C     PROGRAM TO FIND GLOBAL MINIMUM BY REPULSIVE PARTICLE SWARM METHOD
C     WRITTEN BY SK MISHRA, DEPT. OF ECONOMICS, NEHU, SHILLONG (INDIA)
C     -----------------------------------------------------------------
      PARAMETER (N=100,NN=40,MX=100,NSTEP=15,ITRN=10000,NSIGMA=1,ITOP=3)
      PARAMETER (NPRN=100) ! DISPLAYS RESULTS AT EVERY 100 TH ITERATION
C     PARAMETER(N=50,NN=25,MX=100,NSTEP=9,ITRN=10000,NSIGMA=1,ITOP=3)
C     PARAMETER (N=100,NN=15,MX=100,NSTEP=9,ITRN=10000,NSIGMA=1,ITOP=3)
C     IN CERTAIN CASES THE ONE OR THE OTHER SPECIFICATION WORKS BETTER
C     DIFFERENT SPECIFICATIONS OF PARAMETERS MAY SUIT DIFFERENT TYPES
C     OF FUNCTIONS OR DIMENSIONS - ONE HAS TO DO SOME TRIAL AND ERROR
C     -----------------------------------------------------------------
C     N = POPULATION SIZE. IN MOST OF THE CASES N=30 IS OK. ITS VALUE
C     MAY BE INCREASED TO 50 OR 100 TOO. THE PARAMETER NN IS THE SIZE OF
C     RANDOMLY CHOSEN NEIGHBOURS. 15 TO 25 (BUT SUFFICIENTLY LESS THAN
C     N) IS A GOOD CHOICE. MX IS THE MAXIMAL SIZE OF DECISION VARIABLES.
C     IN F(X1, X2,...,XM) M SHOULD BE LESS THAN OR EQUAL TO MX. ITRN IS
C     THE NO. OF ITERATIONS. IT MAY DEPEND ON THE PROBLEM. 200(AT LEAST)
C     TO 500 ITERATIONS MAY BE GOOD ENOUGH. BUT FOR FUNCTIONS LIKE
C     ROSENBROCKOR,GRIEWANK OF LARGE SIZE (SAY M=30) IT IS NEEDED THAT
C     ITRN IS LARGE, SAY 5000 OR EVEN 10000.
C     SIGMA INTRODUCES PERTURBATION & HELPS THE SEARCH JUMP OUT OF LOCAL
C     OPTIMA. FOR EXAMPLE : RASTRIGIN FUNCTION OF DMENSION 3O OR LARGER
C     NSTEP DOES LOCAL SEARCH BY TUNNELLING AND WORKS WELL BETWEEN 5 AND
C     15, WHICH IS MUCH ON THE HIGHER SIDE.
C     ITOP <=1 (RING); ITOP=2 (RING AND RANDOM); ITOP=>3 (RANDOM)
C     NSIGMA=0 (NO CHAOTIC PERTURBATION);NSIGMA=1 (CHAOTIC PERTURBATION)
C     NOTE THAT NSIGMA=1 NEED NOT ALWAYS WORK BETTER (OR WORSE)
C     SUBROUTINE FUNC( ) DEFINES OR CALLS THE FUNCTION TO BE OPTIMIZED.
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      COMMON /KFF/KF,NFCALL,FTIT
      INTEGER IU,IV
      CHARACTER *70 FTIT
      DIMENSION X(N,MX),V(N,MX),A(MX),VI(MX),TIT(50)
      DIMENSION XX(N,MX),F(N),V1(MX),V2(MX),V3(MX),V4(MX),BST(MX)
C     A1 A2 AND A3 ARE CONSTANTS AND W IS THE INERTIA WEIGHT.
C     OCCASIONALLY, TINKERING WITH THESE VALUES, ESPECIALLY A3, MAY BE
C     NEEDED.
