Similar to the computer programs of the preceding papers, the computer program below seeks to solve Li and Sun's Problem 14.4, [10, p. 415], but with 300 unknowns instead of 100 unknowns. Specifically the computer program below tries to minimize the following:
300-1
SIGMA [ 100* ( X(i+1) - X(i)^2 )^2 + ( 1-X(i) )^2 ]
i=1
subject to -5<=X(i)<=5, X(i) integer, i=1, 2, 3,..., 300.
One notes line 85, line 86, line 174, and line 175.
For the purpose of testing the algorithm, none of the 300 elements of the starting solution vector of each JJJJ is made one, the optimal; see line 111 through line 117, which are as follows:
111 FOR J44=1 TO 300
114 IF RND<.5 THEN A(J44 )=2 +FIX(RND*4 ) ELSE A(J44)=-5+FIX(RND*6)
117 NEXT J44.
0 REM DEFDBL A-Z
1 DEFINT J,K,B,X
2 DIM A(10000),X(10000)
81 FOR JJJJ=-32000 TO 32000
85 LB=-FIX(RND*6)
86 UB=FIX(RND*6)
89 RANDOMIZE JJJJ
90 M=-1.5D+38
111 FOR J44=1 TO 300
114 IF RND<.5 THEN A(J44 )=2 +FIX(RND*4 ) ELSE A(J44)=-5+FIX(RND*6)
117 NEXT J44
128 FOR I=1 TO 3200
129 FOR KKQQ=1 TO 300
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
139 FOR IPP=1 TO FIX(1+.3)
140 B=1+FIX(RND*300)
143 GOTO 167
144 REM GOTO 168
145 IF RND<.5 THEN 150 ELSE 167
150 R=(1-RND*2)*A(B)
160 X(B)=(A(B) +RND^3*R)
162 GOTO 168
163 IF RND<.5 THEN X(B)=(A(B)-.001) ELSE X(B)=(A(B) +.001 )
165 GOTO 168
167 IF RND<.5 THEN X(B)=CINT(A(B)-1) ELSE X(B)=CINT(A(B) +1 )
168 REM IF A(B)=0 THEN X(B)=1 ELSE X(B)=0
169 NEXT IPP
171 FOR J44=1 TO 300
174 IF X(J44)>UB THEN X(J44 )=A(J44 )
175 IF X(J44)<LB THEN X(J44 )=A(J44 )
177 NEXT J44
401 SONE=0
402 FOR J44=1 TO 299
411 SONE=SONE+ 100* ( X(J44+1) - X(J44)^2 )^2 + ( 1-X(J44) )^2
421 NEXT J44
689 PD1=-SONE
1111 IF PD1<=M THEN 1670
1452 M=PD1
1454 FOR KLX=1 TO 300
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-100 THEN 1999
1936 PRINT A(96),A(97),A(298),A(299),A(300)
1939 PRINT M,JJJJ,LB,UB
1999 NEXT JJJJ
This BASIC computer program was run via basica/D of Microsoft's GW-BASIC 3.11 interpreter for DOS. See the BASIC manual [11]. Copied by hand from the screen, the computer program's complete output through JJJJ=-31928 is shown below:
1 1 1 1 1
-4 -31989 -4 4
1 1 1 1 1
-4 -31966 -5 5
1 1 1 1 1
0 -31963 -5 4
1 1 1 1 1
0 -31962 -5 4
1 1 1 1 1
-4 -31936 -4 5
1 1 1 1 1
-4 -31935 -4 4
1 1 1 1 1
-4 -31934 -4 4
1 1 1 1 1
0 -31928 -4 4
Above there is no rounding by hand.
M=0 is optimal; see Li and Sun [10, p. 415].
Of the 300 A's, only the 5 A's of line 1936 are shown above.
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 through JJJJ=-31928 was 23 minutes.
Acknowledgment
I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.
References
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[18] Jsun Yui Wong (2014, June 27). A Unified Computer Program for Schittkowski's Test Problem 377, Second Edition. http://nonlinearintegerprogrammingsolver.blogspot.ca/2014_06_01_archive.html
