Like Drezner [1], Heragu and Kusiak [2], and Heragu [3], but unlike Hillier [4] and Nugent, Vollmann, and Ruml [5], the present paper considers a layout problem with locations of sites not given. Specifically the problem of the computer program listed below is the n=30 problem of Nugent et al. [5] with an unknown plant shape, instead of the 5 by 6 plant shape [5, p. 158]. The computer program below attempts to find a cost minimizing shape and assignment (of facilities to locations).
Line 561 through line 995 of the computer program below are slightly different from the mathematical formulation on page 6 of Heragu and Kusiak [2] and on page 140 of Heragu [3].
The following computer program benefits from the computer programs of the present blog and the computer program on pages 229-232 of Conley [6].
2 DEFINT I,J,K
5 DIM B(99),N(99),A(99),H(99),L(99),U(99),X(1111),D(111),P(522)
12 FOR JJJJ=-32000 TO 32000
14 RANDOMIZE JJJJ
16 M=-1D+17
45 FOR IOC=1 TO 90
46 B(IOC)=0
47 NEXT IOC
51 FOR IOCTT=1 TO 90
53 N(IOCTT)=5
57 NEXT IOCTT
58 REM
59 REM
60 REM
61 FOR KLQ=1 TO 90
62 A(KLQ)=B(KLQ)+RND*(N(KLQ)-B(KLQ))
63 NEXT KLQ
71 FOR KLR=1 TO 90
72 H(KLR)=3
73 NEXT KLR
88 FOR JJJ=1 TO 1000 STEP 10
90 FOR INEW=1 TO 1
94 FOR J=INEW*2 TO 0 STEP -1
102 FOR JJ=0 TO 90
128 FOR I=1 TO 20
129 FOR KKQQ=1 TO 90
130 X(KKQQ)=A(KKQQ)
131 NEXT KKQQ
132 FOR K=1 TO 90
133 IF RND<=.5 THEN 298 ELSE 230
230 IF A(K)-(N(K)-B(K))/H(K)^J
255 GOTO 265
260 L(K)=A(K)-(N(K)-B(K))/H(K)^J
265 IF A(K)+(N(K)-B(K))/H(K)^J>N(K) THEN 266 ELSE 268
266 U(K)=N(K)-L(K)
267 GOTO 272
268 U(K)=A(K)+(N(K)-B(K))/H(K)^J-L(K)
272 GOTO 300
298 X(K)=A(K)+2*RND*(2*RND-1)*(1/(1+RND*JJJ))*.05*A(K)
299 GOTO 302
300 X(K)=(L(K)+2*RND*RND*U(K))
302 NEXT K
304 X(JJ)=A(JJ)
306 KLPS=FIX(1+RND*270)
307 FOR KLA1=1 TO KLPS
308 KLA2=FIX(1+90*RND)
309 X(KLA2)=A(KLA2)
310 NEXT KLA1
343 IF RND>.1 GOTO 361
352 IF RND<.5 THEN 353 ELSE 355
353 X(JJ)=B(JJ)
354 GOTO 361
355 X(JJ)=N(JJ)
361 FOR I222=1 TO 90
364 X(I222)=CINT(X(I222))
368 NEXT I222
461 IF RND>.1 GOTO 531
465 IF RND<5/2 THEN 471 ELSE 491
471 IOCT1=1+FIX(RND*90)
474 IOCT2=1+FIX(RND*90)
477 X(IOCT1)=A(IOCT2)
480 X(IOCT2)=A(IOCT1)
481 GOTO 531
491 IOCT6=31+FIX(RND*30)
494 IOCT7=31+FIX(RND*30)
497 X(IOCT6)=A(IOCT7)
500 X(IOCT7)=A(IOCT6)
502 GOTO 531
511 REM
514 REM
517 REM
520 REM
522 REM
531 FOR IOCX=1 TO 90
533 IF X(IOCX)>5 THEN X(IOCX)=3
535 NEXT IOCX
537 REM
538 REM
539 REM
541 FOR IOCY=1 TO 90
543 IF X(IOCY)<0 THEN X(IOCY)=0
545 NEXT IOCY
561 P(11)=ABS(X(1)-X(2))+ABS(X(31)-X(32))+ABS(X(61)-X(62))
562 P(12)=ABS(X(1)-X(3))+ABS(X(31)-X(33))+ABS(X(61)-X(63))
563 P(13)=ABS(X(1)-X(4))+ABS(X(31)-X(34))+ABS(X(61)-X(64))
564 P(14)=ABS(X(1)-X(5))+ABS(X(31)-X(35))+ABS(X(61)-X(65))
565 P(15)=ABS(X(1)-X(6))+ABS(X(31)-X(36))+ABS(X(61)-X(66))
566 P(16)=ABS(X(1)-X(7))+ABS(X(31)-X(37))+ABS(X(61)-X(67))
567 P(17)=ABS(X(1)-X(8))+ABS(X(31)-X(38))+ABS(X(61)-X(68))
568 P(18)=ABS(X(1)-X(9))+ABS(X(31)-X(39))+ABS(X(61)-X(69))
569 P(19)=ABS(X(1)-X(10))+ABS(X(31)-X(40))+ABS(X(61)-X(70))
570 P(20)=ABS(X(1)-X(11))+ABS(X(31)-X(41))+ABS(X(61)-X(71))
571 P(21)=ABS(X(1)-X(12))+ABS(X(31)-X(42))+ABS(X(61)-X(72))
572 P(22)=ABS(X(1)-X(13))+ABS(X(31)-X(43))+ABS(X(61)-X(73))
573 P(23)=ABS(X(1)-X(14))+ABS(X(31)-X(44))+ABS(X(61)-X(74))
574 P(24)=ABS(X(1)-X(15))+ABS(X(31)-X(45))+ABS(X(61)-X(75))
575 P(25)=ABS(X(1)-X(16))+ABS(X(31)-X(46))+ABS(X(61)-X(76))
576 P(26)=ABS(X(1)-X(17))+ABS(X(31)-X(47))+ABS(X(61)-X(77))
577 P(27)=ABS(X(1)-X(18))+ABS(X(31)-X(48))+ABS(X(61)-X(78))
578 P(28)=ABS(X(1)-X(19))+ABS(X(31)-X(49))+ABS(X(61)-X(79))
579 P(29)=ABS(X(1)-X(20))+ABS(X(31)-X(50))+ABS(X(61)-X(80))
580 P(30)=ABS(X(1)-X(21))+ABS(X(31)-X(51))+ABS(X(61)-X(81))
581 P(31)=ABS(X(1)-X(22))+ABS(X(31)-X(52))+ABS(X(61)-X(82))
582 P(32)=ABS(X(1)-X(23))+ABS(X(31)-X(53))+ABS(X(61)-X(83))
583 P(33)=ABS(X(1)-X(24))+ABS(X(31)-X(54))+ABS(X(61)-X(84))
584 P(34)=ABS(X(1)-X(25))+ABS(X(31)-X(55))+ABS(X(61)-X(85))
585 P(35)=ABS(X(1)-X(26))+ABS(X(31)-X(56))+ABS(X(61)-X(86))
586 P(36)=ABS(X(1)-X(27))+ABS(X(31)-X(57))+ABS(X(61)-X(87))
587 P(37)=ABS(X(1)-X(28))+ABS(X(31)-X(58))+ABS(X(61)-X(88))
588 P(38)=ABS(X(1)-X(29))+ABS(X(31)-X(59))+ABS(X(61)-X(89))
589 P(39)=ABS(X(1)-X(30))+ABS(X(31)-X(60))+ABS(X(61)-X(90))
590 P(40)=ABS(X(2)-X(3))+ABS(X(32)-X(33))+ABS(X(62)-X(63))
591 P(41)=ABS(X(2)-X(4))+ABS(X(32)-X(34))+ABS(X(62)-X(64))
592 P(42)=ABS(X(2)-X(5))+ABS(X(32)-X(35))+ABS(X(62)-X(65))
593 P(43)=ABS(X(2)-X(6))+ABS(X(32)-X(36))+ABS(X(62)-X(66))
594 P(44)=ABS(X(2)-X(7))+ABS(X(32)-X(37))+ABS(X(62)-X(67))
595 P(45)=ABS(X(2)-X(8))+ABS(X(32)-X(38))+ABS(X(62)-X(68))
596 P(46)=ABS(X(2)-X(9))+ABS(X(32)-X(39))+ABS(X(62)-X(69))
597 P(47)=ABS(X(2)-X(10))+ABS(X(32)-X(40))+ABS(X(62)-X(70))
598 P(48)=ABS(X(2)-X(11))+ABS(X(32)-X(41))+ABS(X(62)-X(71))
