Jsun Yui Wong

The computer program listed below seeks to solve the following mathematical programming problem:

Maximize w1 * (2 * X(1) ^ 2 + X(1) * X(2)) + w2 * (2 * X(1) - X(2) ^ 2)

subject to

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

X(1) - X(2) <= 4

w1+w2=1

X(1), X(2), w1, w2>=0.

The formuloation above is based on and different from the formulation in Ota, Dash, and Ojha [60, p. 68]. Their formulation [60, p. 68] is as follows:

Minimize w1 * (2 * X(1) ^ 2 + X(1) * X(2)) + w2 * (2 * X(1) - X(2) ^ 2)

subject to

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

X(1) - X(2) <= 4

w1+w2=1

X(1), X(2), w1, w2>=0.

0 REM 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 = -3E+50

90 IF RND < .2 THEN w1 = 0 ELSE IF RND < .25 THEN w1 = .2 ELSE IF RND < .333 THEN w1 = .6 ELSE IF RND < .5 THEN w1 = .8 ELSE w1 = 1

91 w2 = 1 - w1

111 FOR J44 = 1 TO 3

120 A(J44) = ((RND * 8))

121 NEXT J44

128 FOR I = 1 TO 111111

129 FOR KKQQ = 1 TO 3

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

135 FOR IPP = 1 TO FIX(1 + RND * 2)

143 J = 1 + FIX(RND * 2)

149 REM IF J < 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) ELSE X(J) = A(J) + FIX(1 + RND * 3)

169 NEXT IPP

175 FOR J44 = 1 TO 2

176 IF X(J44) < 0## THEN 1670

177 NEXT J44

421 IF X(1) - X(2) > 4 THEN 1670

424 IF X(1) + 3 * X(2) > 10 THEN 1670

465 PDU = w1 * (2 * X(1) ^ 2 + X(1) * X(2)) + w2 * (2 * X(1) - X(2) ^ 2)

466 P = PDU

1111 IF P <= M THEN 1670

1450 M = P

1454 FOR KLX = 1 TO 2

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1557 GOTO 128

1670 NEXT I

1890 IF M < -99999999999 THEN GOTO 1999

1923 PRINT w1, w2

1925 PRINT A(1), A(2), M, JJJJ

1999 NEXT JJJJ

This BASIC computer program was run with QB64v1000-win [80]. The complete output of a single run through JJJJ= -31991 is shown below:

.8 .2

5.5 1.5 56.75 -32000

.2 .8

5.5 1.5 20.75 -31999

1 0

5.5 1.5 68.75 -31998

.2 .8

5.499999 1.499999 20.75 -31997

0 1

4.986213 .9862128 8.99981 -31996

.2 .8

5.5 1.5 20.75 -31995

1 0

5.5 1.5 68.75 -31994

1 0

5.5 1.5 68.75 -31993

.6 .4

5.5 1.5 44.75 -31992

.8 .2

5.5 1.5 56.75 -31991

.

.

.

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 [80], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31991 was 5 seconds, not including the time for “Creating .EXE file" (17 seconds, total, including the time for “Creating .EXE file"). One can compare the computational results above with those in Ota, Dash, and Ojha [60, p. 69, Table 1].

**Acknowledgment**

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

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