      DATA A1,A2,A3,W,SIGMA /.5D00,.5D00,.0005D00,.5D00,1.D-03/
      EPSILON=1.D-08 ! ACCURACY NEEDED FOR TERMINATON
C     --------------------CHOOSING THE TEST FUNCTION ------------------'
      CALL FSELECT(KF,M,FTIT)
C     -----------------------------------------------------------------
      FFMIN=1.D30
      LCOUNT=0
      NFCALL=0
      WRITE(*,*)'4-DIGITS SEED FOR RANDOM NUMBER GENERATION'
      READ(*,*) IU
      DATA FMIN /1.0E30/
C     GENERATE N-SIZE POPULATION OF M-TUPLE PARAMETERS X(I,J) RANDOMLY
      DO I=1,N
        DO J=1,M
        CALL RANDOM(RAND)
         X(I,J)=(RAND-0.5D00)*10
C     WE GENERATE RANDOM(-5,5). HERE MULTIPLIER IS 10. TINKERING IN SOME
C     CASES MAY BE NEEDED
         ENDDO
        F(I)=1.0D30
      ENDDO
C     INITIALISE VELOCITIES V(I) FOR EACH INDIVIDUAL IN THE POPULATION
      DO I=1,N
      DO J=1,M
      CALL RANDOM(RAND)
       V(I,J)=(RAND-0.5D+00)
C       V(I,J)=RAND
      ENDDO
      ENDDO
      DO 100 ITER=1,ITRN
C     LET EACH INDIVIDUAL SEARCH FOR THE BEST IN ITS NEIGHBOURHOOD
        DO I=1,N
           DO J=1,M
           A(J)=X(I,J)
           VI(J)=V(I,J)
           ENDDO
           CALL LSRCH(A,M,VI,NSTEP,FI)
           IF(FI.LT.F(I)) THEN
            F(I)=FI
            DO IN=1,M
            BST(IN)=A(IN)
            ENDDO
C     F(I) CONTAINS THE LOCAL BEST VALUE OF FUNCTION FOR ITH INDIVIDUAL
C     XX(I,J) IS THE M-TUPLE VALUE OF X ASSOCIATED WITH LOCAL BEST F(I)
             DO J=1,M
             XX(I,J)=A(J)
             ENDDO
             ENDIF
        ENDDO
C      NOW LET EVERY INDIVIDUAL RANDOMLY COSULT NN(<<N) COLLEAGUES AND
C      FIND THE BEST AMONG THEM
      DO I=1,N
C     ------------------------------------------------------------------
      IF(ITOP.GE.3) THEN
C     RANDOM TOPOLOGY ******************************************
C     CHOOSE NN COLLEAGUES RANDOMLY AND FIND THE BEST AMONG THEM
          BEST=1.0D30
           DO II=1,NN
                 CALL RANDOM(RAND)
               NF=INT(RAND*N)+1
                IF(BEST.GT.F(NF)) THEN
                 BEST=F(NF)
                NFBEST=NF
                 ENDIF
            ENDDO
      ENDIF
C----------------------------------------------------------------------
      IF(ITOP.EQ.2) THEN
C     RING + RANDOM TOPOLOGY ******************************************
C     REQUIRES THAT THE SUBROUTINE NEIGHBOR IS TURNED ALIVE
       BEST=1.0D30
          CALL NEIGHBOR(I,N,I1,I3)
          DO II=1,NN
                IF(II.EQ.1) NF=I1
                 IF(II.EQ.2) NF=I
                  IF(II.EQ.3) NF=I3
                      IF(II.GT.3) THEN
                     CALL RANDOM(RAND)
                      NF=INT(RAND*N)+1
                     ENDIF
                  IF(BEST.GT.F(NF)) THEN
                  BEST=F(NF)
                  NFBEST=NF
                 ENDIF
             ENDDO
       ENDIF
C---------------------------------------------------------------------
      IF(ITOP.LE.1) THEN