599 P(49)=ABS(X(2)-X(12))+ABS(X(32)-X(42))+ABS(X(62)-X(72))
600 P(50)=ABS(X(2)-X(13))+ABS(X(32)-X(43))+ABS(X(62)-X(73))
601 P(51)=ABS(X(2)-X(14))+ABS(X(32)-X(44))+ABS(X(62)-X(74))
602 P(52)=ABS(X(2)-X(15))+ABS(X(32)-X(45))+ABS(X(62)-X(75))
603 P(53)=ABS(X(2)-X(16))+ABS(X(32)-X(46))+ABS(X(62)-X(76))
604 P(54)=ABS(X(2)-X(17))+ABS(X(32)-X(47))+ABS(X(62)-X(77))
605 P(55)=ABS(X(2)-X(18))+ABS(X(32)-X(48))+ABS(X(62)-X(78))
606 P(56)=ABS(X(2)-X(19))+ABS(X(32)-X(49))+ABS(X(62)-X(79))
607 P(57)=ABS(X(2)-X(20))+ABS(X(32)-X(50))+ABS(X(62)-X(80))
608 P(58)=ABS(X(2)-X(21))+ABS(X(32)-X(51))+ABS(X(62)-X(81))
609 P(59)=ABS(X(2)-X(22))+ABS(X(32)-X(52))+ABS(X(62)-X(82))
610 P(60)=ABS(X(2)-X(23))+ABS(X(32)-X(53))+ABS(X(62)-X(83))
611 P(61)=ABS(X(2)-X(24))+ABS(X(32)-X(54))+ABS(X(62)-X(84))
612 P(62)=ABS(X(2)-X(25))+ABS(X(32)-X(55))+ABS(X(62)-X(85))
613 P(63)=ABS(X(2)-X(26))+ABS(X(32)-X(56))+ABS(X(62)-X(86))
614 P(64)=ABS(X(2)-X(27))+ABS(X(32)-X(57))+ABS(X(62)-X(87))
615 P(65)=ABS(X(2)-X(28))+ABS(X(32)-X(58))+ABS(X(62)-X(88))
616 P(66)=ABS(X(2)-X(29))+ABS(X(32)-X(59))+ABS(X(62)-X(89))
617 P(67)=ABS(X(2)-X(30))+ABS(X(32)-X(60))+ABS(X(62)-X(90))
618 P(68)=ABS(X(3)-X(4))+ABS(X(33)-X(34))+ABS(X(63)-X(64))
619 P(69)=ABS(X(3)-X(5))+ABS(X(33)-X(35))+ABS(X(63)-X(65))
620 P(70)=ABS(X(3)-X(6))+ABS(X(33)-X(36))+ABS(X(63)-X(66))
621 P(71)=ABS(X(3)-X(7))+ABS(X(33)-X(37))+ABS(X(63)-X(67))
622 P(72)=ABS(X(3)-X(8))+ABS(X(33)-X(38))+ABS(X(63)-X(68))
623 P(73)=ABS(X(3)-X(9))+ABS(X(33)-X(39))+ABS(X(63)-X(69))
624 P(74)=ABS(X(3)-X(10))+ABS(X(33)-X(40))+ABS(X(63)-X(70))
625 P(75)=ABS(X(3)-X(11))+ABS(X(33)-X(41))+ABS(X(63)-X(71))
626 P(76)=ABS(X(3)-X(12))+ABS(X(33)-X(42))+ABS(X(63)-X(72))
627 P(77)=ABS(X(3)-X(13))+ABS(X(33)-X(43))+ABS(X(63)-X(73))
628 P(78)=ABS(X(3)-X(14))+ABS(X(33)-X(44))+ABS(X(63)-X(74))
629 P(79)=ABS(X(3)-X(15))+ABS(X(33)-X(45))+ABS(X(63)-X(75))
630 P(80)=ABS(X(3)-X(16))+ABS(X(33)-X(46))+ABS(X(63)-X(76))
631 P(81)=ABS(X(3)-X(17))+ABS(X(33)-X(47))+ABS(X(63)-X(77))
632 P(82)=ABS(X(3)-X(18))+ABS(X(33)-X(48))+ABS(X(63)-X(78))
633 P(83)=ABS(X(3)-X(19))+ABS(X(33)-X(49))+ABS(X(63)-X(79))
634 P(84)=ABS(X(3)-X(20))+ABS(X(33)-X(50))+ABS(X(63)-X(80))
635 P(85)=ABS(X(3)-X(21))+ABS(X(33)-X(51))+ABS(X(63)-X(81))
636 P(86)=ABS(X(3)-X(22))+ABS(X(33)-X(52))+ABS(X(63)-X(82))
637 P(87)=ABS(X(3)-X(23))+ABS(X(33)-X(53))+ABS(X(63)-X(83))
638 P(88)=ABS(X(3)-X(24))+ABS(X(33)-X(54))+ABS(X(63)-X(84))
639 P(89)=ABS(X(3)-X(25))+ABS(X(33)-X(55))+ABS(X(63)-X(85))
640 P(90)=ABS(X(3)-X(26))+ABS(X(33)-X(56))+ABS(X(63)-X(86))
641 P(91)=ABS(X(3)-X(27))+ABS(X(33)-X(57))+ABS(X(63)-X(87))
642 P(92)=ABS(X(3)-X(28))+ABS(X(33)-X(58))+ABS(X(63)-X(88))
643 P(93)=ABS(X(3)-X(29))+ABS(X(33)-X(59))+ABS(X(63)-X(89))
644 P(94)=ABS(X(3)-X(30))+ABS(X(33)-X(60))+ABS(X(63)-X(90))
645 P(95)=ABS(X(4)-X(5))+ABS(X(34)-X(35))+ABS(X(64)-X(65))
646 P(96)=ABS(X(4)-X(6))+ABS(X(34)-X(36))+ABS(X(64)-X(66))
647 P(97)=ABS(X(4)-X(7))+ABS(X(34)-X(37))+ABS(X(64)-X(67))
648 P(98)=ABS(X(4)-X(8))+ABS(X(34)-X(38))+ABS(X(64)-X(68))
649 P(99)=ABS(X(4)-X(9))+ABS(X(34)-X(39))+ABS(X(64)-X(69))
650 P(100)=ABS(X(4)-X(10))+ABS(X(34)-X(40))+ABS(X(64)-X(70))
651 P(101)=ABS(X(4)-X(11))+ABS(X(34)-X(41))+ABS(X(64)-X(71))
652 P(102)=ABS(X(4)-X(12))+ABS(X(34)-X(42))+ABS(X(64)-X(72))
653 P(103)=ABS(X(4)-X(13))+ABS(X(34)-X(43))+ABS(X(64)-X(73))
654 P(104)=ABS(X(4)-X(14))+ABS(X(34)-X(44))+ABS(X(64)-X(74))
655 P(105)=ABS(X(4)-X(15))+ABS(X(34)-X(45))+ABS(X(64)-X(75))
656 P(106)=ABS(X(4)-X(16))+ABS(X(34)-X(46))+ABS(X(64)-X(76))
657 P(107)=ABS(X(4)-X(17))+ABS(X(34)-X(47))+ABS(X(64)-X(77))
658 P(108)=ABS(X(4)-X(18))+ABS(X(34)-X(48))+ABS(X(64)-X(78))
659 P(109)=ABS(X(4)-X(19))+ABS(X(34)-X(49))+ABS(X(64)-X(79))
660 P(110)=ABS(X(4)-X(20))+ABS(X(34)-X(50))+ABS(X(64)-X(80))
661 P(111)=ABS(X(4)-X(21))+ABS(X(34)-X(51))+ABS(X(64)-X(81))
662 P(112)=ABS(X(4)-X(22))+ABS(X(34)-X(52))+ABS(X(64)-X(82))
663 P(113)=ABS(X(4)-X(23))+ABS(X(34)-X(53))+ABS(X(64)-X(83))
664 P(114)=ABS(X(4)-X(24))+ABS(X(34)-X(54))+ABS(X(64)-X(84))
665 P(115)=ABS(X(4)-X(25))+ABS(X(34)-X(55))+ABS(X(64)-X(85))
666 P(116)=ABS(X(4)-X(26))+ABS(X(34)-X(56))+ABS(X(64)-X(86))
667 P(117)=ABS(X(4)-X(27))+ABS(X(34)-X(57))+ABS(X(64)-X(87))
668 P(118)=ABS(X(4)-X(28))+ABS(X(34)-X(58))+ABS(X(64)-X(88))
669 P(119)=ABS(X(4)-X(29))+ABS(X(34)-X(59))+ABS(X(64)-X(89))
670 P(120)=ABS(X(4)-X(30))+ABS(X(34)-X(60))+ABS(X(64)-X(90))
671 P(121)=ABS(X(5)-X(6))+ABS(X(35)-X(36))+ABS(X(65)-X(66))
672 P(122)=ABS(X(5)-X(7))+ABS(X(35)-X(37))+ABS(X(65)-X(67))
673 P(123)=ABS(X(5)-X(8))+ABS(X(35)-X(38))+ABS(X(65)-X(68))
674 P(124)=ABS(X(5)-X(9))+ABS(X(35)-X(39))+ABS(X(65)-X(69))
675 P(125)=ABS(X(5)-X(10))+ABS(X(35)-X(40))+ABS(X(65)-X(70))
676 P(126)=ABS(X(5)-X(11))+ABS(X(35)-X(41))+ABS(X(65)-X(71))
