Computer program for solving mixed integer signomial programming problems, third edition

Jsun Yui Wong

Similar to the computer program of the preceding paper, the computer program listed below aims to solve directly the following signomial programming problem from Chang [18, Example 5 on pp. 1448-1450]:

Minimize

(.6224 * X(1) * X(3) * X(4) + 1.7781 * X(2) * X(3) ^ 2 + 3.1661 * X(1) ^ 2 * X(4) + 19.84 * X(1) ^ 2 * X(3))

subject to

X(1) - .0193 * X(3) >= 0

X(2) - .00954 * X(3) >= 0

pie * X(3) ^ 2)* X(4) + (4 / 3) * pie * X(3) ^ 3) >= 750 * 1728

1<= X(1) <= 1.375, discrete variable with discreteness .0625

.625<= X(2) <= 1, discrete variable with discreteness .0625

45<= X(3) <= 55, continuous variable

80<= X(4) <= 110, continuous variable.

One notes the following line 196 through 451.

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

118 pie = 3.141592654

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

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

123 A(3) = 45 + (RND * 10)

124 A(4) = 80 + (RND * 30)

128 FOR i = 1 TO 500000

129 FOR KKQQ = 1 TO 4

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

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

140 B = 1 + FIX(RND * 4)

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

196 X(1) = 1

198 X(1) = 1 + (.0625 * FIX(RND * 7))

199 X(2) = .625 + (.0625 * FIX(RND * 7))

241 IF X(1) < 1 THEN 1670

242 IF X(1) > 1.375 THEN 1670

244 IF X(2) < .625 THEN 1670

245 IF X(2) > 1 THEN 1670

246 IF X(3) < 45 THEN 1670

247 IF X(3) > 55 THEN 1670

248 IF X(4) < 80 THEN 1670

249 IF X(4) > 110 THEN 1670

251 IF RND < .5 THEN X(1) = X(1) ELSE X(1) = INT(X(1))

333 X(4) = (750 * 1728 - (4 / 3) * pie * X(3) ^ 3) / (pie * X(3) ^ 2)

359 IF X(1) - .0193 * X(3) < 0 THEN 1670

365 IF X(2) - .00954 * X(3) < 0 THEN 1670

441 IF X(1) < 1 THEN 1670

442 IF X(1) > 1.375 THEN 1670

444 IF X(2) < .625 THEN 1670

445 IF X(2) > 1 THEN 1670

446 IF X(3) < 45 THEN 1670

447 IF X(3) > 55 THEN 1670

448 IF X(4) < 80 THEN 1670

449 IF X(4) > 110 THEN 1670

451 IF RND < .5 THEN X(1) = X(1) ELSE X(1) = INT(X(1))

564 PD1 = -(.6224 * X(1) * X(3) * X(4) + 1.7781 * X(2) * X(3) ^ 2 + 3.1661 * X(1) ^ 2 * X(4) + 19.84 * X(1) ^ 2 * X(3))

569 p = PD1

1111 IF p <= M THEN 1670

1452 M = p

1454 FOR KLX = 1 TO 4

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), M, JJJJ

1999 NEXT JJJJ

This computer program was run with qb64v1000-win [103]. Its complete output of one run through JJJJ= -31999 is shown below. GW-BASIC also can handle this computer program.

1 .625 52.45322925101003 80.00000000000505

-6963.31119194227 -32000

**1 .625 52.45322925101045 80.0000000000021****-6963.311191942241 -31999**

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 = -31999 was 5 seconds, counting from "Starting program...". One can compare the computational results presented above with the computational results in Chang [18, Example 5, pages 1448-1450, Table 2 on p. 1450].

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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