Solving an Instance (n=200) of the Michalewicz and Schoenauer Test Problem G3

 

Jsun Yui Wong

  

The computer program listed below seeks to solve the following problem from Michalewicz and Schoenauer [72, p. 10, MIT Press version, n=200]:  

    

maximize     (200^.5)^200 pie   x(i), i=1 through 200   

 

subject  to      

 

sigma x(i)^2=1,  i=1 through 200

 

0<=  X(i) <=1, i=1, 2,..., 200. 

 

One notes line 23, which is 23 A(J44) = RND * .1.

   

0 DEFDBL A-Z

 2 REM    DEFINT K

 3 DIM B(99), N(99), A(100255), H(99), L(99), U(99), X(100250), D(111), P(511), PS(33), J(30003), J44(30003), KKQQ(30003), KLX(30003), W(10111)

 

12 FOR JJJJ = -32000 TO 32000 STEP .01

 

    13 RANDOMIZE JJJJ

 

    16 M = -1D+37

 

    18 FOR J44 = 1 TO 200

 

        21 REM  A(J44) = 1 + RND ^ 4

 

        22 REM  A(J44) = 0 + RND ^ 14

 

        23 A(J44) = RND * .1

     

    25 NEXT J44

 

    128 FOR I = 1 TO 10000

  

        129 FOR KKQQ = 1 TO 200

  

            130 X(KKQQ) = A(KKQQ)

 

        131 NEXT KKQQ

 

        135 FOR IPP = 1 TO (1 + FIX(RND ^ 5 * 5))

 

 

            148 J = 1 + FIX(RND * 205)

 

 

 

            153 REM    GOTO 162

 

            154 IF RND < .333 THEN GOTO 156 ELSE IF RND < .5 THEN GOTO 162 ELSE GOTO 172

 

 

            156 REM

 

            157 R = (1 - RND * 2) * (A(J))

 

            160 X(J) = A(J) + (RND ^ (RND * 30)) * R

 

            161 GOTO 174

 

            162 REM    IF RND < .16666 THEN X(J) = A(J) – FIX(1 + RND * 2.3) ELSE IF RND < .33333 THEN X(J) = A(J) + FIX(1 + RND * 2.3) ELSE IF RND < .5 THEN X(J) = A(J) – FIX(1 + RND * 20.3) ELSE IF RND < .66666 THEN X(J) = A(J) + FIX(1 + RND * 20.3) ELSE IF RND < .83333 THEN X(J) = A(J) – FIX(1 + RND * 200.3) ELSE X(J) = A(J) + FIX(1 + RND * 200.3)

 

            164 IF RND < .5 THEN X(J) = A(J) - FIX(1 + RND * .3) ELSE X(J) = A(J) + FIX(1 + RND * .3)

 

            166 GOTO 174

 

            172 REM             X(J) = A(J - 1) - RND ^ 4

 

        174 NEXT IPP

 

        625 FOR J44 = 1 TO 200

 

 

            627 IF X(J44) < 0## THEN 1670

 

            628 IF X(J44) > 1## THEN 1670

 

        634 NEXT J44

 

 

        641 SUMN = 0

        642 FOR J44 = 2 TO 200

            643 SUMN = SUMN + X(J44) ^ 2

        644 NEXT J44

        649 IF 1 - SUMN < 0## THEN 1670

 

 

        651 X(1) = (1 - SUMN) ^ .5##

        653 REM

 

 

        663 PRO2 = 1

 

        664 FOR J44 = 1 TO 200

 

 

            667 PRO2 = PRO2 * X(J44)

 

        669 NEXT J44

 

        958 P = ((200 ^ .5##) ^ 200## * PRO2)

 

 

        1111 IF P <= M THEN 1670

 

        1452 M = P

 

        1454 FOR KLX = 1 TO 200

 

            1459 A(KLX) = X(KLX)

 

        1460 NEXT KLX

 

        1557 GOTO 128

 

    1670 NEXT I

 

    1671 IF M < -99999 THEN GOTO 1999

 

 

    1900 PRINT A(1), A(2), A(3)

 

    1901 GOTO 1914

 

 

    1903 PRINT A(6), A(7), A(8), A(9), A(10)

    1907 PRINT A(11), A(12), A(13), A(14), A(15)

    1911 PRINT A(16), A(17), A(18), A(19), A(20)

 

    1913 REM   PRINT A(21), A(22), A(23), A(24), A(25)

    1914 PRINT A(198), A(199), A(200), M, JJJJ

1999 NEXT JJJJ

 

This BASIC computer program was run with qb64v1000-win [120].  The complete output of one run through JJJJ =  -31999.99 is shown below:

 

.0707106811375814                  7.071068032459008D-02          7.071068032459008D-02        

7.071067660242236D-02          7.071067967494414D-02          7.071067583937153D-02                

1.000000000000328      -32000

 

.0707106781228336                  7.071067841871505D-02          7.071068592685303D-02        

7.071067397530902D-02        7.071067999092368D-02        7.071068296883752D-02                     

1.000000000000026      -31999.99

 

 

Only six of the 200 values of A(1) through A(200) are shown above, in accordance with line 1900, line 1901, and line 1914.

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen.

The system properties of the computer system used include Intel Core 2 Duo CPU   E8400 @ 3.00GHz  3.00GHz, 4.00GB of RAM, and qb64v1000-win [120].  The wall-clock time (not CPU time) for obtaining the output through JJJJ = -31999.99 was 55 seconds, counting from “Starting program…”.  One can compare the computational results above with those in Michalewicz and Schoenauer [72, p. 11].

 

Acknowledgement

I would like to acknowledge the encouragement of Roberta Clark and Tom Clark.

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