677 P(127)=ABS(X(5)-X(12))+ABS(X(35)-X(42))+ABS(X(65)-X(72))
678 P(128)=ABS(X(5)-X(13))+ABS(X(35)-X(43))+ABS(X(65)-X(73))
679 P(129)=ABS(X(5)-X(14))+ABS(X(35)-X(44))+ABS(X(65)-X(74))
680 P(130)=ABS(X(5)-X(15))+ABS(X(35)-X(45))+ABS(X(65)-X(75))
681 P(131)=ABS(X(5)-X(16))+ABS(X(35)-X(46))+ABS(X(65)-X(76))
682 P(132)=ABS(X(5)-X(17))+ABS(X(35)-X(47))+ABS(X(65)-X(77))
683 P(133)=ABS(X(5)-X(18))+ABS(X(35)-X(48))+ABS(X(65)-X(78))
684 P(134)=ABS(X(5)-X(19))+ABS(X(35)-X(49))+ABS(X(65)-X(79))
685 P(135)=ABS(X(5)-X(20))+ABS(X(35)-X(50))+ABS(X(65)-X(80))
686 P(136)=ABS(X(5)-X(21))+ABS(X(35)-X(51))+ABS(X(65)-X(81))
687 P(137)=ABS(X(5)-X(22))+ABS(X(35)-X(52))+ABS(X(65)-X(82))
688 P(138)=ABS(X(5)-X(23))+ABS(X(35)-X(53))+ABS(X(65)-X(83))
689 P(139)=ABS(X(5)-X(24))+ABS(X(35)-X(54))+ABS(X(65)-X(84))
690 P(140)=ABS(X(5)-X(25))+ABS(X(35)-X(55))+ABS(X(65)-X(85))
691 P(141)=ABS(X(5)-X(26))+ABS(X(35)-X(56))+ABS(X(65)-X(86))
692 P(142)=ABS(X(5)-X(27))+ABS(X(35)-X(57))+ABS(X(65)-X(87))
693 P(143)=ABS(X(5)-X(28))+ABS(X(35)-X(58))+ABS(X(65)-X(88))
694 P(144)=ABS(X(5)-X(29))+ABS(X(35)-X(59))+ABS(X(65)-X(89))
695 P(145)=ABS(X(5)-X(30))+ABS(X(35)-X(60))+ABS(X(65)-X(90))
696 P(146)=ABS(X(6)-X(7))+ABS(X(36)-X(37))+ABS(X(66)-X(67))
697 P(147)=ABS(X(6)-X(8))+ABS(X(36)-X(38))+ABS(X(66)-X(68))
698 P(148)=ABS(X(6)-X(9))+ABS(X(36)-X(39))+ABS(X(66)-X(69))
699 P(149)=ABS(X(6)-X(10))+ABS(X(36)-X(40))+ABS(X(66)-X(70))
700 P(150)=ABS(X(6)-X(11))+ABS(X(36)-X(41))+ABS(X(66)-X(71))
701 P(151)=ABS(X(6)-X(12))+ABS(X(36)-X(42))+ABS(X(66)-X(72))
702 P(152)=ABS(X(6)-X(13))+ABS(X(36)-X(43))+ABS(X(66)-X(73))
703 P(153)=ABS(X(6)-X(14))+ABS(X(36)-X(44))+ABS(X(66)-X(74))
704 P(154)=ABS(X(6)-X(15))+ABS(X(36)-X(45))+ABS(X(66)-X(75))
705 P(155)=ABS(X(6)-X(16))+ABS(X(36)-X(46))+ABS(X(66)-X(76))
706 P(156)=ABS(X(6)-X(17))+ABS(X(36)-X(47))+ABS(X(66)-X(77))
707 P(157)=ABS(X(6)-X(18))+ABS(X(36)-X(48))+ABS(X(66)-X(78))
708 P(158)=ABS(X(6)-X(19))+ABS(X(36)-X(49))+ABS(X(66)-X(79))
709 P(159)=ABS(X(6)-X(20))+ABS(X(36)-X(50))+ABS(X(66)-X(80))
710 P(160)=ABS(X(6)-X(21))+ABS(X(36)-X(51))+ABS(X(66)-X(81))
711 P(161)=ABS(X(6)-X(22))+ABS(X(36)-X(52))+ABS(X(66)-X(82))
712 P(162)=ABS(X(6)-X(23))+ABS(X(36)-X(53))+ABS(X(66)-X(83))
713 P(163)=ABS(X(6)-X(24))+ABS(X(36)-X(54))+ABS(X(66)-X(84))
714 P(164)=ABS(X(6)-X(25))+ABS(X(36)-X(55))+ABS(X(66)-X(85))
715 P(165)=ABS(X(6)-X(26))+ABS(X(36)-X(56))+ABS(X(66)-X(86))
716 P(166)=ABS(X(6)-X(27))+ABS(X(36)-X(57))+ABS(X(66)-X(87))
717 P(167)=ABS(X(6)-X(28))+ABS(X(36)-X(58))+ABS(X(66)-X(88))
718 P(168)=ABS(X(6)-X(29))+ABS(X(36)-X(59))+ABS(X(66)-X(89))
719 P(169)=ABS(X(6)-X(30))+ABS(X(36)-X(60))+ABS(X(66)-X(90))
720 P(170)=ABS(X(7)-X(8))+ABS(X(37)-X(38))+ABS(X(67)-X(68))
721 P(171)=ABS(X(7)-X(9))+ABS(X(37)-X(39))+ABS(X(67)-X(69))
722 P(172)=ABS(X(7)-X(10))+ABS(X(37)-X(40))+ABS(X(67)-X(70))
723 P(173)=ABS(X(7)-X(11))+ABS(X(37)-X(41))+ABS(X(67)-X(71))
724 P(174)=ABS(X(7)-X(12))+ABS(X(37)-X(42))+ABS(X(67)-X(72))
725 P(175)=ABS(X(7)-X(13))+ABS(X(37)-X(43))+ABS(X(67)-X(73))
726 P(176)=ABS(X(7)-X(14))+ABS(X(37)-X(44))+ABS(X(67)-X(74))
727 P(177)=ABS(X(7)-X(15))+ABS(X(37)-X(45))+ABS(X(67)-X(75))
728 P(178)=ABS(X(7)-X(16))+ABS(X(37)-X(46))+ABS(X(67)-X(76))
729 P(179)=ABS(X(7)-X(17))+ABS(X(37)-X(47))+ABS(X(67)-X(77))
730 P(180)=ABS(X(7)-X(18))+ABS(X(37)-X(48))+ABS(X(67)-X(78))
731 P(181)=ABS(X(7)-X(19))+ABS(X(37)-X(49))+ABS(X(67)-X(79))
732 P(182)=ABS(X(7)-X(20))+ABS(X(37)-X(50))+ABS(X(67)-X(80))
733 P(183)=ABS(X(7)-X(21))+ABS(X(37)-X(51))+ABS(X(67)-X(81))
734 P(184)=ABS(X(7)-X(22))+ABS(X(37)-X(52))+ABS(X(67)-X(82))
735 P(185)=ABS(X(7)-X(23))+ABS(X(37)-X(53))+ABS(X(67)-X(83))
736 P(186)=ABS(X(7)-X(24))+ABS(X(37)-X(54))+ABS(X(67)-X(84))
737 P(187)=ABS(X(7)-X(25))+ABS(X(37)-X(55))+ABS(X(67)-X(85))
738 P(188)=ABS(X(7)-X(26))+ABS(X(37)-X(56))+ABS(X(67)-X(86))
739 P(189)=ABS(X(7)-X(27))+ABS(X(37)-X(57))+ABS(X(67)-X(87))
740 P(190)=ABS(X(7)-X(28))+ABS(X(37)-X(58))+ABS(X(67)-X(88))
741 P(191)=ABS(X(7)-X(29))+ABS(X(37)-X(59))+ABS(X(67)-X(89))
742 P(192)=ABS(X(7)-X(30))+ABS(X(37)-X(60))+ABS(X(67)-X(90))
743 P(193)=ABS(X(8)-X(9))+ABS(X(38)-X(39))+ABS(X(68)-X(69))
744 P(194)=ABS(X(8)-X(10))+ABS(X(38)-X(40))+ABS(X(68)-X(70))
745 P(195)=ABS(X(8)-X(11))+ABS(X(38)-X(41))+ABS(X(68)-X(71))
746 P(196)=ABS(X(8)-X(12))+ABS(X(38)-X(42))+ABS(X(68)-X(72))
747 P(197)=ABS(X(8)-X(13))+ABS(X(38)-X(43))+ABS(X(68)-X(73))
748 P(198)=ABS(X(8)-X(14))+ABS(X(38)-X(44))+ABS(X(68)-X(74))
749 P(199)=ABS(X(8)-X(15))+ABS(X(38)-X(45))+ABS(X(68)-X(75))
750 P(200)=ABS(X(8)-X(16))+ABS(X(38)-X(46))+ABS(X(68)-X(76))
751 P(201)=ABS(X(8)-X(17))+ABS(X(38)-X(47))+ABS(X(68)-X(77))
752 P(202)=ABS(X(8)-X(18))+ABS(X(38)-X(48))+ABS(X(68)-X(78))
753 P(203)=ABS(X(8)-X(19))+ABS(X(38)-X(49))+ABS(X(68)-X(79))
754 P(204)=ABS(X(8)-X(20))+ABS(X(38)-X(50))+ABS(X(68)-X(80))