C     RING TOPOLOGY **************************************************
C     REQUIRES THAT THE SUBROUTINE NEIGHBOR IS TURNED ALIVE
        BEST=1.0D30
           CALL NEIGHBOR(I,N,I1,I3)
              DO II=1,3
              IF (II.NE.I) THEN
             IF(II.EQ.1) NF=I1
              IF(II.EQ.3) NF=I3
                  IF(BEST.GT.F(NF)) THEN
                   BEST=F(NF)
                   NFBEST=NF
                  ENDIF
                  ENDIF
            ENDDO
       ENDIF
C---------------------------------------------------------------------
C     IN THE LIGHT OF HIS OWN AND HIS BEST COLLEAGUES EXPERIENCE, THE
C     INDIVIDUAL I WILL MODIFY HIS MOVE AS PER THE FOLLOWING CRITERION
C     FIRST, ADJUSTMENT BASED ON ONES OWN EXPERIENCE
C     AND OWN BEST EXPERIENCE IN THE PAST (XX(I))
           DO J=1,M
           CALL RANDOM(RAND)
           V1(J)=A1*RAND*(XX(I,J)-X(I,J))
C     THEN BASED ON THE OTHER COLLEAGUES BEST EXPERIENCE WITH WEIGHT W
C     HERE W IS CALLED AN INERTIA WEIGHT 0.01< W < 0.7
C     A2 IS THE CONSTANT NEAR BUT LESS THAN UNITY
           CALL RANDOM(RAND)
           V2(J)=V(I,J)
           IF(F(NFBEST).LT.F(I)) THEN
           V2(J)=A2*W*RAND*(XX(NFBEST,J)-X(I,J))
           ENDIF
C     THEN SOME RANDOMNESS AND A CONSTANT A3 CLOSE TO BUT LESS THAN UNITY
           CALL RANDOM(RAND)
           RND1=RAND
           CALL RANDOM(RAND)
            V3(J)=A3*RAND*W*RND1
C            V3(J)=A3*RAND*W
C     THEN ON PAST VELOCITY WITH INERTIA WEIGHT W
           V4(J)=W*V(I,J)
C     FINALLY A SUM OF THEM
           V(I,J)= V1(J)+V2(J)+V3(J)+V4(J)
           ENDDO
      ENDDO
C     CHANGE X
      DO I=1,N
      DO J=1,M
      RANDS=0.D00
C     ------------------------------------------------------------------
      IF(NSIGMA.EQ.1) THEN
       CALL RANDOM(RAND) ! FOR CHAOTIC PERTURBATION
       IF(DABS(RAND-.5D00).LT.SIGMA) RANDS=RAND-0.5D00
C     SIGMA CONDITIONED RANDS INTRODUCES CHAOTIC ELEMENT IN TO LOCATION
C     IN SOME CASES THIS PERTURBATION HAS WORKED VERY EFFECTIVELY WITH
C     PARAMETER (N=100,NN=15,MX=100,NSTEP=9,ITRN=100000,NSIGMA=1,ITOP=2)
      ENDIF
C     -----------------------------------------------------------------
      X(I,J)=X(I,J)+V(I,J)*(1.D00+RANDS)
      ENDDO
      ENDDO
       DO I=1,N
         IF(F(I).LT.FMIN) THEN
         FMIN=F(I)
         II=I
         DO J=1,M
         BST(J)=XX(II,J)
         ENDDO
         ENDIF
         ENDDO
      IF(LCOUNT.EQ.NPRN) THEN
      LCOUNT=0
      WRITE(*,*)'OPTIMAL SOLUTION UPTO THIS (FUNCTION CALLS=',NFCALL,')'
      WRITE(*,*)'X = ',(BST(J),J=1,M),' MIN F = ',FMIN
C      WRITE(*,*)'NO. OF FUNCTION CALLS = ',NFCALL
      IF(DABS(FFMIN-FMIN).LT.EPSILON) GOTO 999
      FFMIN=FMIN
      ENDIF
      LCOUNT=LCOUNT+1
  100 CONTINUE
  999 WRITE(*,*)'------------------------------------------------------'
      WRITE(*,*)'FINAL X = ',(BST(J),J=1,M),' FINAL MIN F = ',FMIN
      WRITE(*,*)'COMPUTATION OVER:FOR ',FTIT
      WRITE(*,*)'NO. OF VARIABLES=',M,'  END.'
