Computer program for solving mixed integer fractional posynomial programming (MIFPP) problems

 

Computer program for solving mixed integer fractional posynomial programming (MIFPP) problems

Jsun Yui Wong

Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the immediately following mixed integer fractional posynomial programming(MIFPP) problem in Chang [19, Example 4]:

          

Minimize           

((ABS(X(5) ^ 1.8) * X(1) * X(3) ^ .3 * X(4) ^ 1.5 * X(5)) + (X(2) * X(3) ^ 1.8 * X(4) ^ 1.3 * X(5)) + (X(1) * X(2) * X(3) ^ 1.7)) / (X(1) * X(3) * X(4) + X(2) * X(3) ^ 2.3 * X(4) ^ 1.4)

subject to

         2 * X(1) + X(1) * X(3) ^ 1.6 >= 5

         X(1) + X(2) >= 1 

         X(2) + X(4) <= 6 

         X(1) + X(2) + X(5) >= 3 

            1 <=X(3) <= 7

            1 <=X(4) <= 6

            1 <=X(5) <= 5

where X(1) and X(2) are binary variables,

X(3) and X(4) are continuous variables, and 

X(5) is an absolute continuous variable.

One notes the following line 228, line 229, and line 230, which are 

228 FOR J44 = 1 TO 5

229 IF RND < .5 THEN X(J44) = X(J44) ELSE X(J44) = INT(X(J44))

230 NEXT J44.

      

0 DEFDBL A-Z

1 REM 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), PN(22), NN(22)

85 FOR JJJJ = -32000 TO 32000

    89 RANDOMIZE JJJJ

    90 M = -3D+30

    125 FOR J44 = 1 TO 5

        126 A(J44) = 0 + RND * 4

    127 NEXT J44

    128 FOR i = 1 TO 5000

        129 FOR KKQQ = 1 TO 5

            130 X(KKQQ) = A(KKQQ)

        131 NEXT KKQQ

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

            140 B = 1 + FIX(RND * 5)

            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

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

        168 NEXT IPP

        203 X(1) = INT(X(1))

        204 X(2) = INT(X(2))

        217 FOR J44 = 1 TO 2

            218 IF X(J44) < 0 THEN 1670

            219 IF X(J44) > 1 THEN 1670

        220 NEXT J44

        222 IF X(3) < 1 THEN 1670

        223 IF X(3) > 7 THEN 1670

        224 IF X(4) < 1 THEN 1670

        225 IF X(4) > 6 THEN 1670

        226 IF X(5) < 1 THEN 1670

        227 IF X(5) > 5 THEN 1670

        228 FOR J44 = 1 TO 5

            229 IF RND < .5 THEN X(J44) = X(J44) ELSE X(J44) = INT(X(J44))

        230 NEXT J44

        242 IF 2 * X(1) + X(1) * X(3) ^ 1.6 < 5 THEN 1670

        244 IF X(1) + X(2) < 1 THEN 1670

        246 IF X(2) + X(4) > 6 THEN 1670

        248 IF X(1) + X(2) + X(5) < 3 THEN 1670

        565 PD1 = -((ABS(X(5) ^ 1.8) * X(1) * X(3) ^ .3 * X(4) ^ 1.5 * X(5)) + (X(2) * X(3) ^ 1.8 * X(4) ^ 1.3 * X(5)) + (X(1) * X(2) * X(3) ^ 1.7)) / (X(1) * X(3) * X(4) + X(2) * X(3) ^ 2.3 * X(4) ^ 1.4)

        569 p = PD1

        1111 IF p <= M THEN 1670

        1452 M = p

        1454 FOR KLX = 1 TO 5

            1455 A(KLX) = X(KLX)

        1456 NEXT KLX

    1670 NEXT i

    1775 IF M < -999999999 THEN 1999

    1904 PRINT A(1), A(2), A(3), A(4), A(5), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [103].  Its complete output of one run through JJJJ=  -31982 is shown below.  GW-BASIC also can handle this computer program.

1         1         7         5         1

-.3632313212586026         -32000

1         1         7         5         1

-.3632313212586026         -31997

1         1         7         5         1

-.3632313212586026         -31996

1         1         7         5         1

-.3632313212586026         -31995

1         1         7         5         1

-.3632313212586026         -31993

1         1         7         5         1

-.3632313212586026         -31988

1         1         7         5         1

-.3632313212586026         -31986

1         1         7         5         1

-.3632313212586026         -31985

1         1         7         5         1

-.3632313212586026         -31984

1         1         7         5         1

-.3632313212586026         -31982

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with QB64v1000-win [103], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31982 was 2 seconds, counting from "Starting program...".  One can see the computational results of Chang [19, Example 4, pages 383-385].

The computational results presented above were obtained from the following computer system:

Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz

Installed memory (RAM): 4.00GB (3.87 GB usable)

System type: 64-bit Operating System.

