Jsun Yui Wong
The computer program listed below uses Example 1 on pages 242-245 of Heragu (2008) to illustrate an algorithm for solving quadratic assignment problems.
0 DEFSNG A-Z
3 DEFINT I,J,K
4 DIM X(466),A(466),L(466),K(466),P(466),B(466),S(466)
5 FOR JJJJ=-32000 TO 32000
14 RANDOMIZE JJJJ
16 M=-1D+17
51 A(1)=0:A(5)=0
52 A(2)=1:A(6)=0
53 A(3)=0:A(7)=1
54 A(4)=1:A(8)=1
126 IMAR=10+FIX(RND*0)
128 FOR I=1 TO IMAR
129 FOR KK=1 TO 8
131 X(KK)=A(KK)
132 NEXT KK
330 IJM=1+FIX(RND*4)
331 IJN=1+FIX(RND*4)
333 X(IJM)=A(IJN):X(IJN)=A(IJM)
335 X(IJM+4)=A(IJN+4):X(IJN+4)=A(IJM+4)
501 B(1)=ABS(X(1)-X(2))+ABS(X(5)-X(6))
502 B(2)=ABS(X(1)-X(3))+ABS(X(5)-X(7))
503 B(3)=ABS(X(1)-X(4))+ABS(X(5)-X(8))
504 B(4)=ABS(X(2)-X(3))+ABS(X(6)-X(7))
505 B(5)=ABS(X(2)-X(4))+ABS(X(6)-X(8))
506 B(6)=ABS(X(3)-X(4))+ABS(X(7)-X(8))
1380 PH=-17*B(1)-12*B(2)-11*B(3)-12*B(4)-4*B(5)-4*B(6)
1588 P=PH
1651 IF P<=M THEN 1670
1657 FOR KEW=1 TO 8
1658 A(KEW)=X(KEW)
1659 NEXT KEW
1661 M=P
1663 MM=PR
1666 GOTO 128
1670 NEXT I
1890 IF M>-400 THEN 1912 ELSE 1999
1912 PRINT A(1),A(2),A(3),A(4)
1913 PRINT A(5),A(6),A(7),A(8)
1927 PRINT M,JJJJ
1999 NEXT JJJJ
This BASIC computer program was run with the IBM basica/D interpreter, and the output produced during the first second of running is presented below. (What immediately follows is a manual copy from the computer screen.)
0 0 1 1
0 1 1 0
-76 -32000
1 0 0 1
0 0 1 1
-76 -31999
0 0 1 1
0 1 1 0
-76 -31998
1 0 0 1
0 0 1 1
-76 -31997
0 1 1 0
1 1 0 0
-76 -31996
Interpreted in accordance with line 1912 through line 1927, the output through JJJJ=-31996 was produced during the first second of running on a personal computer with an Intel 2.66 GHz. chip and the IBM basica/D interpreter.
References
Gavett. J. W. and N. V. Plyter, "The Optimal Assignment of Facilities to Locations by Branch and Bound," Operations Research 14, 210-232 (Mar.-Apr. 1966).
Heragu, S. S. Facilities Design, Third Edition. Boca Raton, Florida: CRC Press, 2008.
Land, A. H., "A Problem of Assignment with Inter-Related Costs," Operational Research Quarterly 14, 185-199 (June 1963).
Pierce, J. F. and W. B. Crowston, "Tree-Search Algorithms for Quadratic Assignment Problems," Naval Research Logistics Quarterly, 18, 1-36 (1971).