      END
C     ----------------------------------------------------------------
      SUBROUTINE LSRCH(A,M,VI,NSTEP,FI)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      CHARACTER *70 FTIT
      COMMON /KFF/KF,NFCALL,FTIT
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION A(*),B(100),VI(*)
      AMN=1.0D30
      DO J=1,NSTEP
         DO JJ=1,M
         B(JJ)=A(JJ)+(J-(NSTEP/2)-1)*VI(JJ)
         ENDDO
      CALL FUNC(B,M,FI)
        IF(FI.LT.AMN) THEN
        AMN=FI
        DO JJ=1,M
        A(JJ)=B(JJ)
        ENDDO
        ENDIF
      ENDDO
      FI=AMN
      RETURN
      END
C     -----------------------------------------------------------------
C     THIS SUBROUTINE IS NEEDED IF THE NEIGHBOURHOOD HAS RING TOPOLOGY
C     EITHER PURE OR HYBRIDIZED
       SUBROUTINE NEIGHBOR(I,N,J,K)
       IF(I-1.GE.1 .AND. I.LT.N) THEN
       J=I-1
       K=I+1
       ELSE
       IF(I-1.LT.1) THEN
       J=N-I+1
       K=I+1
       ENDIF
       IF(I.EQ.N) THEN
       J=I-1
       K=1
       ENDIF
       ENDIF
       RETURN
       END
C     -----------------------------------------------------------------
      SUBROUTINE RANDOM(RAND1)
       DOUBLE PRECISION  RAND1
       COMMON /RNDM/IU,IV
      INTEGER IU,IV
       RAND=REAL(RAND1)
       IV=IU*65539
       IF(IV.LT.0) THEN
       IV=IV+2147483647+1
       ENDIF
       RAND=IV
       IU=IV
       RAND=RAND*0.4656613E-09
       RAND1=DBLE(RAND)
       RETURN
       END
C     -----------------------------------------------------------------
      SUBROUTINE FSELECT(KF,M,FTIT)
C     THE PROGRAM REQUIRES INPUTS FROM THE USER ON THE FOLLOWING ------
C     (1) FUNCTION CODE (KF), (2) NO. OF VARIABLES IN THE FUNCTION (M);
      CHARACTER *70 TIT(100),FTIT
      WRITE(*,*)'----------------------------------------------------'
      DATA TIT(1)/'KF=1 NEW FUNCTION(N#1) 2-VARIABLES M=2'/
      DATA TIT(2)/'KF=2 NEW FUNCTION(N#2) 2-VARIABLES M=2'/
      DATA TIT(3)/'KF=3 NEW FUNCTION(N#3) 2-VARIABLES M=2'/
      DATA TIT(4)/'KF=4 NEW FUNCTION(N#4) 2-VARIABLES M=2'/
      DATA TIT(5)/'KF=5 NEW QUINTIC FUNCTION M-VARIABLES M=?'/
      DATA TIT(6)/'KF=6 NEW NEEDLE-EYE FUNCTION (N#6) M-VARIABLES M=?'/
      DATA TIT(7)/'KF=7 NEW ZERO-SUM FUNCTION (N#7) M-VARIABLES M=?'/
      DATA TIT(8)/'KF=8 CORANA FUNCTION 4-VARIABLES M=4'/
      DATA TIT(9)/'KF=9 MODIFIED RCOS FUNCTION 2-VARIABLES M=2'/
      DATA TIT(10)/'KF=10 FREUDENSTEIN ROTH FUNCTION 2-VARIABLES M=2'/
      DATA TIT(11)/'KF=11 ANNS XOR FUNCTION 9-VARIABLES M=9'/
      DATA TIT(12)/'KF=12 PERM FUNCTION #1 (SET BETA) 4-VARIABLES M=4'/
      DATA TIT(13)/'KF=13 PERM FUNCTION #2 (SET BETA) M-VARIABLES M=?'/
      DATA TIT(14)/'KF=14 POWER-SUM FUNCTION 4-VARIABLES M=4'/
      DATA TIT(15)/'KF=15 GOLDSTEIN PRICE FUNCTION 2-VARIABLES M=2'/
      DATA TIT(16)/'KF=16 BUKIN 6TH FUNCTION 2-VARIABLES M=2'/
      DATA TIT(17)/'KF=17 NEW FUNCTION (N#8) 2-VARIABLES M=2'/
      DATA TIT(18)/'KF=18 DEFL CORRUG SPRING FUNCTION M-VARIABLES M=?'/
      DATA TIT(19)/'KF=19 NEW FACTORIAL FUNCTION M-VARIABLES M=?'/
      DATA TIT(20)/'KF=20 NEW DECANOMIAL FUNCTION 2-VARIABLES M=2'/
      DATA TIT(21)/'KF=21 JUDGE FUNCTION 2-VARIABLES M=2'/
      DATA TIT(22)/'KF=22 NEW DODECAL FUNCTION 3-VARIABLES M=3'/
      DATA TIT(23)/'KF=23 NEW SUM-EQ-PROD FUNCTION 2-VARIABLES M=2'/