Acknowledgement

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

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Computer program for solving nonlinear fractional programming problems

 

Computer program for solving nonlinear fractional programming problems

Jsun Yui Wong

Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the following nonlinear fractional programming problem from Tsai [87, Example 3 on p. 408]:

          

Minimize     (2 + X(5)) / (X(1) * X(2) * (2 * (X(3) + X(4)))) - X(5) ^ .5 * X(3) ^ 1.5 + 2 * X(2) + X(4)               

subject to         

        (8 / (((X(1) * (X(2) + 3 * X(4)) ^ 2)))) + 1 / X(5) ^ 3 <= 2 

         -2 * X(1) + X(3) - X(4) <= 10 

         X(1) + X(3) + .5 * X(5) <= 8 

         .1 <= X(1), X(2), X(3), X(4), X(5) <= 10.    

0 DEFDBL A-Z

1 REM 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), PN(22), NN(22)

85 FOR JJJJ = -32000 TO 32000

    89 RANDOMIZE JJJJ

    90 M = -3D+30

    115 pie = 3.141592654

    117 GOTO 125

    119 A(1) = 1 + (.0625 * FIX(RND * 7))

    121 A(2) = .625 + (.0625 * FIX(RND * 7))

    123 A(3) = 45 + (RND * 10)

    120 A(4) = 80 + (RND * 30)

    125 FOR J44 = 1 TO 5

        126 A(J44) = .1 + RND * 9.9

    127 NEXT J44

    128 FOR i = 1 TO 500000

        129 FOR KKQQ = 1 TO 5

            130 X(KKQQ) = A(KKQQ)

        131 NEXT KKQQ

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

            140 B = 1 + FIX(RND * 5)

            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

            211 FOR J44 = 1 TO 5

            213 IF X(J44) < .1 THEN 1670

            215 IF X(J44) > 10 THEN 1670

        219 NEXT J44

  

        375 IF (8 / (((X(1) * (X(2) + 3 * X(4)) ^ 2)))) + 1 / X(5) ^ 3 > 2 THEN 1670

        377 IF -2 * X(1) + X(3) - X(4) > 10 THEN 1670

        379 IF X(1) + X(3) + .5 * X(5) > 8 THEN 1670

        

          565 PD1 = -(2 + X(5)) / (X(1) * X(2) * (2 * (X(3) + X(4)))) + X(5) ^ .5 * X(3) ^ 1.5 - 2 * X(2) - X(4)

        569 p = PD1

        1111 IF p <= M THEN 1670

        1452 M = p

        1454 FOR KLX = 1 TO 5

            1455 A(KLX) = X(KLX)

        1456 NEXT KLX

    1670 NEXT i

    1775 IF M < -9999999 THEN 1999

    1904 PRINT A(1), A(2), A(3), A(4), A(5), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [103].  Its complete output of one run through JJJJ=  -31991 is shown below.  GW-BASIC also can handle this computer program.

.3586192585093245       .8476962170684296       5.694762580849228  

.8354290937326228       3.893236321282895       22.7993155960042 

-31996

.3693760028638626       .796675401020093      5.843293980521027

.8374134567250838      3.57466003323022        22.85713354880498

-31991

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. On a personal computer with QB64v1000-win [103], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31991 was 10 seconds, counting from "Starting program...".  One can compare the computational results presented above  with the computational results in Tsai [87, Example 3 on p. 408].

The computational results presented above were obtained from the following computer system:

Processor: Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz 2.26 GHz

Installed memory (RAM): 4.00GB (3.87 GB usable)

System type: 64-bit Operating System.

Acknowledgement

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

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Solving the following system of 20 nonlinear equations

 

Solving the following system of 20 nonlinear equations                                     

Jsun Yui Wong

Similar to the computer programs of the preceding papers, the computer program listed below aims to solve simultaneously the following system of 20 nonlinear equations from Sharma and Gupta [79, p. 9, Problem 7]:       

X i2  * X i+1 -1 = 0,  i=1, 2, 3,..., 19

X 20 2  * X 1  - 1 = 0.  (The 20 is an underscript, and the 2 is a superscript.)

The two lines above involve superscripts and underscripts, so one contrasts them with line 219 and line 461, which are 219 X(20) = 1 / X(19) ^ 2 and 461 PD1 = -ABS(X(20) ^ 2 * X(1) - 1), respectively.  It is clearer if one can see Sharma and Gupta [79, p. 9, Problem 7], which is open access for free.

