Jsun Yui Wong

The computer program listed below seeks to solve the following 2-objective nonlinear mixed-integer preemptive goal programming problem from Ignizio [47, pp. 209-210] with the streamlined procedure of Hillier and Lieberman [42, pp. 289-291]:

Minimize { (X(4)) , ( X(6)) }

subject to

X(1) ^ 2 + 2 * X(2) + X(3) - X(4) =20

X(1) + X(1) * X(2) + X(5) - X(6) =10

X(1)=0, 1, 2, ...

X(2)=0, 1, 2, ...

All variables are nonnegative.

One notes line 1320, which is 1320 P = -10 ^ 20 * X(4) - X(6).

0 DEFDBL A-Z

1 REM DEFINT X, A

2 DIM N(99), A(45222), X(45012), D(111), P(111), PS(33), J44(45202), J(45211), AA(99), STIO(45303)

81 FOR JJJJ = -32000 TO 32000

85 RANDOMIZE JJJJ

87 M = -4E+250

120 FOR J44 = 1 TO 6

121 A(J44) = FIX(RND * 5)

123 NEXT J44

128 FOR I = 0 TO FIX(RND * 30000)

129 FOR KKQQ = 1 TO 6

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

135 FOR IPP = 1 TO FIX(1 + RND * 3.3)

143 j = 1 + FIX(RND * 6)

144 IF RND < .5 THEN GOTO 156 ELSE GOTO 162

145 GOTO 162

154 REM IF j > 3.5 THEN GOTO 162 ELSE GOTO 156

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

158 X(j) = A(j) + (RND ^ (RND * 15)) * r

161 GOTO 169

162 IF RND < .5 THEN X(j) = A(j) - FIX(1 + RND * 3.3) ELSE X(j) = A(j) + FIX(1 + RND * 3.3)

169 NEXT IPP

221 FOR J44 = 1 TO 6

230 IF X(J44) < 0 THEN 1670

231 NEXT J44

232 X(1) = INT(X(1))

233 X(2) = INT(X(2))

1252 X(3) = 20 + X(4) - X(1) ^ 2 - 2 * X(2)

1254 X(5) = 10 + X(6) - X(1) - X(1) * X(2)

1267 FOR J44 = 1 TO 6

1269 IF X(J44) < 0 THEN 1670

1270 NEXT J44

1293 X(1) = INT(X(1))

1295 X(2) = INT(X(2))

1320 P = -10 ^ 20 * X(4) - X(6)

1418 IF P <= M THEN 1670

1420 M = P

1442 FOR KLX = 1 TO 6

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1557 GOTO 128

1670 NEXT I

1677 IF M < -4D+200 THEN 1999

1931 PRINT A(1), A(2), A(3), A(4), A(5), A(6), M, JJJJ

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [103]. The complete output of a single run through JJJJ=-31997 is shown below:

**2 2 12 0 4****0 0 -32000**

3 0 11 2.122757576172983D-282

7 5.334281726365734D-262 -7.457039392538717D-262

-31999

1 4 11.00000319772738 3.197727382885525D-06

5.520649189382835 .5206491893828358 -319772738288553.1

-31998

**1 1 17 0 8****0 0 -31997**

.

.

.

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 [103], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31997 was 3 seconds, not including the time for “Creating .EXE file.”

Remark 3 and remark 4 on page 198 of Winston and Venkataramanan [104] are noteworthy.

**Acknowledgement**

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

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