Computer Program for Solving Mixed-Integer/Integer/Mixed-Discrete Nonlinear Programming Problems Involving Signomial Parts: an Illustration

 

Computer Program for Solving Mixed-Integer/Integer/Mixed-Discrete Nonlinear Programming Problems Involving Signomial Parts:  an Illustration    

Jsun Yui Wong

Similar to the computer program of the preceding paper, the computer program listed below seeks to solve the following problem from Porn, Bjork, and Westerlund [72, p. 116 (9 of 13), Example 3]:          

Minimize

    

-1*  ( -2 * X(1) - 3 * X(2) - 1.5 * X(4) - 2 * X(5) + .5 * X(6)    )         

  

subject to 

                  X(1)^2 + X(4)  = 1.25

                 X(2) ^ 1.5 + 1.5 * X(5) = 3

         X(1) + X(4) <= 1.6 

        1.333 * X(2) + X(5) <= 3 

        -X(4) - X(5) + X(6) <= 0

        X(1), X(2), X(3) >= 0    

        (X(4), X(5), X(6)) element  { 0, 1 }.     

0 REM    DEFDBL A-Z

1 REM    DEFINT I, J, K

2 DIM B(99), N(99), A(20), H(99), L(99), U(99), X(20), 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), PN(22), NN(22)

79 FOR JJJJ = -32000 TO 32000

    89 RANDOMIZE JJJJ

    90 M = -3D+30

    104 FOR J44 = 1 TO 6

        107 A(J44) = RND

    108 NEXT J44

    123 FOR I = 1 TO 60000

        129 FOR KKQQ = 1 TO 6

            130 X(KKQQ) = A(KKQQ)

        131 NEXT KKQQ

        139 FOR IPP = 1 TO FIX(1 + RND * 4)

            140 B = 1 + FIX(RND * 6)

            144 IF RND < .5 THEN 160 ELSE GOTO 167

            160 r = (1 - RND * 2) * A(B)

            164 X(B) = A(B) + (RND ^ (RND * 15)) * r

            165 GOTO 168

            167 IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)

        168 NEXT IPP

        177 FOR J44 = 4 TO 6

            178 X(J44) = INT(X(J44))

        179 NEXT J44

        185 IF (1.25 - X(4)) < 0## THEN 1670

        188 X(1) = (1.25 - X(4)) ^ .5

        198 FOR J44 = 1 TO 6

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

        200 NEXT J44

        207 IF X(4) > 1## THEN 1670

        208 IF X(5) > 1## THEN 1670

        209 IF X(6) > 1## THEN 1670

        319 IF X(1) + X(4) > 1.6 THEN 1670

        320 IF 1.333 * X(2) + X(5) > 3 THEN 1670

        321 IF -X(4) - X(5) + X(6) > 0 THEN 1670

        446 PD1 = -2 * X(1) - 3 * X(2) - 1.5 * X(4) - 2 * X(5) + .5 * X(6) - 100000 * ABS(X(2) ^ 1.5 + 1.5 * X(5) - 3)

        466 P = PD1

        1111 IF P <= M THEN 1670

        1452 M = P

        1454 FOR KLX = 1 TO 6

            1455 A(KLX) = X(KLX)

        1456 NEXT KLX

    1670 NEXT I

    1889 IF M < -7.7 THEN 1999

    1899 PRINT A(1), A(2), A(3), A(4), A(5), A(6), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [101].  Its complete output of one run through JJJJ= -31997 is shown below:

1.118034      1.310371      2.083565       0      1

1         -7.669487         -32000

1.118034   1.310371   .7253669    0   1

1      -7.669487      -31999

1.118034   1.310371   .5079655    0   1

1      -7.669487      -31997

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with Processor Intel Pentium CPU G620@ 2.60GHz, 4.00 GB of RAM (3.89 GB usable), 64-bit Operating System, and QB64v1000-win [101], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31997 was 3 seconds, counting from "Starting program...".  One can compare the computational results above with those in Porn, Bjork, and Westerlund [72, p. 116 (9 of 13), Example 3].          

Acknowledgement

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

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