0 DEFDBL A-Z

1 REM 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), PN(22), NN(22)

85 FOR JJJJ = -32000 TO 32000

    89 RANDOMIZE JJJJ

    90 M = -3D+30

    116 A(1) = 0 + RND * 2

    128 FOR i = 1 TO 500000

        129 FOR KKQQ = 1 TO 20

            130 X(KKQQ) = A(KKQQ)

        131 NEXT KKQQ

        139 FOR IPP = 1 TO FIX(1 + RND * 20)

            140 B = 1 + FIX(RND * 20)

            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

        201 X(2) = 1 / X(1) ^ 2

        202 X(3) = 1 / X(2) ^ 2

        203 X(4) = 1 / X(3) ^ 2

        204 X(5) = 1 / X(4) ^ 2

        205 X(6) = 1 / X(5) ^ 2

        206 X(7) = 1 / X(6) ^ 2

        207 X(8) = 1 / X(7) ^ 2

        208 X(9) = 1 / X(8) ^ 2

        209 X(10) = 1 / X(9) ^ 2

        210 X(11) = 1 / X(10) ^ 2

        211 X(12) = 1 / X(11) ^ 2

        212 X(13) = 1 / X(12) ^ 2

        213 X(14) = 1 / X(13) ^ 2

        214 X(15) = 1 / X(14) ^ 2

        215 X(16) = 1 / X(15) ^ 2

        216 X(17) = 1 / X(16) ^ 2

        217 X(18) = 1 / X(17) ^ 2

        218 X(19) = 1 / X(18) ^ 2

        219 X(20) = 1 / X(19) ^ 2

        333 FOR J44 = 1 TO 20

            335 IF X(J44) < 0 THEN 1670

        337 NEXT J44

        461 PD1 = -ABS(X(20) ^ 2 * X(1) - 1)

        466 P = PD1

        1111 IF P <= M THEN 1670

        1452 M = P

        1454 FOR KLX = 1 TO 20

            1455 A(KLX) = X(KLX)

        1456 NEXT KLX

    1670 NEXT i

    1777 IF M < -.988 THEN 1999

    1904 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), A(9), A(10), A(11), A(12), A(13), A(14), A(15), A(16), A(17), A(18), A(19), A(20), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [102].  Its complete output of one run through JJJJ=  -31986 is shown below:

0      1.#INF      0      1.#INF      0

1.#INF      0      1.#INF      0      1.#INF      

0      1.#INF      0      1.#INF      0

1.#INF      0       1.#INF      0       1.#INF                  

 -1.#IND      -31999

1      1      1      1      1

1       1      1      1      1

1       1      1      1      1

1       1      1      1      1

0      -31996

1      1      1      1      1

1       1      1      1      1

1       1      1      1      1

1       1      1      1      1

0      -31995

1      1      1      1      1

1       1      1      1      1

1       1      1      1      1

1       1      1      1      1

0      -31986

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen.  By using the following computer system and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31986 was 70 seconds, counting from "Starting program...".    

The computational results presented above were obtained from the following computer system:  

Processor:                            Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz   2.26 GHz  

Installed memory (RAM): 4.00GB (3.87 GB usable)

System type:                       64-bit Operating System.

Acknowledgement

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

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Seeking multiple integer solutions to X(1) ^ 2 + X(2) ^ 2 = X(3) ^ 2

 Seeking multiple integer solutions to  X(1) ^ 2 + X(2) ^ 2 = X(3) ^ 2                                             

Jsun Yui Wong

Similar to the computer programs of the preceding papers except the last several papers, the computer program listed below aims to find integer solutions for  X(1) ^ 2 + X(2) ^ 2) = X(3) ^ 2.   

One notes line 116, which is  116 A(1) = (RND * 1000000).

0 DEFDBL A-Z

1 REM 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), PN(22), NN(22)

85 FOR JJJJ = -32000 TO 32000

    89 RANDOMIZE JJJJ

    90 M = -3D+30

    116 A(1) = (RND * 1000000)

    117 A(2) = (RND * 1000000)

    118 A(3) = (RND * 1000000)

    128 FOR i = 1 TO 10000

        129 FOR KKQQ = 1 TO 3

            130 X(KKQQ) = A(KKQQ)

        131 NEXT KKQQ

        139 FOR IPP = 1 TO FIX(1 + RND * 3)

            140 B = 1 + FIX(RND * 3)

            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

        333 FOR J44 = 1 TO 3

            335 X(J44) = INT(X(J44))

        337 NEXT J44

        423 IF X(1) < 1 THEN 1670

        424 IF X(2) < 1 THEN 1670

        429 IF X(3) < 1 THEN 1670

        455 PD1 = -ABS(-X(1) ^ 2 - X(2) ^ 2 + X(3) ^ 2)

        466 P = PD1

        1111 IF P <= M THEN 1670

        1452 M = P

        1454 FOR KLX = 1 TO 3

            1455 A(KLX) = X(KLX)

        1456 NEXT KLX

    1670 NEXT i

    1777 IF M < -.5 THEN 1999

    1904 PRINT A(1), A(2), A(3), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [102].  Its complete output of one run through JJJJ=  -31852 is shown below:

187986   104720   215186   0   -31951

840   35275   35285   0   -31852

Above there is no rounding by hand; it is just straight copying by hand from the monitor screen.  By using the following computer system and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31852 was 4 seconds, counting from "Starting program...".    

The computational results presented above were obtained from the following computer system:  

Processor:                            Intel (R) Core (TM) i5 CPU M 430 @2.27 GHz   2.26 GHz  

Installed memory (RAM): 4.00GB (3.87 GB usable)

System type:                       64-bit Operating System.

Acknowledgement

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

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