A General Nonlinear Integer/Discrete/Continuous Programming Solver Applied to a Single-Row Layout Problem of Eight Facilities with Clearance Requirement

Jsun Yui Wong

The following computer program seeks to solve Problem Lit-Cl-4 in Anjos and Vannelli [3, page 10].  The source of this problem is Heragu and Kusiak [13].  The article by Kumar, Hadjinicola, and Lin [17, page 70, Table 1] also considers this problem.

0 REM DEFDBL A-Z
1 DEFINT I,J,K,X,A
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)
3 DIM HS(49,49)
4 DIM PE(49,49)
5 DIM SD(49,49)
27 HR(1)=.05:HR(2)=.03:HR(3)=.06
28   HR(4)=.04:HR(5)=.02:HR(6)=.06:HR(7)=9.000001E-02:HR(8)=.02
31 FOR IL=1 TO 7
32 FOR JL=IL+1 TO 8
33 READ HS(IL,JL)
34 NEXT JL
35 NEXT IL
64 DATA 5,2,4,1,0,0,6
65 DATA 3,0,2,2,2,0
66 DATA 0,0,0,0,5
67 DATA 5,2,2,10
68 DATA 10,0,0
69 DATA 5,1
70 DATA 10
78 FOR JJJJ=-32000 TO 32000
79 RANDOMIZE JJJJ
80 M=-1D+37
81 FOR J44=1 TO 8
83 A(J44)=J44
84 NEXT J44
126 REM IMAR=10+FIX(RND*1000)
128 FOR I=1 TO 100
129 FOR KKQQ=1 TO 8
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
133 III=1+FIX(RND*8)
134 JJJ=1+FIX(RND*8)
221    X(III)=A(JJJ)
223    X(JJJ)=A(III)
225 FOR II=1 TO 7
227 FOR JJ=II+1 TO 8
231 SD(II,JJ)=0
235 SD(II,JJ)=.5*HR(II)+.5*HR(JJ)
239 FOR KK = 1 TO 8
241 IF X(II)<X(JJ) THEN 245 ELSE 249
245 IF X(KK)>X(II) AND X(KK) <X(JJ) THEN HHR(KK)=HR(KK) ELSE HHR(KK)=0
247 GOTO 255
249 IF X(KK)>X(JJ) AND X(KK) <X(II) THEN HHR(KK)=HR(KK) ELSE HHR(KK)=0
255 SD(II,JJ)=SD(II,JJ)+HHR(KK)
261 NEXT KK
267 NEXT JJ
271 NEXT II
305 PDU=0
309 FOR IW=1 TO 7
312 FOR J88=IW+1 TO 8
318 PDU=PDU-HS(IW,J88)*SD(IW,J88)
320 NEXT J88
321 NEXT IW
359 POB1=               PDU
444 P1NEWMAY=POB1
466 P=P1NEWMAY
1111 IF P<=M THEN 1670
1452 M=P
1454 FOR KLX=1 TO 8
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1557 GOTO 128
1670 NEXT I
1889 IF M<-6.5 THEN 1999
1901 PRINT A(1),A(2),A(3),A(4),A(5)
1902 PRINT A(6),A(7),A(8),M,JJJJ
1999 NEXT JJJJ

This BASIC computer program was run with Microsoft's GW BASIC 3.11 interpreter.  The complete output through JJJJ=-31988 is shown below.  What follows is a hand copy from the computer-monitor screen; immediately below there is no rounding by hand.

3   2   1   5   6
7   8   4   -6.295   -32000

3   2   1   5   7
8   6   4   -6.445001   -31999

3   2   1   5   6
7   8   4   -6.295   -31998

3   2   1   5   6
7   8   4   -6.295   -31997

3   2   1   5   7
8   6   4   -6.445001   -31996

3   2   1   5   7
8   6   4   -6.445001   -31993

3   2   1   5   6
7   8   4   -6.295   -31992

3   2   1   5   7
8   6   4   -6.445001   -31991

6   7   8   4   3
2   1   5   -6.295   -31988

On a personal computer with a Pentium Dual-Core CPU E5200 @2.50GHz, 2.50 GHz, 960 MB of RAM, and the IBM basica/D interpreter, version GW BASIC 3.11,  the wall-clock time through JJJJ= -31988 was four seconds.

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