      DATA TIT(24)/'KF=24 NEW AM-EQ-GM FUNCTION M-VARIABLES M=?'/
      DATA TIT(25)/'KF=25 YAO-LIU FUNCTION#2 M-VARIABLES M=?'/
      DATA TIT(26)/'KF=26 YAO-LIU FUNCTION#3 M-VARIABLES M=?'/
      DATA TIT(27)/'KF=27 YAO-LIU FUNCTION#4 M-VARIABLES M=?'/
      DATA TIT(28)/'KF=28 YAO-LIU FUNCTION#6 M-VARIABLES M=?'/
      DATA TIT(29)/'KF=29 YAO-LIU FUNCTION#7 M-VARIABLES M=?'/
      DATA TIT(30)/'KF=30 YAO-LIU FUNCTION#12 M-VARIABLES M=?'/
      DATA TIT(31)/'KF=31 YAO-LIU FUNCTION#13 M-VARIABLES M=?'/
      DATA TIT(32)/'KF=32 YAO-LIU FUNCTION#14 2-VARIABLES M=2'/
      DATA TIT(33)/'KF=33 YAO-LIU FUNCTION#15 4-VARIABLES M=4'/
      DATA TIT(34)/'KF=34 WOOD FUNCTION : 4-VARIABLES M=4'/
      DATA TIT(35)/'KF=35 FENTON-EASON FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(36)/'KF=36 HOUGEN FUNCTION : 5-VARIABLES M=5'/
      DATA TIT(37)/'KF=37 GIUNTA FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(38)/'KF=38 EGGHOLDER FUNCTION : M-VARIABLES M=?'/
      DATA TIT(39)/'KF=39 TRID FUNCTION : M-VARIABLES M=?'/
      DATA TIT(40)/'KF=40 GRIEWANK FUNCTION : M-VARIABLES M=?'/
      DATA TIT(41)/'KF=41 WEIERSTRASS FUNCTION : M-VARIABLES M=?'/
      DATA TIT(42)/'KF=42 LEVY-3 FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(43)/'KF=43 LEVY-5 FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(44)/'KF=44 LEVY-8 FUNCTION : 3-VARIABLES M=3'/
      DATA TIT(45)/'KF=45 RASTRIGIN FUNCTION : M-VARIABLES M=?'/
      DATA TIT(46)/'KF=46 ACKLEY FUNCTION : M-VARIABLES M=?'/
      DATA TIT(47)/'KF=47 MICHALEWICZ FUNCTION : M-VARIABLES M=?'/
      DATA TIT(48)/'KF=48 SCHWEFEL FUNCTION : M-VARIABLES M=?'/
      DATA TIT(49)/'KF=49 SHUBERT FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(50)/'KF=50 DIXON-PRICE FUNCTION : M-VARIABLES M=?'/
      DATA TIT(51)/'KF=51 SHEKEL FUNCTION : 4-VARIABLES M=4'/
      DATA TIT(52)/'KF=52 PAVIANI FUNCTION : 10-VARIABLES M=10'/
      DATA TIT(53)/'KF=53 BRANIN FUNCTION#1 : 2-VARIABLES M=2'/
      DATA TIT(54)/'KF=54 BRANIN FUNCTION#2 : 2-VARIABLES M=2'/
      DATA TIT(55)/'KF=55 BOHACHEVSKY FUNCTION#1 : 2-VARIABLES M=2'/
      DATA TIT(56)/'KF=56 BOHACHEVSKY FUNCTION#2 : 2-VARIABLES M=2'/
      DATA TIT(57)/'KF=57 BOHACHEVSKY FUNCTION#3 : 2-VARIABLES M=2'/
      DATA TIT(58)/'KF=58 EASOM FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(59)/'KF=59 ROSENBROCK FUNCTION : M-VARIABLES M=?'/
      DATA TIT(60)/'KF=60 CROSS-LEGGED TABLE FUNCTION:2-VARIABLES M=2'/
      DATA TIT(61)/'KF=61 CROSS FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(62)/'KF=62 CROSS-IN-TRAY FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(63)/'KF=63 CROWNED CROSS FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(64)/'KF=64 TT-HOLDER FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(65)/'KF=65 HOLDER-TABLE FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(66)/'KF=66 CARROM-TABLE FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(67)/'KF=67 PENHOLDER FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(68)/'KF=68 BIRD FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(69)/'KF=69 CHICHINADZE FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(70)/'KF=70 MCCORMICK FUNCTION : 2-VARIABLES M=2'/
      DATA TIT(71)/'KF=71 GLANKWAHMDEE FUNCTION : 5-VARIABLES M=5'/
