A computer program for solving mixed-integer nonlinear programs: a Misener example
Jsun Yui Wong
Similar to the computer program of the preceding paper, the computer program listed below aims to solve the following nonlinear program from Misener [62, p. 1/5]:
Maximize
X(1) + X(2)
subject to
8 * X(1) ^ 3 - 2 * X(1) ^ 4 - 8 * X(1) ^ 2 + X(2) <= 2
32 * X(1) ^ 3 - 4 * X(1) ^ 4 - 88 * X(1) ^ 2 + 96 * X(1) + X(2) <= 36
X(1) epsilon [0, 3]
X(2) epsilon {0, 1, 2, 3, 4}
where X(1) is a continuous variable, and X(2) is a discrete variable.
0 REM DEFDBL A-Z
1 REM DEFINT I, J, K
2 REM 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
91 A(1) = RND * 3
92 A(2) = INT(RND * 4)
128 FOR i = 1 TO 5000
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 1)
141 B = 1 + FIX(RND * 2)
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
177 X(2) = INT(X(2))
222 IF 8 * X(1) ^ 3 - 2 * X(1) ^ 4 - 8 * X(1) ^ 2 + X(2) > 2 THEN 1670
229 IF 32 * X(1) ^ 3 - 4 * X(1) ^ 4 - 88 * X(1) ^ 2 + 96 * X(1) + X(2) > 36 THEN 1670
324 IF X(1) > 3 THEN 1670
325 IF X(1) < 0 THEN 1670
343 IF X(2) > 4 THEN 1670
345 IF X(2) < 0 THEN 1670
464 PD1 = X(1) + X(2)
469 P = PD1
1111 IF P <= M THEN 1670
1452 M = P
1454 FOR KLX = 1 TO 2
1455 A(KLX) = X(KLX)
1459 NEXT KLX
1670 NEXT i
1777 IF M < -999999999 THEN 1999
1888 PRINT A(1), A(2), M, JJJJ
1999 NEXT JJJJ
This computer program was run with qb64v1000-win [102]. Its complete output of one run through JJJJ= -31987 is shown below:
2.541196 2 4.541196 -32000
2.366025 3 5.366025 -31999
2.707107 1 3.707107 -31998
2.707107 1 3.707107 -31997
3 0 3 -31996
2.366025 3 5.366025 -31995
2.541196 2 4.541196 -31994
2.541196 2 4.541196 -31993
2.541196 2 4.541196 -31992
.6339745 3 3.633975 -31991
2.366025 3 5.366025 -31990
2.541196 2 4.541196 -31989
2.366025 3 5.366025 -31988
2.366025 3 5.366025 -31987
Above there is no rounding by hand; it is just straight copying by hand from the monitor screen. By using the following computer system and QB64v1000-win [102], the wall-clock time (not CPU time) for obtaining the output through JJJJ = -31987 was 2 seconds, counting from "Starting program...". One can compare the computational results above with those in Misener [62, p. 2/5].
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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