755 P(205)=ABS(X(8)-X(21))+ABS(X(38)-X(51))+ABS(X(68)-X(81))
756 P(206)=ABS(X(8)-X(22))+ABS(X(38)-X(52))+ABS(X(68)-X(82))
757 P(207)=ABS(X(8)-X(23))+ABS(X(38)-X(53))+ABS(X(68)-X(83))
758 P(208)=ABS(X(8)-X(24))+ABS(X(38)-X(54))+ABS(X(68)-X(84))
759 P(209)=ABS(X(8)-X(25))+ABS(X(38)-X(55))+ABS(X(68)-X(85))
760 P(210)=ABS(X(8)-X(26))+ABS(X(38)-X(56))+ABS(X(68)-X(86))
761 P(211)=ABS(X(8)-X(27))+ABS(X(38)-X(57))+ABS(X(68)-X(87))
762 P(212)=ABS(X(8)-X(28))+ABS(X(38)-X(58))+ABS(X(68)-X(88))
763 P(213)=ABS(X(8)-X(29))+ABS(X(38)-X(59))+ABS(X(68)-X(89))
764 P(214)=ABS(X(8)-X(30))+ABS(X(38)-X(60))+ABS(X(68)-X(90))
765 P(215)=ABS(X(9)-X(10))+ABS(X(39)-X(40))+ABS(X(69)-X(70))
766 P(216)=ABS(X(9)-X(11))+ABS(X(39)-X(41))+ABS(X(69)-X(71))
767 P(217)=ABS(X(9)-X(12))+ABS(X(39)-X(42))+ABS(X(69)-X(72))
768 P(218)=ABS(X(9)-X(13))+ABS(X(39)-X(43))+ABS(X(69)-X(73))
769 P(219)=ABS(X(9)-X(14))+ABS(X(39)-X(44))+ABS(X(69)-X(74))
770 P(220)=ABS(X(9)-X(15))+ABS(X(39)-X(45))+ABS(X(69)-X(75))
771 P(221)=ABS(X(9)-X(16))+ABS(X(39)-X(46))+ABS(X(69)-X(76))
772 P(222)=ABS(X(9)-X(17))+ABS(X(39)-X(47))+ABS(X(69)-X(77))
773 P(223)=ABS(X(9)-X(18))+ABS(X(39)-X(48))+ABS(X(69)-X(78))
774 P(224)=ABS(X(9)-X(19))+ABS(X(39)-X(49))+ABS(X(69)-X(79))
775 P(225)=ABS(X(9)-X(20))+ABS(X(39)-X(50))+ABS(X(69)-X(80))
776 P(226)=ABS(X(9)-X(21))+ABS(X(39)-X(51))+ABS(X(69)-X(81))
777 P(227)=ABS(X(9)-X(22))+ABS(X(39)-X(52))+ABS(X(69)-X(82))
778 P(228)=ABS(X(9)-X(23))+ABS(X(39)-X(53))+ABS(X(69)-X(83))
779 P(229)=ABS(X(9)-X(24))+ABS(X(39)-X(54))+ABS(X(69)-X(84))
780 P(230)=ABS(X(9)-X(25))+ABS(X(39)-X(55))+ABS(X(69)-X(85))
781 P(231)=ABS(X(9)-X(26))+ABS(X(39)-X(56))+ABS(X(69)-X(86))
782 P(232)=ABS(X(9)-X(27))+ABS(X(39)-X(57))+ABS(X(69)-X(87))
783 P(233)=ABS(X(9)-X(28))+ABS(X(39)-X(58))+ABS(X(69)-X(88))
784 P(234)=ABS(X(9)-X(29))+ABS(X(39)-X(59))+ABS(X(69)-X(89))
785 P(235)=ABS(X(9)-X(30))+ABS(X(39)-X(60))+ABS(X(69)-X(90))
786 P(236)=ABS(X(10)-X(11))+ABS(X(40)-X(41))+ABS(X(70)-X(71))
787 P(237)=ABS(X(10)-X(12))+ABS(X(40)-X(42))+ABS(X(70)-X(72))
788 P(238)=ABS(X(10)-X(13))+ABS(X(40)-X(43))+ABS(X(70)-X(73))
789 P(239)=ABS(X(10)-X(14))+ABS(X(40)-X(44))+ABS(X(70)-X(74))
790 P(240)=ABS(X(10)-X(15))+ABS(X(40)-X(45))+ABS(X(70)-X(75))
791 P(241)=ABS(X(10)-X(16))+ABS(X(40)-X(46))+ABS(X(70)-X(76))
792 P(242)=ABS(X(10)-X(17))+ABS(X(40)-X(47))+ABS(X(70)-X(77))
793 P(243)=ABS(X(10)-X(18))+ABS(X(40)-X(48))+ABS(X(70)-X(78))
794 P(244)=ABS(X(10)-X(19))+ABS(X(40)-X(49))+ABS(X(70)-X(79))
795 P(245)=ABS(X(10)-X(20))+ABS(X(40)-X(50))+ABS(X(70)-X(80))
796 P(246)=ABS(X(10)-X(21))+ABS(X(40)-X(51))+ABS(X(70)-X(81))
797 P(247)=ABS(X(10)-X(22))+ABS(X(40)-X(52))+ABS(X(70)-X(82))
798 P(248)=ABS(X(10)-X(23))+ABS(X(40)-X(53))+ABS(X(70)-X(83))
799 P(249)=ABS(X(10)-X(24))+ABS(X(40)-X(54))+ABS(X(70)-X(84))
800 P(250)=ABS(X(10)-X(25))+ABS(X(40)-X(55))+ABS(X(70)-X(85))
801 P(251)=ABS(X(10)-X(26))+ABS(X(40)-X(56))+ABS(X(70)-X(86))
802 P(252)=ABS(X(10)-X(27))+ABS(X(40)-X(57))+ABS(X(70)-X(87))
803 P(253)=ABS(X(10)-X(28))+ABS(X(40)-X(58))+ABS(X(70)-X(88))
804 P(254)=ABS(X(10)-X(29))+ABS(X(40)-X(59))+ABS(X(70)-X(89))
805 P(255)=ABS(X(10)-X(30))+ABS(X(40)-X(60))+ABS(X(70)-X(90))
806 P(256)=ABS(X(11)-X(12))+ABS(X(41)-X(42))+ABS(X(71)-X(72))
807 P(257)=ABS(X(11)-X(13))+ABS(X(41)-X(43))+ABS(X(71)-X(73))
808 P(258)=ABS(X(11)-X(14))+ABS(X(41)-X(44))+ABS(X(71)-X(74))
809 P(259)=ABS(X(11)-X(15))+ABS(X(41)-X(45))+ABS(X(71)-X(75))
810 P(260)=ABS(X(11)-X(16))+ABS(X(41)-X(46))+ABS(X(71)-X(76))
811 P(261)=ABS(X(11)-X(17))+ABS(X(41)-X(47))+ABS(X(71)-X(77))
812 P(262)=ABS(X(11)-X(18))+ABS(X(41)-X(48))+ABS(X(71)-X(78))
813 P(263)=ABS(X(11)-X(19))+ABS(X(41)-X(49))+ABS(X(71)-X(79))
814 P(264)=ABS(X(11)-X(20))+ABS(X(41)-X(50))+ABS(X(71)-X(80))
815 P(265)=ABS(X(11)-X(21))+ABS(X(41)-X(51))+ABS(X(71)-X(81))
816 P(266)=ABS(X(11)-X(22))+ABS(X(41)-X(52))+ABS(X(71)-X(82))
817 P(267)=ABS(X(11)-X(23))+ABS(X(41)-X(53))+ABS(X(71)-X(83))
818 P(268)=ABS(X(11)-X(24))+ABS(X(41)-X(54))+ABS(X(71)-X(84))
819 P(269)=ABS(X(11)-X(25))+ABS(X(41)-X(55))+ABS(X(71)-X(85))
820 P(270)=ABS(X(11)-X(26))+ABS(X(41)-X(56))+ABS(X(71)-X(86))
821 P(271)=ABS(X(11)-X(27))+ABS(X(41)-X(57))+ABS(X(71)-X(87))
822 P(272)=ABS(X(11)-X(28))+ABS(X(41)-X(58))+ABS(X(71)-X(88))
823 P(273)=ABS(X(11)-X(29))+ABS(X(41)-X(59))+ABS(X(71)-X(89))
824 P(274)=ABS(X(11)-X(30))+ABS(X(41)-X(60))+ABS(X(71)-X(90))
825 P(275)=ABS(X(12)-X(13))+ABS(X(42)-X(43))+ABS(X(72)-X(73))
826 P(276)=ABS(X(12)-X(14))+ABS(X(42)-X(44))+ABS(X(72)-X(74))
827 P(277)=ABS(X(12)-X(15))+ABS(X(42)-X(45))+ABS(X(72)-X(75))
828 P(278)=ABS(X(12)-X(16))+ABS(X(42)-X(46))+ABS(X(72)-X(76))
829 P(279)=ABS(X(12)-X(17))+ABS(X(42)-X(47))+ABS(X(72)-X(77))
830 P(280)=ABS(X(12)-X(18))+ABS(X(42)-X(48))+ABS(X(72)-X(78))
831 P(281)=ABS(X(12)-X(19))+ABS(X(42)-X(49))+ABS(X(72)-X(79))
