The following computer program seeks to solve the transformer design model on page 258 of Papalambros and Wilde [35] plus the modification that X(5) and X(6) are continuous variables [35, p. 258]. That is in contrast to the earlier edition. This modification is implemented by line 145 of the following computer program.
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
100 FOR KLQ=1 TO 6
101 A(KLQ)=1+FIX(RND*10)
102 NEXT KLQ
126 IMAR=10+FIX(RND*1500)
128 FOR I=1 TO IMAR
129 FOR KKQQ=1 TO 6
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+RND*3)
140 B=1+FIX(RND*6)
145 IF B=5 OR B=6 GOTO 164
159 REM FOR IPP=1 TO FIX(1+RND*3)
160 REM B=1+FIX(RND*6)
161 IF JJJJ<-31000 THEN 162 ELSE 164
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 6
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
194 X(7)=-2.07+.001*X(1)*X(2)*X(3)*X(4)*X(5)*X(6)
195 X(8)=-.00062*X(1)*X(4)*X(5)^2 *( X(1)+X(2)+X(3) ) -.00058*X(2)*X(3) *X(6)^2 *(X(1)+1.57*X(2)+X(4) ) +1.2
211 FOR J44=1 TO 6
212 IF X(J44)<0 THEN 1670
214 NEXT J44
221 FOR J44=7 TO 8
222 IF X(J44)<0 THEN P(J44)=9000000!*X(J44) ELSE P(J44)=0
223 NEXT J44
225 PTOTAL=P(7) +P(8)
569 P=-.0204*X(1)*X(4)*(X(1)+X(2)+X(3) ) -.0187*X(2)*X(3)*(X(1)+1.57*X(2)+X(4) ) -.0607*X(1)*X(4)*X(5)^2 *(X(1)+X(2)+X(3) ) -.0437*X(2)*X(3)*X(6)^2 *(X(1)+1.57*X(2)+X(4) ) +PTOTAL
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 8
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-131.06 THEN 1999
1904 PRINT A(1),A(2),A(3)
1907 PRINT A(4),A(5),A(6)
1908 PRINT A(7),A(8)
1989 PRINT M,JJJJ
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=-31717 is shown below. What follows is a hand copy from the computer-monitor screen; below there is no rounding by hand.
5 4 9
10 .9417716942259909 1.221103893634372
2.113998212871504D-06 4.255816646443064D-02
-131.0573108496266 -31998
5 4 9
10 .9554880511619355 1.203573362878344
1.055456053111747D-07 4.692354209584065D-02
-131.0559753298313 -31816
5 4 9
10 .9454661009311858 1.216331190689866
2.147976241317906D-11 4.383658270016441D-02
-131.0487522710977 -31806
5 4 9
10 .9522007136578346 1.20772847041976
5.66636332299808D-09 .0459710778736738
-131.0487990984942 -31717
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 4 minutes and 20 seconds.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
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