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|
*DECK PLSPLX
SUBROUTINE PLSPLX(N,M,MAXM,MINMAX,COUT,APLUS,B,INEGAL,BINF,BSUP,
> XOBJ,F,EPS,IMTHD,IMPR,IERR)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Solves a linear programming problem using the revisited simplex
* method.
* PLSLPX = Linear Programming SimPLeX
*
*Copyright:
* Copyright (C) 2002 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s):
* A. Hebert and R. Chambon
*
*Parameters: input/ouput
* N number of control variables.
* M number of constraints.
* MAXM first dimension of matrix APLUS.
* MINMAX type of optimization (=-1: minimize; =1: maximize).
* COUT costs of control variables.
* APLUS coefficient matrix for the linear constraints.
* B right hand sides corresponding to the coefficient matrix.
* INEGAL constraint relations (=-1 for .GE.; =0 for .EQ.; =1 for .LE.).
* BINF lower bounds of control variables.
* BSUP upper bounds of control variables.
* EPS tolerence used for SIMPLEX calculation.
* IMTHD type of solution (=1: SIMPLEX/LEMKE; =3: MAP).
* IMPR print flag.
*
*Parameters: ouput
* XOBJ control variables.
* F objective function.
* IERR return code (=0: normal completion).
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER N,M,MAXM,MINMAX,INEGAL(M),IMTHD,IMPR,IERR
DOUBLE PRECISION B(M+1),BINF(N),BSUP(N),XOBJ(N),EPS,COUT(N),
> APLUS(MAXM,N+M),F
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION DUMY,DELTA,DELTAM,CSTE,XIJ,XIKI,BBAR,PM,QM
INTEGER I,J,MP1,MP2,IDIMC,JJ,IJK,J1,IPHASE,IND,K,IP,IQ,L,LL,
> LARTF
LOGICAL LARTIF
INTEGER, ALLOCATABLE, DIMENSION(:) :: IVARS
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: CRE,BORNE,XIK,BGAR,
> GSUP
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:) :: BASE0,AGAR
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(IVARS(M+2))
ALLOCATE(CRE(N+M),BORNE(N+M),XIK(M+2),BGAR(M+2),GSUP(N+M))
ALLOCATE(BASE0(M+2,M+2),AGAR(2,N+M))
*
CRE(:N+M)=0.0D0
LARTIF = .FALSE.
IF(M.GT.MAXM) THEN
IERR = 9
GO TO 500
ENDIF
MP1 = M+1
MP2 = M+2
*----
* ORGANIZATION OF THE SIMPLEX TABLES
*----
DO 3 I=1,M
DUMY = 0.0D0
DO 1 J=1,N
DUMY = DUMY + APLUS(I,J)*BINF(J)
1 CONTINUE
*
BGAR(I) = B(I)-DUMY
IF(BGAR(I).GE.0.0) GOTO 3
DO 2 J=1,N
APLUS(I,J) = -APLUS(I,J)
2 CONTINUE
*
BGAR(I) = -BGAR(I)
B(I) = -B(I)
INEGAL(I) = -INEGAL(I)
3 CONTINUE
*
CSTE = 0.0D0
DO 4 J=1,N
CSTE = CSTE + COUT(J)*BINF(J)
GSUP(J) = BSUP(J) - BINF(J)
AGAR(1,J) = REAL(MINMAX)*COUT(J)
4 CONTINUE
*
DO 8 J=1,N
AGAR(2,J) = 0.0D0
DO 7 I=1,M
AGAR(2,J) = AGAR(2,J) - APLUS(I,J)
7 CONTINUE
8 CONTINUE
*