832 P(282)=ABS(X(12)-X(20))+ABS(X(42)-X(50))+ABS(X(72)-X(80))
833 P(283)=ABS(X(12)-X(21))+ABS(X(42)-X(51))+ABS(X(72)-X(81))
834 P(284)=ABS(X(12)-X(22))+ABS(X(42)-X(52))+ABS(X(72)-X(82))
835 P(285)=ABS(X(12)-X(23))+ABS(X(42)-X(53))+ABS(X(72)-X(83))
836 P(286)=ABS(X(12)-X(24))+ABS(X(42)-X(54))+ABS(X(72)-X(84))
837 P(287)=ABS(X(12)-X(25))+ABS(X(42)-X(55))+ABS(X(72)-X(85))
838 P(288)=ABS(X(12)-X(26))+ABS(X(42)-X(56))+ABS(X(72)-X(86))
839 P(289)=ABS(X(12)-X(27))+ABS(X(42)-X(57))+ABS(X(72)-X(87))
840 P(290)=ABS(X(12)-X(28))+ABS(X(42)-X(58))+ABS(X(72)-X(88))
841 P(291)=ABS(X(12)-X(29))+ABS(X(42)-X(59))+ABS(X(72)-X(89))
842 P(292)=ABS(X(12)-X(30))+ABS(X(42)-X(60))+ABS(X(72)-X(90))
843 P(293)=ABS(X(13)-X(14))+ABS(X(43)-X(44))+ABS(X(73)-X(74))
844 P(294)=ABS(X(13)-X(15))+ABS(X(43)-X(45))+ABS(X(73)-X(75))
845 P(295)=ABS(X(13)-X(16))+ABS(X(43)-X(46))+ABS(X(73)-X(76))
846 P(296)=ABS(X(13)-X(17))+ABS(X(43)-X(47))+ABS(X(73)-X(77))
847 P(297)=ABS(X(13)-X(18))+ABS(X(43)-X(48))+ABS(X(73)-X(78))
848 P(298)=ABS(X(13)-X(19))+ABS(X(43)-X(49))+ABS(X(73)-X(79))
849 P(299)=ABS(X(13)-X(20))+ABS(X(43)-X(50))+ABS(X(73)-X(80))
850 P(300)=ABS(X(13)-X(21))+ABS(X(43)-X(51))+ABS(X(73)-X(81))
851 P(301)=ABS(X(13)-X(22))+ABS(X(43)-X(52))+ABS(X(73)-X(82))
852 P(302)=ABS(X(13)-X(23))+ABS(X(43)-X(53))+ABS(X(73)-X(83))
853 P(303)=ABS(X(13)-X(24))+ABS(X(43)-X(54))+ABS(X(73)-X(84))
854 P(304)=ABS(X(13)-X(25))+ABS(X(43)-X(55))+ABS(X(73)-X(85))
855 P(305)=ABS(X(13)-X(26))+ABS(X(43)-X(56))+ABS(X(73)-X(86))
856 P(306)=ABS(X(13)-X(27))+ABS(X(43)-X(57))+ABS(X(73)-X(87))
857 P(307)=ABS(X(13)-X(28))+ABS(X(43)-X(58))+ABS(X(73)-X(88))
858 P(308)=ABS(X(13)-X(29))+ABS(X(43)-X(59))+ABS(X(73)-X(89))
859 P(309)=ABS(X(13)-X(30))+ABS(X(43)-X(60))+ABS(X(73)-X(90))
860 P(310)=ABS(X(14)-X(15))+ABS(X(44)-X(45))+ABS(X(74)-X(75))
861 P(311)=ABS(X(14)-X(16))+ABS(X(44)-X(46))+ABS(X(74)-X(76))
862 P(312)=ABS(X(14)-X(17))+ABS(X(44)-X(47))+ABS(X(74)-X(77))
863 P(313)=ABS(X(14)-X(18))+ABS(X(44)-X(48))+ABS(X(74)-X(78))
864 P(314)=ABS(X(14)-X(19))+ABS(X(44)-X(49))+ABS(X(74)-X(79))
865 P(315)=ABS(X(14)-X(20))+ABS(X(44)-X(50))+ABS(X(74)-X(80))
866 P(316)=ABS(X(14)-X(21))+ABS(X(44)-X(51))+ABS(X(74)-X(81))
867 P(317)=ABS(X(14)-X(22))+ABS(X(44)-X(52))+ABS(X(74)-X(82))
868 P(318)=ABS(X(14)-X(23))+ABS(X(44)-X(53))+ABS(X(74)-X(83))
869 P(319)=ABS(X(14)-X(24))+ABS(X(44)-X(54))+ABS(X(74)-X(84))
870 P(320)=ABS(X(14)-X(25))+ABS(X(44)-X(55))+ABS(X(74)-X(85))
871 P(321)=ABS(X(14)-X(26))+ABS(X(44)-X(56))+ABS(X(74)-X(86))
872 P(322)=ABS(X(14)-X(27))+ABS(X(44)-X(57))+ABS(X(74)-X(87))
873 P(323)=ABS(X(14)-X(28))+ABS(X(44)-X(58))+ABS(X(74)-X(88))
874 P(324)=ABS(X(14)-X(29))+ABS(X(44)-X(59))+ABS(X(74)-X(89))
875 P(325)=ABS(X(14)-X(30))+ABS(X(44)-X(60))+ABS(X(74)-X(90))
876 P(326)=ABS(X(15)-X(16))+ABS(X(45)-X(46))+ABS(X(75)-X(76))
877 P(327)=ABS(X(15)-X(17))+ABS(X(45)-X(47))+ABS(X(75)-X(77))
878 P(328)=ABS(X(15)-X(18))+ABS(X(45)-X(48))+ABS(X(75)-X(78))
879 P(329)=ABS(X(15)-X(19))+ABS(X(45)-X(49))+ABS(X(75)-X(79))
880 P(330)=ABS(X(15)-X(20))+ABS(X(45)-X(50))+ABS(X(75)-X(80))
881 P(331)=ABS(X(15)-X(21))+ABS(X(45)-X(51))+ABS(X(75)-X(81))
882 P(332)=ABS(X(15)-X(22))+ABS(X(45)-X(52))+ABS(X(75)-X(82))
883 P(333)=ABS(X(15)-X(23))+ABS(X(45)-X(53))+ABS(X(75)-X(83))
884 P(334)=ABS(X(15)-X(24))+ABS(X(45)-X(54))+ABS(X(75)-X(84))
885 P(335)=ABS(X(15)-X(25))+ABS(X(45)-X(55))+ABS(X(75)-X(85))
886 P(336)=ABS(X(15)-X(26))+ABS(X(45)-X(56))+ABS(X(75)-X(86))
887 P(337)=ABS(X(15)-X(27))+ABS(X(45)-X(57))+ABS(X(75)-X(87))
888 P(338)=ABS(X(15)-X(28))+ABS(X(45)-X(58))+ABS(X(75)-X(88))
889 P(339)=ABS(X(15)-X(29))+ABS(X(45)-X(59))+ABS(X(75)-X(89))
890 P(340)=ABS(X(15)-X(30))+ABS(X(45)-X(60))+ABS(X(75)-X(90))
891 P(341)=ABS(X(16)-X(17))+ABS(X(46)-X(47))+ABS(X(76)-X(77))
892 P(342)=ABS(X(16)-X(18))+ABS(X(46)-X(48))+ABS(X(76)-X(78))
893 P(343)=ABS(X(16)-X(19))+ABS(X(46)-X(49))+ABS(X(76)-X(79))
894 P(344)=ABS(X(16)-X(20))+ABS(X(46)-X(50))+ABS(X(76)-X(80))
895 P(345)=ABS(X(16)-X(21))+ABS(X(46)-X(51))+ABS(X(76)-X(81))
896 P(346)=ABS(X(16)-X(22))+ABS(X(46)-X(52))+ABS(X(76)-X(82))
897 P(347)=ABS(X(16)-X(23))+ABS(X(46)-X(53))+ABS(X(76)-X(83))
898 P(348)=ABS(X(16)-X(24))+ABS(X(46)-X(54))+ABS(X(76)-X(84))
899 P(349)=ABS(X(16)-X(25))+ABS(X(46)-X(55))+ABS(X(76)-X(85))
900 P(350)=ABS(X(16)-X(26))+ABS(X(46)-X(56))+ABS(X(76)-X(86))
901 P(351)=ABS(X(16)-X(27))+ABS(X(46)-X(57))+ABS(X(76)-X(87))
902 P(352)=ABS(X(16)-X(28))+ABS(X(46)-X(58))+ABS(X(76)-X(88))
903 P(353)=ABS(X(16)-X(29))+ABS(X(46)-X(59))+ABS(X(76)-X(89))
904 P(354)=ABS(X(16)-X(30))+ABS(X(46)-X(60))+ABS(X(76)-X(90))
905 P(355)=ABS(X(17)-X(18))+ABS(X(47)-X(48))+ABS(X(77)-X(78))
906 P(356)=ABS(X(17)-X(19))+ABS(X(47)-X(49))+ABS(X(77)-X(79))
907 P(357)=ABS(X(17)-X(20))+ABS(X(47)-X(50))+ABS(X(77)-X(80))
