X(B)=A(B)+(RND^(RND*10) )*R
179 NEXT IPP
181 IF ABS(X(2))<.0000001 THEN 1670
182 X(8)= 12 -X(1)/X(2)
185 X(9)= -5 +X(1)/X(2)
188 X(10)= 40 -X(2)*X(3)
190 IF ABS( X(4)) <.0000001 THEN 1670
191 X(11)= 1- ( 1.5*X(6) +1.9 ) /X(4)
192 IF ABS( X(5)) <.0000001 THEN 1670
193 X(12)= 1.002467532# - ( 1.1*X(7) +1.9 ) /X(5)
194 IF ABS(( X(1) * X(2)^2 * X(3) ) )<.0000001 THEN 1670
195 X(13)= 1- 27/( X(1) * X(2)^2 * X(3) )
196 IF ABS (( X(1) * X(2)^2 * X(3) ^2 ) )<.0000001 THEN 1670
197 X(14)= 1- 397.5 /( X(1) * X(2)^2 * X(3) ^2 )
198 IF ABS ( ( X(2) * X(3) * X(6) ^4 ) )<.0000001 THEN 1670
199 X(15)= 1- 1.93*X(4)^3 / ( X(2) * X(3) * X(6) ^4 )
200 IF ABS( ( X(2) * X(3) * X(7) ^4 ) )<.0000001 THEN 1670
201 X(16)= 1- 1.93*X(5)^3 / ( X(2) * X(3) * X(7) ^4 )
204 IF ABS( (110*X(6)^3 ) ) <.0000001 THEN 1670
205 X(17)= 1- ( ( 745*X(4)/(X(2)*X(3)) )^2 + 16900000#) ^.5 / (110*X(6)^3 )
208 IF ABS( (85*X(7)^3 ) )<.0000001 THEN 1670
209 X(18)= 1- ( ( 745*X(5)/(X(2)*X(3)) )^2 + 157500000#) ^.5 / (85*X(7)^3 )
221 IF X(1)<2.6 THEN 1670
222 IF X(2)<.7 THEN 1670
223 IF X(3)<17 THEN 1670
224 IF X(4)<7.3 THEN 1670
225 IF X(5)<7.3 THEN 1670
226 IF X(6)<2.9 THEN 1670
227 IF X(7)<5 THEN 1670
231 IF X(1)>3.6 THEN 1670
232 IF X(2)>.8 THEN 1670
233 IF X(3)>28 THEN 1670
234 IF X(4)>8.3 THEN 1670
235 IF X(5)>8.3 THEN 1670
236 IF X(6)>3.9 THEN 1670
237 IF X(7)>5.5 THEN 1670
421 FOR J44=8 TO 18
422 IF X(J44)<0 THEN P(J44)=9000000!*X(J44) ELSE P(J44)=0
423 NEXT J44
425 PTOTAL=P(8)+P(9)+P(10) +P(11)+P(12)+P(13)+P(14) +P(15)+P(16)+P(17)+P(18)
569 P= -.7854*X(1)*X(2)^2 *(3.3333*X(3)^2+14.9334*X(3)-43.0934 ) +1.508*X(1)*(X(6) ^2 +X(7)^2 ) -7.477*(X(6)^3 +X(7) ^3 ) -.7854*( X(4)*X(6)^2 +X(5)*X(7) ^2 ) +PTOTAL
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 18
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-2998.77 THEN 1999
1904 PRINT A(1),A(2),A(3)
1907 PRINT A(4),A(5),A(6)
1989 PRINT A(7),M,JJJJ
1990 PRINT A(8),A(9)
1991 PRINT A(10),A(11),A(12)
1992 PRINT A(13),A(14),A(15)
1993 PRINT A(16),A(17),A(18)
1999 NEXT JJJJ
This BASIC computer program was run via basica/D of Microsoft's GW-BASIC 3.11 interpreter for DOS. The complete output through JJJJ=-31999 is shown below. What follows is a hand copy from the computer-monitor screen; below there is no rounding by hand.
3.499999955296516 .6999999880790711 17
7.300000190734863 7.700000002980232 3.359999952837825
5.289999825879932 -2998.631502803308 -31982
6.999999978712627 2.12873735305763D-08
28.10000020265579 4.931510628957177D-02 1.151144091160461D-08
7.391523702726792D-02 .1979984895824379 .5049809955171642
.9054503581123036 8.711443202614813D-03 1.898909155188588D-03
3.5 .6999999880790711 17
7.300000369548798 7.700000375509262 3.359999960288405
5.290000092238188 -2998.631701402511 -31960
6.999999914850506 8.514949401128291D-08
28.10000020265579 4.931512804571248D-02 2.196003320853457D-08
7.391524885561507D-02 .1979984998259412 .504980963531294
.9054503634320382 8.711449500538024D-03 1.899059851030838D-03
On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM, and the IBM basica/D interpreter, version GW BASIC 3.11, the wall-clock time for obtaining the output shown above was twelve seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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[56] 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/
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