BGAR(MP1) = 0.0
BGAR(MP2) = 0.0
*
DO 9 I=1,M
BGAR(MP2) = BGAR(MP2) - BGAR(I)
9 CONTINUE
*----
* SLACK VARIABLES
*----
IDIMC = N
DO 13 I=1,M
IF(INEGAL(I).EQ.0) GOTO 13
IDIMC = IDIMC + 1
GSUP(IDIMC) = 1.0E+25
DO 12 J=1,M
APLUS(J,IDIMC) = 0.0D0
12 CONTINUE
*
APLUS(I,IDIMC) = REAL(INEGAL(I))
AGAR(1,IDIMC) = 0.0D0
AGAR(2,IDIMC) = -REAL(INEGAL(I))
13 CONTINUE
*
DO 15 I=1,MP2
IVARS(I) = IDIMC + I
DO 14 J=1,MP2
BASE0(I,J) = 0.0D0
14 CONTINUE
BASE0(I,I) = 1.0D0
15 CONTINUE
*
IF(IMPR.GE.6) THEN
WRITE (6,800)
WRITE (6,840) N,M,IDIMC
DO 510 J=1,N+M,12
JJ = MIN0(J+11,N+M)
WRITE (6,841) (J1,J1=J,JJ)
DO 505 I=1,M
WRITE (6,805) I,(APLUS(I,J1),J1=J,JJ)
505 CONTINUE
IF(JJ.NE.N+M) WRITE (6,803)
510 CONTINUE
*
WRITE (6,810) (I,COUT(I),I=1,N)
WRITE (6,820) (I,BGAR(I),I=1,MP2)
WRITE (6,830) (I,INEGAL(I),I=1,M)
WRITE (6,835) (I,GSUP(I),I=1,IDIMC)
ENDIF
*----
* END OF PHASE 1 IF BGAR(M+2)=0 +- EPS
*----
IERR = 0
IND=0
LARTF=0
DO 11 I=1,IDIMC
IF(GSUP(I).EQ.0.0) GSUP(I)=1.0E-6
BORNE(I)=0.0
11 CONTINUE
*
IPHASE = 1
*
10 IF((IPHASE.EQ.2) .AND. (.NOT.LARTIF)) GOTO 21
IF((ABS(BGAR(MP2)).LT.EPS) .OR. (LARTIF)) THEN
IPHASE=2
LARTIF=.FALSE.
IJK=1
99 IF(.NOT.((IJK.GT.IDIMC) .OR. (LARTIF))) THEN
IF(IVARS(IJK).GT.IDIMC) THEN
LARTIF=.TRUE.
LARTF=IJK
ENDIF
IJK=IJK+1
GOTO 99
ENDIF
ENDIF
*----
* RETURN IF NO BASE SWITCH HAS BEEN DONE
*----
20 IND=MP2
21 IF(IPHASE.EQ.2) IND=MP2-1
IF(IMPR.GE.6) THEN
WRITE (6,845) IPHASE
WRITE (6,843)
WRITE (6,850)
DO 520 J=1,MP2,12
JJ=MIN0(J+11,MP2)
WRITE (6,841) (J1,J1=J,JJ)
DO 515 I=1,MP2
WRITE (6,805) I,(BASE0(I,J1),J1=J,JJ)
515 CONTINUE
IF(JJ.NE.MP2) WRITE (6,803)
520 CONTINUE
WRITE (6,820) (I,BGAR(I),I=1,MP2)
WRITE (6,855) (I,IVARS(I),I=1,MP2)
WRITE (6,860) (I,BORNE(I),I=1,IDIMC)
ENDIF
*----
* SELECTION OF THE BASE K VECTOR TO PICK IN
*----
K=0
DELTAM=0.0D0
DO 100 J=1,IDIMC
DELTA=0.0D0
DO 30 JJ=1,MP2
IF(IVARS(JJ).EQ.J) GOTO 90
30 CONTINUE
DELTA=BASE0(IND,MP1)*AGAR(1,J)+BASE0(IND,MP2)*AGAR(2,J)
DO 35 I=1,M
DELTA=DELTA+BASE0(IND,I)*APLUS(I,J)
35 CONTINUE
IF(IMPR.GE.7) WRITE (6,865) J,DELTA
*
IF(BORNE(J).EQ.GSUP(J)) GOTO 45
IF(DELTA.GE.0.0) GOTO 90
IF(K.EQ.0) GOTO 40
39 IF(DELTA.GE.DELTAM) GOTO 90
40 K=J
DELTAM=DELTA
GOTO 90
45 IF(DELTA.LE.0.0) GOTO 90
DELTA=-DELTA
IF(K.EQ.0) GOTO 40
IF(K.GT.0) GOTO 39
*
90 CRE(J)=DELTA
100 CONTINUE
*
IF(IMPR.GE.7) THEN
WRITE (6,870) (I,CRE(I),I=1,N+M)
WRITE (6,875) K
ENDIF
*
IF(K.NE.0) GOTO 125
DO 105 JJ=1,M
IF(IVARS(JJ).GT.IDIMC) GOTO 110
105 CONTINUE
IF(IPHASE.EQ.2) GOTO 115
IERR=1
GO TO 500
110 IF(IPHASE.EQ.2) GOTO 115
IF(IMTHD.EQ.1) THEN
* no solution.