908 P(358)=ABS(X(17)-X(21))+ABS(X(47)-X(51))+ABS(X(77)-X(81))
909 P(359)=ABS(X(17)-X(22))+ABS(X(47)-X(52))+ABS(X(77)-X(82))
910 P(360)=ABS(X(17)-X(23))+ABS(X(47)-X(53))+ABS(X(77)-X(83))
911 P(361)=ABS(X(17)-X(24))+ABS(X(47)-X(54))+ABS(X(77)-X(84))
912 P(362)=ABS(X(17)-X(25))+ABS(X(47)-X(55))+ABS(X(77)-X(85))
913 P(363)=ABS(X(17)-X(26))+ABS(X(47)-X(56))+ABS(X(77)-X(86))
914 P(364)=ABS(X(17)-X(27))+ABS(X(47)-X(57))+ABS(X(77)-X(87))
915 P(365)=ABS(X(17)-X(28))+ABS(X(47)-X(58))+ABS(X(77)-X(88))
916 P(366)=ABS(X(17)-X(29))+ABS(X(47)-X(59))+ABS(X(77)-X(89))
917 P(367)=ABS(X(17)-X(30))+ABS(X(47)-X(60))+ABS(X(77)-X(90))
918 P(368)=ABS(X(18)-X(19))+ABS(X(48)-X(49))+ABS(X(78)-X(79))
919 P(369)=ABS(X(18)-X(20))+ABS(X(48)-X(50))+ABS(X(78)-X(80))
920 P(370)=ABS(X(18)-X(21))+ABS(X(48)-X(51))+ABS(X(78)-X(81))
921 P(371)=ABS(X(18)-X(22))+ABS(X(48)-X(52))+ABS(X(78)-X(82))
922 P(372)=ABS(X(18)-X(23))+ABS(X(48)-X(53))+ABS(X(78)-X(83))
923 P(373)=ABS(X(18)-X(24))+ABS(X(48)-X(54))+ABS(X(78)-X(84))
924 P(374)=ABS(X(18)-X(25))+ABS(X(48)-X(55))+ABS(X(78)-X(85))
925 P(375)=ABS(X(18)-X(26))+ABS(X(48)-X(56))+ABS(X(78)-X(86))
926 P(376)=ABS(X(18)-X(27))+ABS(X(48)-X(57))+ABS(X(78)-X(87))
927 P(377)=ABS(X(18)-X(28))+ABS(X(48)-X(58))+ABS(X(78)-X(88))
928 P(378)=ABS(X(18)-X(29))+ABS(X(48)-X(59))+ABS(X(78)-X(89))
929 P(379)=ABS(X(18)-X(30))+ABS(X(48)-X(60))+ABS(X(78)-X(90))
930 P(380)=ABS(X(19)-X(20))+ABS(X(49)-X(50))+ABS(X(79)-X(80))
931 P(381)=ABS(X(19)-X(21))+ABS(X(49)-X(51))+ABS(X(79)-X(81))
932 P(382)=ABS(X(19)-X(22))+ABS(X(49)-X(52))+ABS(X(79)-X(82))
933 P(383)=ABS(X(19)-X(23))+ABS(X(49)-X(53))+ABS(X(79)-X(83))
934 P(384)=ABS(X(19)-X(24))+ABS(X(49)-X(54))+ABS(X(79)-X(84))
935 P(385)=ABS(X(19)-X(25))+ABS(X(49)-X(55))+ABS(X(79)-X(85))
936 P(386)=ABS(X(19)-X(26))+ABS(X(49)-X(56))+ABS(X(79)-X(86))
937 P(387)=ABS(X(19)-X(27))+ABS(X(49)-X(57))+ABS(X(79)-X(87))
938 P(388)=ABS(X(19)-X(28))+ABS(X(49)-X(58))+ABS(X(79)-X(88))
939 P(389)=ABS(X(19)-X(29))+ABS(X(49)-X(59))+ABS(X(79)-X(89))
940 P(390)=ABS(X(19)-X(30))+ABS(X(49)-X(60))+ABS(X(79)-X(90))
941 P(391)=ABS(X(20)-X(21))+ABS(X(50)-X(51))+ABS(X(80)-X(81))
942 P(392)=ABS(X(20)-X(22))+ABS(X(50)-X(52))+ABS(X(80)-X(82))
943 P(393)=ABS(X(20)-X(23))+ABS(X(50)-X(53))+ABS(X(80)-X(83))
944 P(394)=ABS(X(20)-X(24))+ABS(X(50)-X(54))+ABS(X(80)-X(84))
945 P(395)=ABS(X(20)-X(25))+ABS(X(50)-X(55))+ABS(X(80)-X(85))
946 P(396)=ABS(X(20)-X(26))+ABS(X(50)-X(56))+ABS(X(80)-X(86))
947 P(397)=ABS(X(20)-X(27))+ABS(X(50)-X(57))+ABS(X(80)-X(87))
948 P(398)=ABS(X(20)-X(28))+ABS(X(50)-X(58))+ABS(X(80)-X(88))
949 P(399)=ABS(X(20)-X(29))+ABS(X(50)-X(59))+ABS(X(80)-X(89))
950 P(400)=ABS(X(20)-X(30))+ABS(X(50)-X(60))+ABS(X(80)-X(90))
951 P(401)=ABS(X(21)-X(22))+ABS(X(51)-X(52))+ABS(X(81)-X(82))
952 P(402)=ABS(X(21)-X(23))+ABS(X(51)-X(53))+ABS(X(81)-X(83))
953 P(403)=ABS(X(21)-X(24))+ABS(X(51)-X(54))+ABS(X(81)-X(84))
954 P(404)=ABS(X(21)-X(25))+ABS(X(51)-X(55))+ABS(X(81)-X(85))
955 P(405)=ABS(X(21)-X(26))+ABS(X(51)-X(56))+ABS(X(81)-X(86))
956 P(406)=ABS(X(21)-X(27))+ABS(X(51)-X(57))+ABS(X(81)-X(87))
957 P(407)=ABS(X(21)-X(28))+ABS(X(51)-X(58))+ABS(X(81)-X(88))
958 P(408)=ABS(X(21)-X(29))+ABS(X(51)-X(59))+ABS(X(81)-X(89))
959 P(409)=ABS(X(21)-X(30))+ABS(X(51)-X(60))+ABS(X(81)-X(90))
960 P(410)=ABS(X(22)-X(23))+ABS(X(52)-X(53))+ABS(X(82)-X(83))
961 P(411)=ABS(X(22)-X(24))+ABS(X(52)-X(54))+ABS(X(82)-X(84))
962 P(412)=ABS(X(22)-X(25))+ABS(X(52)-X(55))+ABS(X(82)-X(85))
963 P(413)=ABS(X(22)-X(26))+ABS(X(52)-X(56))+ABS(X(82)-X(86))
964 P(414)=ABS(X(22)-X(27))+ABS(X(52)-X(57))+ABS(X(82)-X(87))
965 P(415)=ABS(X(22)-X(28))+ABS(X(52)-X(58))+ABS(X(82)-X(88))
966 P(416)=ABS(X(22)-X(29))+ABS(X(52)-X(59))+ABS(X(82)-X(89))
967 P(417)=ABS(X(22)-X(30))+ABS(X(52)-X(60))+ABS(X(82)-X(90))
968 P(418)=ABS(X(23)-X(24))+ABS(X(53)-X(54))+ABS(X(83)-X(84))
969 P(419)=ABS(X(23)-X(25))+ABS(X(53)-X(55))+ABS(X(83)-X(85))
970 P(420)=ABS(X(23)-X(26))+ABS(X(53)-X(56))+ABS(X(83)-X(86))
971 P(421)=ABS(X(23)-X(27))+ABS(X(53)-X(57))+ABS(X(83)-X(87))
972 P(422)=ABS(X(23)-X(28))+ABS(X(53)-X(58))+ABS(X(83)-X(88))
973 P(423)=ABS(X(23)-X(29))+ABS(X(53)-X(59))+ABS(X(83)-X(89))
974 P(424)=ABS(X(23)-X(30))+ABS(X(53)-X(60))+ABS(X(83)-X(90))
975 P(425)=ABS(X(24)-X(25))+ABS(X(54)-X(55))+ABS(X(84)-X(85))
976 P(426)=ABS(X(24)-X(26))+ABS(X(54)-X(56))+ABS(X(84)-X(86))
977 P(427)=ABS(X(24)-X(27))+ABS(X(54)-X(57))+ABS(X(84)-X(87))
978 P(428)=ABS(X(24)-X(28))+ABS(X(54)-X(58))+ABS(X(84)-X(88))
979 P(429)=ABS(X(24)-X(29))+ABS(X(54)-X(59))+ABS(X(84)-X(89))
980 P(430)=ABS(X(24)-X(30))+ABS(X(54)-X(60))+ABS(X(84)-X(90))
981 P(431)=ABS(X(25)-X(26))+ABS(X(55)-X(56))+ABS(X(85)-X(86))
982 P(432)=ABS(X(25)-X(27))+ABS(X(55)-X(57))+ABS(X(85)-X(87))
983 P(433)=ABS(X(25)-X(28))+ABS(X(55)-X(58))+ABS(X(85)-X(88))
