A computer program for solving mixed-integer nonllnear programs
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 Tsai and Lin [89, p. 47, Example 2]:
Minimize
X(1) ^ .5 * X(2) + 3 * LOG(X(1))
subject to
-X(1) + X(2) <= 5
X(1) ^ .5 – X(2) <= 6
X(1) epsilon {0.1, 0.5, 0.7, 1.2}
-6 <= X(2) <= 4.
One notes that X(1) is a discrete variable, and X(2) is a free 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
111 IF RND < .25 THEN A(1) = .1 ELSE IF RND < .3333 THEN A(1) = .5 ELSE IF RND < .5 THEN A(1) = .7 ELSE A(1) = 1.2
112 A(2) = -6 + RND * 10
128 FOR i = 1 TO 20000
129 FOR KKQQ = 1 TO 2
130 X(KKQQ) = A(KKQQ)
131 NEXT KKQQ
139 FOR IPP = 1 TO FIX(1 + RND * 2)
141 B = 1 + FIX(RND * 2)
144 REM IF RND < .9999 THEN 160 ELSE GOTO 167
147 IF B = 2 THEN 160 ELSE GOTO 167
160 r = (1 - RND * 2) * A(B)
164 X(B) = A(B) + (RND ^ (RND * 15)) * r
165 GOTO 168
166 REM IF RND < .5 THEN X(B) = A(B) - FIX(RND * 2) ELSE X(B) = A(B) + FIX(RND * 2)
167 IF RND < .25 THEN X(1) = .1 ELSE IF RND < .3333 THEN X(1) = .5 ELSE IF RND < .5 THEN X(1) = .7 ELSE X(1) = 1.2
168 NEXT IPP
177 REM X(3) = INT(X(3))
181 IF -X(1) + X(2) > 5 THEN 1670
184 IF X(1) ^ .5 - X(2) > 6 THEN 1670
324 IF X(1) > 1.2 THEN 1670
325 IF X(1) < .1 THEN 1670
343 IF X(2) > 4 THEN 1670
345 IF X(2) < -6 THEN 1670
441 PD1 = -X(1) ^ .5 * X(2) - 3 * LOG(X(1))
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 < -999999 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= -31995 is shown below:
.1 -5.683772 8.705122 -32000
.1 -5.683772 8.705122 -31999
.1 1.667091E-07 6.907755 -31998
.1 -5.683772 8.705122 -31997
.1 -5.683772 8.705122 -31996
.1 -5.683772 8.705122 -31995
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 = -31995 was 2 seconds, counting from “Starting program…”. One can compare the computational results above with those in Tsai and Lin [89, p. 47; Table 1 on p. 47].
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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