IERR=2
GO TO 500
ELSEIF(IMTHD.EQ.3) THEN
* no feasible solution in the reduced domain. Go to PHASE 2 with
* modified constraints.
IERR=2
GO TO 115
ENDIF
*
115 DO 999 I=1,MP2
DO 950 J=1,IDIMC
XIJ=0.0D0
DO 920 JJ=1,M
IF(J.EQ.IVARS(JJ)) GOTO 950
920 CONTINUE
IF(BORNE(J).NE.GSUP(J)) GOTO 950
XIJ=BASE0(I,MP1)*AGAR(1,J)+BASE0(I,MP2)*AGAR(2,J)
DO 925 JJ=1,M
XIJ=XIJ+BASE0(I,JJ)*APLUS(JJ,J)
925 CONTINUE
BGAR(I)=BGAR(I)-XIJ*GSUP(J)
950 CONTINUE
999 CONTINUE
DO 400 I=1,N
DO 390 J=1,M
IF(IVARS(J).NE.I) GO TO 390
XOBJ(I)=BINF(I)+BGAR(J)
GO TO 400
390 CONTINUE
XOBJ(I)=BINF(I)+BORNE(I)
400 CONTINUE
DO 410 I=1,IDIMC
CRE(I)=CRE(I)*REAL(MINMAX)
410 CONTINUE
F=REAL(-MINMAX)*BGAR(MP1)+CSTE
IF(IMPR.GE.5) THEN
WRITE (6,890) F,(I,XOBJ(I),I=1,N)
WRITE (6,820) (I,BGAR(I),I=1,MP2)
WRITE (6,855) (I,IVARS(I),I=1,MP2)
WRITE (6,860) (I,BORNE(I),I=1,IDIMC)
ENDIF
GO TO 500
*----
* SELECTION OF THE VECTOR TO PICK OUT
*----
125 IF(IMPR.GE.7) WRITE (6,880)
IP=0
IQ=0
*
IF(K.GT.N+M) THEN
WRITE(6,'(1X,A)') 'PLSPLX: AGAR OVERFLOW.'
IERR=10
GO TO 500
ENDIF
DO 200 I=1,M
*
BBAR=0.0D0
DO 150 J=1,IDIMC
IF(BORNE(K).EQ.GSUP(K) .AND. J.EQ.K) GOTO 150
DO 130 JJ=1,M
IF(J.EQ.IVARS(JJ)) GOTO 150
130 CONTINUE
IF(BORNE(J).NE.GSUP(J)) GOTO 150
XIJ=BASE0(I,MP1)*AGAR(1,J)+BASE0(I,MP2)*AGAR(2,J)
DO 135 JJ=1,M
XIJ=XIJ+BASE0(I,JJ)*APLUS(JJ,J)
135 CONTINUE
BBAR=BBAR-GSUP(J)*XIJ
IF(IMPR.GE.7) THEN
WRITE (6,885) I,J,XIJ,BBAR
ENDIF
150 CONTINUE
BBAR=BBAR+BGAR(I)
XIKI=BASE0(I,MP1)*AGAR(1,K)+BASE0(I,MP2)*AGAR(2,K)
DO 155 JJ=1,M
XIKI=XIKI+BASE0(I,JJ)*APLUS(JJ,K)
155 CONTINUE
XIK(I)=XIKI
*----
* CASE I: XOBJ(K)=0.0
*----
IF(BORNE(K).EQ.GSUP(K)) GOTO 175
IF(ABS(XIKI).LT.EPS) GOTO 200
IF(XIKI.GT.0.0) GOTO 165
IF(LARTIF.AND.I.EQ.LARTF) GOTO 165
*----
* TEST FOR ARTIFICIAL VARIABLES
*----
IF(IVARS(I).GT.IDIMC) GOTO 200
IF(IQ.EQ.0) GOTO 160
IF(QM.LE.((GSUP(IVARS(I))-BBAR)/(-XIKI))) GOTO 200
160 CONTINUE
IQ=I
QM=(GSUP(IVARS(I))-BBAR)/(-XIKI)
GOTO 200
165 CONTINUE
IF(IP.EQ.0) GOTO 170
IF(PM.LE.(BBAR/XIKI)) GOTO 200
170 IP=I
PM=BBAR/XIKI
GOTO 200
*----
* CASE II: XOBJ(K) = UPPER BOUND
