Jsun Yui Wong

Based on the computer program in Wong [39], the computer program listed below seeks to solve the following problem from Jaberipour and Khorram [13, pp. 741-742, Example 4]:

Maximize R1 + R2 + R3, defined in lines 301, 303, and 305 below,

1<=X(i)<=5, i=1,..., 20.

One notes that line 223 through line 235 in Wong [39] are 223 FOR j41 = 1 TO 20, 225 X(j41) = INT(X(j41)), and 235 NEXT j41, respectively, here line 223 through line 235 are 223 REM FOR j41 = 1 TO 20, 225 REM X(j41) = INT(X(j41)), and 235 REM NEXT j41, respectively.

0 DEFDBL A-Z

2 DEFINT K

3 DIM B(99), N(99), A(99), H(99), L(99), U(99), X(1111), D(111), P(111), PS(33)

12 FOR JJJJ = -32000 TO 32000 STEP .01

14 RANDOMIZE JJJJ

16 M = -1D+37

71 FOR J40 = 1 TO 20

74 A(J40) = (1 + RND * 4)

75 REM A(2) = (2 + RND * 200)

77 NEXT J40

128 FOR I = 1 TO 50000

129 FOR KKQQ = 1 TO 20

130 X(KKQQ) = A(KKQQ)

131 NEXT KKQQ

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

181 J = 1 + FIX(RND * 20)

183 R = (1 - RND * 2) * A(J)

187 X(J) = A(J) + (RND ^ (RND * 10)) * R

222 NEXT IPP

223 REM FOR j41 = 1 TO 20

225 REM X(j41) = INT(X(j41))

235 REM NEXT j41

256 FOR J47 = 1 TO 20

257 IF X(J47) < 1 THEN 1670

258 IF X(J47) > 5 THEN 1670

259 NEXT J47

260 SUM1 = 0

261 FOR J44 = 1 TO 20

265 SUM1 = SUM1 + J44 * X(J44)

269 NEXT J44

270 SUM2 = 0

271 FOR J44 = 1 TO 20

275 SUM2 = SUM2 + X(J44)

279 NEXT J44

280 SUM3 = 0

281 FOR J44 = 1 TO 10

285 SUM3 = SUM3 + J44 * X(2 * J44)

289 NEXT J44

290 SUM4 = 0

291 FOR J44 = 1 TO 10

295 SUM4 = SUM4 + X(2 * J44 - 1)

299 NEXT J44

301 R1 = SUM1 / SUM2

303 R2 = SUM3 / SUM4

305 R3 = SUM4 / SUM3

307 GOTO 347

311 X(3) = 6 - 2 * X(1) - X(2)

313 X(4) = 8 - 3 * X(1) - X(2)

315 X(5) = 1 - X(1) + X(2)

322 FOR J44 = 3 TO 5

325 IF X(J44) < 0 THEN X(J44) = X(J44) ELSE X(J44) = 0

327 NEXT J44

343 REM

347 POBA = R1 + R2 + R3

466 P = POBA

1111 IF P <= M THEN 1670

1452 M = P

1454 FOR KLX = 1 TO 20

1455 A(KLX) = X(KLX)

1456 NEXT KLX

1557 REM GOTO 128

1670 NEXT I

1889 IF M < 38.5 THEN 1999

1900 PRINT A(1), A(2), A(3), A(4), A(5)

1901 PRINT A(6), A(7), A(8), A(9), A(10)

1910 PRINT A(11), A(12), A(13), A(14), A(15)

1911 PRINT A(16), A(17), A(18), A(19), A(20)

1922 PRINT M, JJJJ

1999 NEXT JJJJ

This BASIC computer program was run with qb64v1000-win [38]. The complete output through JJJJ = -31999.99 is shown below:

1.000000023530792 1.000000024888448 1.000000000215454

4.99999989275312 1.000000013115532

4.999999050387178 1.000000004188031 4.999999988517495

1.000000056133371 4.999999959762943

1.000000000922831 4.999999615140256 1.000000020098937

4.99999984112548 1.000000000652795

4.999999972860543 1.000000034610626 4.999999991891256

1.000000003723272 4.999999999750646

38.60118504510297 -32000

1.00000000253903 1.00000007567784 1.0000000016618036

4.999999332843052 1.000000011102316

4.999999060760837 1.000000000755814 4.99999999608387

1.00000001700265 4.999999967689313

1.000000128005934 4.999999915208235 1.00000002506695

4.999999998575465 1.00000033396696

4.999999991851928 1.000000000964161 4.999999899827006

1.00000008758909 4.999999999953226

38.60118400559084 -31999.99

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 [38], the **wall-clock time** for obtaining the output through JJJJ= -31999.99 was 10 seconds, total, including the time for "Creating .EXE file." One can compare the computational results above with those on page 742 of Jaberipour and Khorram [13].

**Acknowledgment**

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

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