Jsun Yui Wong

The computer program listed below seeks to solve the following problem based on the first problem on p. 2462 of Varshney and Mradula [85, p. 2462]:

Minimize

- ( -.4388203 / X(1) - 2.663113 / X(2) - 49.60277 / X(3) - 2.66616 / X(4) - 9.938173 / X(5) - .002437891 / X(6) - .08937845 / X(7) - 1.206554 / X(8) - .044436 / X(9) - .2094497 / X(10) )

subject to

4 * X(1) + 4.9 * X(2) + 5.9 * X(3) + 7.75 * X(4) + 8.92 * X(5) + 6 * X(6) + 7 * X(7) + 9 * X(8) + 11 * X(9) + 12 * X(10) + 100 * (X(1) / 4 + X(2) / 4 + X(3) / 4 + X(4) / 4 + X(5) / 4) + 100 * (X(6) / 4 + X(7) / 4 + X(8) / 4 + X(9) / 4 + X(10) / 4) <= 10000

2<= X(1) <= 395

2<= X(2) <= 382

2<=X(3) <= 439

2<=X(4) <= 368

2<=X(5) <= 416

2<=X(6) <= 30

2<=X(7) <= 30

2<=X(8) <= 30

2<=X(9) <= 30

2<=X(10) <= 30

X(1) through X(10) are general integer variables.

The following computer program was used to solve the problem above.

0 DEFDBL A-Z

1 DEFINT K

2 DIM B(99), N(99), A(2002), H(99), L(99), U(99), X(2002), D(111), P(111), PS(33), J44(2002), J(99), AA(99), HR(32), HHR(32), LHS(44), PLHS(44), LB(22), UB(22), PX(22), CC(20), RR(20), WW(20), AL(50), SW(50), SV(50), C2(22), C3(22), C4(22), C5(22)

81 FOR JJJJ = -32000 TO 32000

85 RANDOMIZE JJJJ

87 M = -4E+250

121 FOR J44 = 1 TO 5

122 A(J44) = RND * 50

123 NEXT J44

124 FOR J44 = 6 TO 10

125 A(J44) = RND * 3

126 NEXT J44

128 FOR I = 0 TO FIX(RND * 20000)

129 FOR KKQQ = 1 TO 10

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

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

143 j = 1 + FIX(RND * 10)

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

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)

164 REM IF A(J) = 0 THEN X(J) = 1 ELSE X(J) = 0

169 NEXT IPP

171 FOR J44 = 1 TO 10

173 X(J44) = INT(X(J44))

174 IF X(J44) < 2 THEN 1670

175 NEXT J44

188 IF X(1) > 395 THEN 1670

189 IF X(2) > 382 THEN 1670

190 IF X(3) > 439 THEN 1670

191 IF X(4) > 368 THEN 1670

192 IF X(5) > 416 THEN 1670

193 IF X(6) > 30 THEN 1670

194 IF X(7) > 30 THEN 1670

195 IF X(8) > 30 THEN 1670

196 IF X(9) > 30 THEN 1670

197 IF X(10) > 30 THEN 1670

227 IF 4 * X(1) + 4.9 * X(2) + 5.9 * X(3) + 7.75 * X(4) + 8.92 * X(5) + 6 * X(6) + 7 * X(7) + 9 * X(8) + 11 * X(9) + 12 * X(10) + 100 * (X(1) / 4 + X(2) / 4 + X(3) / 4 + X(4) / 4 + X(5) / 4) + 100 * (X(6) / 4 + X(7) / 4 + X(8) / 4 + X(9) / 4 + X(10) / 4) > 10000 THEN 1670

499 P = -.4388203 / X(1) - 2.663113 / X(2) - 49.60277 / X(3) - 2.66616 / X(4) - 9.938173 / X(5) - .002437891 / X(6) - .08937845 / X(7) - 1.206554 / X(8) - .044436 / X(9) - .2094497 / X(10)

1111 IF P <= M THEN 1670

1420 M = P

1444 FOR KLX = 1 TO 10

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1488 REM

1489 LHS = 4 * X(1) + 4.9 * X(2) + 5.9 * X(3) + 7.75 * X(4) + 8.92 * X(5) + 6 * X(6) + 7 * X(7) + 9 * X(8) + 11 * X(9) + 12 * X(10) + 100 * (X(1) / 4 + X(2) / 4 + X(3) / 4 + X(4) / 4 + X(5) / 4) + 100 * (X(6) / 4 + X(7) / 4 + X(8) / 4 + X(9) / 4 + X(10) / 4)

1557 GOTO 128

1670 NEXT I

1889 IF M < -.8441043 THEN 1999

1926 PRINT A(1), A(2), A(3), A(4), A(5), A(6), A(7), A(8), A(9), A(10), M, JJJJ

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [91]. The complete output of a single run through JJJJ= -31962 is shown below:

**13 32 136 31 59****2 6 21 4 9****-.8441042055052964 -31993**

13 32 136 31 59

2 6 21 4 9

-.8441042055052964 -31987

13 32 136 31 59

2 6 21 4 9

-.8441042055052964 -31972

13 32 136 31 59

2 6 21 4 9

-.8441042055052964 -31962

.

.

.

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 [91], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31962 was 2 seconds, not including the time for “Creating .EXE file" (18 seconds, total, including the time for “Creating .EXE file"). One can compare the computational results above with those in Varshney and Mradula [85, p. 2462].

Acknowledgment

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

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