984 P(434)=ABS(X(25)-X(29))+ABS(X(55)-X(59))+ABS(X(85)-X(89))
985 P(435)=ABS(X(25)-X(30))+ABS(X(55)-X(60))+ABS(X(85)-X(90))
986 P(436)=ABS(X(26)-X(27))+ABS(X(56)-X(57))+ABS(X(86)-X(87))
987 P(437)=ABS(X(26)-X(28))+ABS(X(56)-X(58))+ABS(X(86)-X(88))
988 P(438)=ABS(X(26)-X(29))+ABS(X(56)-X(59))+ABS(X(86)-X(89))
989 P(439)=ABS(X(26)-X(30))+ABS(X(56)-X(60))+ABS(X(86)-X(90))
990 P(440)=ABS(X(27)-X(28))+ABS(X(57)-X(58))+ABS(X(87)-X(88))
991 P(441)=ABS(X(27)-X(29))+ABS(X(57)-X(59))+ABS(X(87)-X(89))
992 P(442)=ABS(X(27)-X(30))+ABS(X(57)-X(60))+ABS(X(87)-X(90))
993 P(443)=ABS(X(28)-X(29))+ABS(X(58)-X(59))+ABS(X(88)-X(89))
994 P(444)=ABS(X(28)-X(30))+ABS(X(58)-X(60))+ABS(X(88)-X(90))
995 P(445)=ABS(X(29)-X(30))+ABS(X(59)-X(60))+ABS(X(89)-X(90))
1088 FOR INSI=11 TO 445
1091 IF P(INSI)<.5 THEN P(INSI)=999999! ELSE P(INSI)=P(INSI)
1095 NEXT INSI
1238 P11B=3*P(11)+2*P(12)+.001*P(13)+.001*P(14)+2*P(15)+10*P(16)+5*P(17)+.001*P(18)+5*P(19)+2*P(20)
1239 P12B=5*P(21)+.001*P(22)+.001*P(23)+2*P(24)
1240 P13B=.001*P(25)+5*P(26)+6*P(27)+3*P(28)+.001*P(29)+1*P(30)+10*P(31)+.001*P(32)+10*P(33)+2*P(34)+1*P(35)+1*P(36)+1*P(37)+.001*P(38)+1*P(39)
1241 P14B=4*P(40)+.001*P(41)+10*P(42)+4*P(43)+.001*P(44)+.001*P(45)+2*P(46)+2*P(47)+1*P(48)+.001*P(49)+5*P(50)+.001*P(51)+.001*P(52)+.001*P(53)+.001*P(54)
1242 P15B=2*P(55)+.001*P(56)+1*P(57)+6*P(58)+1*P(59)+.001*P(60)+1*P(61)+2*P(62)+2*P(63)+5*P(64)+1*P(65)+10*P(66)+5*P(67)
1243 P16B=3*P(68)+4*P(69)+.001*P(70)+5*P(71)+5*P(72)+5*P(73)+1*P(74)+4*P(75)+1*P(76)+.001*P(77)+4*P(78)+.001*P(79)+4*P(80)+.001*P(81)+6*P(82)
1244 P17B=3*P(83)+2*P(84)+5*P(85)+5*P(86)+2*P(87)+1*P(88)+.001*P(89)+.001*P(90)+3*P(91)+1*P(92)+.001*P(93)+2*P(94)+.001*P(95)+.001*P(96)+.001*P(97)
1245 P18B=2*P(98)+2*P(99)+.001*P(100)+6*P(101)+.001*P(102)+2*P(103)+5*P(104)+2*P(105)+5*P(106)+1*P(107)+1*P(108)+1*P(109)+1*P(110)+2*P(111)+2*P(112)
1246 P19B=4*P(113)+.001*P(114)+2*P(115)+.001*P(116)+2*P(117)+2*P(118)+5*P(119)+5*P(120)+5*P(121)+2*P(122)+.001*P(123)+.001*P(124)+.001*P(125)+.001*P(126)+2*P(127)
1247 P20B=.001*P(128)+.001*P(129)+.001*P(130)+.001*P(131)+2*P(132)+1*P(133)+.001*P(134)+.001*P(135)+2*P(136)+.001*P(137)+5*P(138)+1*P(139)+.001*P(140)+2*P(141)+1*P(142)
1248 P21B=.001*P(143)+2*P(144)+1*P(145)+1*P(146)+2*P(147)+2*P(148)+1*P(149)+4*P(150)+10*P(151)+10*P(152)+2*P(153)+5*P(154)+5*P(155)+.001*P(156)+5*P(157)
1249 P22B=.001*P(158)+.001*P(159)+.001*P(160)+10*P(161)+.001*P(162)+.001*P(163)+.001*P(164)+4*P(165)+.001*P(166)+10*P(167)+1*P(168)+1*P(169)+10*P(170)+10*P(171)+5*P(172)
1250 P23B=10*P(173)+10*P(174)+6*P(175)+.001*P(176)+.001*P(177)+10*P(178)+2*P(179)+1*P(180)+10*P(181)+1*P(182)+5*P(183)+5*P(184)+2*P(185)+3*P(186)+5*P(187)
1251 P24B=.001*P(188)+2*P(189)+.001*P(190)+1*P(191)+3*P(192)+1*P(193)+3*P(194)+5*P(195)+.001*P(196)+.001*P(197)+.001*P(198)+2*P(199)+4*P(200)+5*P(201)+2*P(202)
1252 P25B=10*P(203)+6*P(204)+.001*P(205)+5*P(206)+5*P(207)+2*P(208)+5*P(209)+.001*P(210)+5*P(211)+5*P(212)+.001*P(213)+2*P(214)+10*P(215)+2*P(216)+1*P(217)
1253 P26B=5*P(218)+2*P(219)+.001*P(220)+3*P(221)+.001*P(222)+2*P(223)+.001*P(224)+.001*P(225)+4*P(226)+.001*P(227)+5*P(228)+2*P(229)+.001*P(230)+5*P(231)+2*P(232)
1254 P27B=2*P(233)+5*P(234)+2*P(235)+5*P(236)+5*P(237)+6*P(238)+.001*P(239)+1*P(240)+5*P(241)+5*P(242)+.001*P(243)+5*P(244)+2*P(245)+3*P(246)+5*P(247)
1255 P28B=.001*P(248)+5*P(249)+2*P(250)+10*P(251)+10*P(252)+1*P(253)+5*P(254)+2*P(255)+.001*P(256)+.001*P(257)+1*P(258)+2*P(259)+1*P(260)+.001*P(261)+2*P(262)
1256 P29B=.001*P(263)+.001*P(264)+.001*P(265)+6*P(266)+6*P(267)+.001*P(268)+4*P(269)+5*P(270)+3*P(271)+2*P(272)+2*P(273)+10*P(274)+5*P(275)+5*P(276)+2*P(277)
1257 P30B=.001*P(278)+.001*P(279)+.001*P(280)+.001*P(281)+2*P(282)+.001*P(283)+4*P(284)+5*P(285)+10*P(286)+1*P(287)+.001*P(288)+.001*P(289)+.001*P(290)+.001*P(291)+1*P(292)
1258 P31B=2*P(293)+.001*P(294)+4*P(295)+2*P(296)+2*P(297)+1*P(298)+.001*P(299)+6*P(300)+2*P(301)+1*P(302)+5*P(303)+5*P(304)+.001*P(305)+.001*P(306)+1*P(307)
1259 P32B=5*P(308)+5*P(309)+2*P(310)+1*P(311)+.001*P(312)+5*P(313)+3*P(314)+10*P(315)+.001*P(316)+.001*P(317)+4*P(318)+2*P(319)+.001*P(320)+.001*P(321)+4*P(322)
1260 P33B=2*P(323)+5*P(324)+5*P(325)+4*P(326)+5*P(327)+1*P(328)+.001*P(329)+1*P(330)+.001*P(331)+5*P(332)+.001*P(333)+2*P(334)+.001*P(335)+.001*P(336)+5*P(337)
1261 P34B=1*P(338)+1*P(339)+.001*P(340)+.001*P(341)+3*P(342)+.001*P(343)+2*P(344)+2*P(345)+.001*P(346)+2*P(347)+.001*P(348)+5*P(349)+.001*P(350)+5*P(351)+2*P(352)
1262 P35B=5*P(353)+10*P(354)+2*P(355)+2*P(356)+.001*P(357)+.001*P(358)+.001*P(359)+6*P(360)+5*P(361)+3*P(362)+5*P(363)+.001*P(364)+.001*P(365)+5*P(366)+1*P(367)
1263 P36B=5*P(368)+1*P(369)+2*P(370)+10*P(371)+10*P(372)+4*P(373)+.001*P(374)+.001*P(375)+5*P(376)+.001*P(377)+.001*P(378)+.001*P(379)+.001*P(380)+5*P(381)+5*P(382)