*----
175 IF(ABS(XIKI).LT.EPS) GOTO 200
IF(XIKI.GT.0.0) GOTO 185
IF(IQ.EQ.0) GOTO 180
IF(QM.GE.(BBAR/XIKI)) GOTO 200
180 IQ=I
QM=BBAR/XIKI
GOTO 200
*----
* TEST FOR ARTIFICIAL VARIABLES
*----
185 IF(IVARS(I).GT.IDIMC) GOTO 200
IF(IP.EQ.0) GOTO 190
IF(PM.GE.((BBAR-GSUP(IVARS(I)))/XIKI)) GOTO 200
190 IP=I
PM=(BBAR-GSUP(IVARS(I)))/XIKI
200 CONTINUE
*
IF(IMPR.GE.7) WRITE (6,894) IQ,QM,IP,PM
*
XIK(MP1)=BASE0(MP1,MP1)*AGAR(1,K)+BASE0(MP1,MP2)*AGAR(2,K)
XIK(MP2)=BASE0(MP2,MP1)*AGAR(1,K)+BASE0(MP2,MP2)*AGAR(2,K)
DO 204 JJ=1,M
XIK(MP1)=XIK(MP1)+BASE0(MP1,JJ)*APLUS(JJ,K)
XIK(MP2)=XIK(MP2)+BASE0(MP2,JJ)*APLUS(JJ,K)
204 CONTINUE
*
IF(BORNE(K).EQ.GSUP(K)) GOTO 250
IF(IP.EQ.0) GOTO 205
IF(IQ.EQ.0) GOTO 220
IF(QM.LE.PM) GOTO 210
GOTO 220
205 IF(IQ.EQ.0) GOTO 211
210 IF(QM.LE.GSUP(K)) GOTO 215
211 BORNE(K)=GSUP(K)
GOTO 20
215 L=IQ
LL=IVARS(L)
IF(LL.LE.IDIMC) BORNE(LL)=GSUP(LL)
IVARS(L)=K
IF(IMPR.GE.7) WRITE (6,895) L,LL,IVARS(L)
GOTO 300
220 IF(PM.GT.GSUP(K)) GOTO 211
L=IP
LL=IVARS(L)
IF(LL.LE.IDIMC) BORNE(LL)=0.0
IVARS(L)=K
IF(IMPR.GE.7) WRITE (6,895) L,LL,IVARS(L)
GOTO 300
*
250 IF(IP.EQ.0) GOTO 255
IF(IQ.EQ.0) GOTO 265
IF(QM.GE.PM) GOTO 256
GOTO 265
255 IF(IQ.EQ.0) GOTO 257
256 IF(QM.GE.0.0) GOTO 260
257 BORNE(K)=0.0
GOTO 20
260 L=IQ
LL=IVARS(L)
IF(LL.LE.IDIMC) BORNE(LL)=0.0
IVARS(L)=K
IF(IMPR.GE.7) WRITE (6,895) L,LL,IVARS(L)
GOTO 300
265 IF(PM.LE.0.0) GOTO 257
L=IP
LL=IVARS(L)
IF(LL.LE.IDIMC) BORNE(LL)=GSUP(LL)
IVARS(L)=K
IF(IMPR.GE.7) WRITE (6,895) L,LL,IVARS(L)
*
* PIVOTAGE SUR XIK
300 IF(IMPR.GE.7) WRITE (6,905) L,XIK(L)
DO 325 I=1,MP2
IF(I.EQ.L) GOTO 325
BGAR(I)=BGAR(I)-BGAR(L)/XIK(L)*XIK(I)
325 CONTINUE
BGAR(L)=BGAR(L)/XIK(L)
*
DO 375 I=1,MP2
IF(I.EQ.L) GOTO 375
DO 335 J=1,MP2
BASE0(I,J)=BASE0(I,J)-(BASE0(L,J)/XIK(L))*XIK(I)
335 CONTINUE
375 CONTINUE
DO 380 J=1,MP2
BASE0(L,J)=BASE0(L,J)/XIK(L)
380 CONTINUE
*
GOTO 10
*----
* SCRATCH STORAGE DEALLOCATION
*----
500 DEALLOCATE(AGAR,BASE0)
DEALLOCATE(GSUP,BGAR,XIK,BORNE,CRE)
DEALLOCATE(IVARS)
RETURN
*
* .................................................................
