Heat Exchanger Network Design with Nonlinear Programming

Jsun Yui Wong

The computer program listed below seeks to solve the following problem from Ryoo and Sahinidis [43, p. 564, Example 5]:

Minimize            X(1) + X(2) + X(3) 

subject to

        100000 * ( X(4)-100) = (120 *X(1)* (300 - X(4)) 

        100000 * (X(5) - X(4))) = 80 *X(2)* (400 - X(5))

        100000 * (500 - X(5)) = 40 *X(3)* (600-500)     

        0<=X(1) < = 15834 
       
        0<=X(2) < = 36250 

        0<=X(3) < = 10000 

        100<=X(4) < = 300 

        100<= X(5) <=400.     


0 DEFDBL A-Z

2 DEFINT K

3 DIM B(99), N(99), A(99), H(99), L(99), U(99), X(1111), D(111), P(111), PS(33)

12 FOR JJJJ = -32000 TO 32000 STEP .01

    14 RANDOMIZE JJJJ

    16 M = -1D+37

    84 A(1) = 0 + (RND * 15836)

    85 A(2) = 0 + (RND * 46250)

    86 A(3) = 0 + (RND * 10000)

    88 A(4) = 100 + (RND * 200)
    90 A(5) = 100 + (RND * 300)

    128 FOR I = 1 TO 50000


        129 FOR KKQQ = 1 TO 5

            130 X(KKQQ) = A(KKQQ)
        131 NEXT KKQQ
        133 FOR IPP = 1 TO (1 + FIX(RND * 2))

            181 j = 1 + FIX(RND * 5)


            189 r = (1 - RND * 2) * A(j)

            190 X(j) = A(j) + (RND ^ (RND * 10)) * r

        222 NEXT IPP



        224 FOR J44 = 1 TO 3
            227 IF X(J44) < 0## THEN 1670

        229 NEXT J44

        231 IF X(4) < 100## THEN 1670
        232 IF X(5) < 100## THEN 1670



        236 IF X(1) > 15834## THEN 1670



        237 IF X(2) > 36250## THEN 1670


        238 IF X(3) > 10000## THEN 1670


        241 IF X(4) > 300## THEN 1670


        243 IF X(5) > 400## THEN 1670


        244 X(3) = (100000 * (500 - X(5))) / (40 * (100))

        245 X(1) = (100000 * (-100 + X(4))) / (120 * (300 - X(4)))

        246 X(2) = (100000 * (-X(4) + X(5))) / (80 * (400 - X(5)))


        247 FOR J44 = 1 TO 3
            248 IF X(J44) < 0## THEN 1670

        249 NEXT J44

        257 IF X(4) < 100## THEN 1670
        259 IF X(5) < 100## THEN 1670


        276 IF X(1) > 15834## THEN 1670


        286 IF X(2) > 36250## THEN 1670


        296 IF X(3) > 10000## THEN 1670


        298 IF X(4) > 300## THEN 1670


        300 IF X(5) > 400## THEN 1670
        455 POBA = -X(1) - X(2) - X(3)

        466 P = POBA

        1111 IF P <= M THEN 1670


        1450 M = P
        1454 FOR KLX = 1 TO 5

            1455 A(KLX) = X(KLX)
        1456 NEXT KLX
        1557 GOTO 128

    1670 NEXT I
    1889 REM IF M < 11 THEN 1999

    1907 PRINT A(1), A(2), A(3), A(4), A(5)


    1908 PRINT M, JJJJ

1999 NEXT JJJJ


This BASIC computer program was run with QB64v1000-win [54]. The complete output through JJJJ = -31999.99 is shown below:

579.3067378950841      1359.971236996797      5109.971297583114
182.0175994854676      295.6011480966754
-7049.249272475995      -32000

579.3067211553962      1359.971273893866      5109.971277426733
182.0175980873007      295.6011489029307
-7049.249272475995      -31999.99

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM and QB64v1000-win [54], the wall-clock time (not CPU time) for obtaining the output through
JJJJ =  -31999.96000000001 was 2 seconds, not including the time for “Creating .EXE file”  (10 seconds, total, including the time for “Creating .EXE file”).  One can compare the computational results above with those on p. 564 of Ryoo and Sahinidis [43, p. 564, Example 5]. 
       
Acknowledgment

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

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