1264 P38B=1*P(383)+.001*P(384)+5*P(385)+2*P(386)+1*P(387)+2*P(388)+10*P(389)+10*P(390)+5*P(391)+2*P(392)+1*P(393)+3*P(394)+1*P(395)+5*P(396)+6*P(397)
1265 P39B=5*P(398)+5*P(399)+3*P(400)+4*P(401)+.001*P(402)+1*P(403)+.001*P(404)+.001*P(405)+.001*P(406)+5*P(407)+.001*P(408)+.001*P(409)+5*P(410)+.001*P(411)+4*P(412)
1266 P40B=4*P(413)+5*P(414)+.001*P(415)+2*P(416)+5*P(417)+.001*P(418)+4*P(419)+4*P(420)+1*P(421)+.001*P(422)+2*P(423)+2*P(424)+5*P(425)+5*P(426)+.001*P(427)
1267 P41B=1*P(428)+.001*P(429)+.001*P(430)+1*P(431)+.001*P(432)+10*P(433)+1*P(434)+.001*P(435)+.001*P(436)+.001*P(437)+.001*P(438)+.001*P(439)+.001*P(440)+.001*P(441)+10*P(442)
1268 P42B=2*P(443)+2*P(444)+2*P(445)
1388 P1=P11B+P12B+P13B+P14B+P15B+P16B+P17B+P18B+P19B+P20B+P21B+P22B+P23B+P24B+P25B+P26B
1395 P2=P27B+P28B+P29B+P30B+P31B+P32B+P33B+P34B+P35B+P36B+P37B+P38B+P39B+P40B+P41B+P42B
1397 P4=0
1398 P3=0
1448 P5=P1+P2+P3+P4
1450 P=-P5
1451 IF P<=M THEN 1670
1452 M=P
1453 PP1=P5
1454 FOR KLX=1 TO 90
1455 A(KLX)=X(KLX)
1456 NEXT KLX
1457 GOTO 128
1670 NEXT I
1702 NEXT JJ
1706 NEXT J
1777 NEXT INEW
1778 REM
1888 NEXT JJJ
1890 IF M>-2733 THEN 1916 ELSE 1999
1916 PRINT JJJJ,M,PP1
1917 PRINT A(1),A(2),A(3),A(4),A(5)
1918 PRINT A(6),A(7),A(8),A(9),A(10)
1920 PRINT A(11),A(12),A(13),A(14),A(15)
1922 PRINT A(16),A(17),A(18),A(19),A(20)
1923 PRINT A(21),A(22),A(23),A(24),A(25)
1924 PRINT A(26),A(27),A(28),A(29),A(30)
1925 PRINT A(31),A(32),A(33),A(34),A(35)
1926 PRINT A(36),A(37),A(38),A(39),A(40)
1927 PRINT A(41),A(42),A(43),A(44),A(45)
1928 PRINT A(46),A(47),A(48),A(49),A(50)
1929 PRINT A(51),A(52),A(53),A(54),A(55)
1930 PRINT A(56),A(57),A(58),A(59),A(60)
1931 PRINT A(61),A(62),A(63),A(64),A(65)
1932 PRINT A(66),A(67),A(68),A(69),A(70)
1933 PRINT A(71),A(72),A(73),A(74),A(75)
1934 PRINT A(76),A(77),A(78),A(79),A(80)
1935 PRINT A(81),A(82),A(83),A(84),A(85)
1936 PRINT A(86),A(87),A(88),A(89),A(90)
1999 NEXT JJJJ
The .001s of line 1238 and other lines above are the 0s of the n=30 case, Nugent et al. [5, p. 170].
This BASIC computer program was run with the IBM basica/D interpreter, and its output through JJJJ=-31980 (in compressed form and to be interpreted in accordance with line 1916 through line 1936; copied manually from the computer monitor) is presented below.
-31984 -2698.471 2698.471
2 2 1 1 1
3 2 2 1 2
2 3 3 0 3
3 2 3 2 0
1 2 1 2 3
1 3 2 1 2
3 4 3 2 4
3 3 1 3 2
2 3 4 3 1
2 1 3 1 2
3 3 2 4 2
2 2 2 1 2
2 3 3 4 3
4 3 4 2 2
4 2 3 3 3
3 2 3 3 3
4 4 3 2 4
2 2 5 3 3
-31980 -2702.486 2702.486
4 4 3 3 3
4 2 3 2 4
4 2 2 3 4
3 3 3 3 3
2 4 3 2 2
4 4 2 3 3
3 2 2 3 3
1 2 2 2 2
3 2 1 1 1
1 3 3 2 1
2 2 4 3 3
3 2 1 1 2
3 4 3 1 4
3 2 2 1 2
2 3 3 3 2
2 2 3 4 1
4 3 2 3 2
1 1 2 4 1
The better objective function value, shown above, is 2698 at JJJJ=-31984. (The last three digits of 2698.471 shown above should be disregarded because these are due to the artificial flows, the .001s.) One notes that 3062, the minimum objective function value of the older problem [7], to 2698 is 1.1349 to 1.
The output above was produced in 20 hours on a personal computer with an Intel 2.66 GHz. chip and the IBM interpreter, which is slower than the corresponding compiler.
If one makes changes to the computer program above, such as a change of changing line 128 above to 128 FOR I=1 TO 21, one may or may not obtain 2698, which may or may not be optimal. That leads to a general remedy that in general, in order to increase the probability of getting an optimal solution, one preferably should run several computers simultaneously, each with a different line 128, for example; instead of line 128, another line can be chosen. This multicomputer approach can mitigate the possible danger of missed optimality and can produce a usable solution faster than just running one computer.
References
[1] Z. Drezner, DISCON: A New Method for the Layout Problem, Operations Research 28 (1980) 1375-1384.
[2] S.S. Heragu, A. Kusiak, Efficient models for the facility layout problem, European Journal of Operational Research 53 (1991) 1-13.
[3] S.S. Heragu, Recent models and techniques for solving the layout problem, European Journal of Operational Research 57 (1992) 136-144.
[4] F.S. Hillier, Quantitative tools for plant layout analysis, J. Indust. Eng. 14 (1963) 33-40.
[5] C.E. Nugent, T.E. Vollmann, J. Ruml, An experimental comparison of techniques for the assignment of facilities to locations, Operations Research 16 (1968) 150-173.
[6] W.C. Conley, Optimization: A Simplified Approach, Petrocelli, Princeton, New Jersey, 1981.
[7] E. M. Loiola, N. M. M. de Abreu, P. O. Boaventura-Netto, P. Hahn, T. Querido, A survey for the quadratic assignment problem, European Journal of Operational Research 176 (2007) 657-690.