* ...
* ... F O R M A T S
* ...
* .................................................................
*
800 FORMAT (///25X,35H- - - - SIMPLEX ALGORITHM - - -)
803 FORMAT (//10X,8HCONTN.../)
805 FORMAT (1X,I4,1P,12E10.2)
810 FORMAT (//10X,28H+ + + + + TABLE COUT(N) :/
1 3(/6(1X,5HCOUT(,I4,4H) = ,1P,E10.3,:)))
820 FORMAT (//10X,30H+ + + + + TABLE BGAR(M+2) :/
1 3(/6(1X,5HBGAR(,I4,4H) = ,1P,E10.3,:)))
830 FORMAT (//10X,30H+ + + + + TABLE INEGAL(M) :/
1 3(/6(1X,5HINEG(,I4,4H) = ,I4,:)))
835 FORMAT (//10X,32H+ + + + + TABLE GSUP(IDIMC) :/
1 5(/6(1X,5HGSUP(,I4,4H) = ,1P,E10.3,:)))
840 FORMAT (//34H-- NUMBER OF CONTROL VARIABLES (N):,I4/
1 10X,29H-- NOMBER OF CONSTRAINTS (M):,I4/
2 10X,38H-- NUMBER OF SLACK VARIABLES (IDIMC) :,I4//10X,
3 32H+ + + + + TABLE APLUS(M,N+M) :/)
841 FORMAT (1X,12I10)
843 FORMAT (/10X,34H-- SELECTION OF VECTOR TO PICK IN.)
845 FORMAT (///25X,42H- - - - - START OF ITERATION - - - - -//
1 10X,17H-- PHASE NUMBER :,I4/)
850 FORMAT (//10X,34H+ + + + + TABLE BASE0(M+2,M+2) : /)
855 FORMAT (//10X,31H+ + + + + TABLE IVARS(M+2) :/
1 2(/6(1X,5HIVAR(,I4,3H) =,I5,:)))
860 FORMAT (//10X,33H+ + + + + TABLE BORNE(IDIMC) :/
1 5(/6(1X,5HBORN(,I4,3H) =,1P,E11.3,:)))
865 FORMAT (/10X,21H-- CANDIDATE VECTOR :,I4,2X,7HVALUE :,1P,E10.3)
870 FORMAT (//10X,29H+ + + + + TABLE CRE(N+M) :/
1 3(/6(1X,4HCRE(,I4,3H) =,1P,E11.3,:)))
875 FORMAT (/10X,19H-- SELECTED PIVOT :,I4)
880 FORMAT (/10X,35H-- SELECTION OF VECTOR TO PICK OUT.)
885 FORMAT(//10X,3HI =,I4,5X,3HJ =,I4,5X,5HXIJ =,1P,E11.3,5X,
1 6HBBAR =,E11.3)
890 FORMAT (//10X,28HOPTIMAL OBJECTIVE FUNCTION =,1P,E12.4//10X,
1 28H+ + + + + TABLE XOBJ(N) :/5(/6(1X,5HXOBJ(,I4,3H) =,1P,
2 E11.3,:)))
894 FORMAT (10X,27H-- SELECTED VARIABLES ATE :/15X,4HIQ =,I4,5X,
1 4HQM =,1P,E11.3,10X,4HIP =,I4,5X,4HPM =,E11.3)
895 FORMAT (10X,3HL =,I4,5X,4HLL =,I4,5X,10HIVARS(L) =,I5)
905 FORMAT (10X,25H-- START OF PIVOTING; L =,I4,5X,8HXIK(L) =,
1 1P,E11.3)
END
|