      DATA TIT(72)/'KF=72 FLETCHER-POWELL FUNCTION : M-VARIABLES M=?'/
      DATA TIT(73)/'KF=73 POWELL FUNCTION: M-VARIABLES M (MULT OF 4)=?'/
      DATA TIT(74)/'KF=74 HARTMANN FUNCTION: 3-VARIABLES M=3'/
      DATA TIT(75)/'KF=75 COLVILLE FUNCTION: 4-VARIABLES M=4'/
      DATA TIT(76)/'KF=76 HIMMELBLAU FUNCTION: 2-VARIABLES M=2'/
      DATA TIT(77)/'KF=77 BEALE FUNCTION: 2-VARIABLES M=2'/
      DATA TIT(78)/'KF=78 BOOTH FUNCTION: 2-VARIABLES M=2'/
      DATA TIT(79)/'KF=79 HUMP FUNCTION: 2-VARIABLES M=2'/
      DATA TIT(80)/'KF=80 MATYAS FUNCTION: 2-VARIABLES M=2'/
      DATA TIT(81)/'KF=81 MISHRA_1 FUNCTION: M-VARIABLES M=?'/
      DATA TIT(82)/'KF=82 MISHRA_2 FUNCTION: M-VARIABLES M=?'/
      DATA TIT(83)/'KF=83 ZAKHAROV FUNCTION: M-VARIABLES M=?'/
      DATA TIT(84)/'KF=84 MULTIMOD FUNCTION: 2-VARIABLES M=2'/
      DATA TIT(85)/'KF=85 NONLINEAR FUNCTION: M-VARIABLES M=?'/
      DATA TIT(86)/'KF=86 QUADRATIC FUNCTION: 2-VARIABLES M=2'/
      DATA TIT(87)/'KF=87 TRIGON FUNCTION: M-VARIABLES M=?'/
      DATA TIT(88)/'KF=88 WAVY-1 FUNCTIONS: M-VARIABLES M=?'/
      DATA TIT(89)/'KF=89 WAVY-2 FUNCTIONS: M-VARIABLES M=?'/
      DATA TIT(90)/'KF=90 TREFETHEN FUNCTION: 2-VARIABLES M=2'/
      DATA TIT(91)/'KF=91 ALPINE FUNCTION: M-VARIABLES M=?'/
C     -----------------------------------------------------------------
      DO I=1,91
      WRITE(*,*)TIT(I)
      ENDDO
      WRITE(*,*)'----------------------------------------------------'
      WRITE(*,*)'FUNCTION CODE [KF] AND NO. OF VARIABLES [M] ?'
      READ(*,*) KF,M
      FTIT=TIT(KF) ! STORE THE NAME OF THE CHOSEN FUNCTION IN FTIT
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FUNC(X,M,F)
C     TEST FUNCTIONS FOR GLOBAL OPTIMIZATION PROGRAM
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      COMMON /KFF/KF,NFCALL,FTIT
      INTEGER IU,IV
      DIMENSION X(*)
      CHARACTER *70 FTIT
      PI=4.D+00*DATAN(1.D+00)! DEFINING THE VALUE OF PI
      NFCALL=NFCALL+1 ! INCREMENT TO NUMBER OF FUNCTION CALLS
C     KF IS THE CODE OF THE TEST FUNCTION
C     -----------------------------------------------------------------
      IF(KF.EQ.1) THEN
C     FUNCTION #1 MIN AT -0.18467 APPROX AT (-8.4666, -10) APPROX
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*20
      ENDIF
      ENDDO
      F=DABS(DCOS(DSQRT(DABS(X(1)**2+X(2)))))**0.5 +0.01*X(1)+.01*X(2)
      RETURN
      ENDIF
C     ----------------------------------------------------------------
      IF(KF.EQ.2) THEN
C     FUNCTION #2 MIN = -0.199409 APPROX AT (-9.94112, -10) APPROX
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*20
      ENDIF
      ENDDO
      F=DABS(DSIN(DSQRT(DABS(X(1)**2+X(2)))))**0.5 +0.01*X(1)+.01*X(2)
      RETURN
      ENDIF
C     ----------------------------------------------------------------
      IF(KF.EQ.3) THEN
C     FUNCTION #3 MIN = -1.01983 APPROX AT (-1.98682, -10.00000) APPROX
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*20
      ENDIF
      ENDDO
      F1=DSIN(( DCOS(X(1))+DCOS(X(2)) )**2)**2
      F2=DCOS(( DSIN(X(1))+DSIN(X(2)) )**2)**2
      F=(F1+F2+X(1))**2 ! IS MULTIMODAL
      F=F+ 0.01*X(1)+0.1*X(2) ! MAKES UNIMODAL
      RETURN
      ENDIF
C     ----------------------------------------------------------------
      IF(KF.EQ.4) THEN
C     FUNCTION  #4 MIN = -2.28395 APPROX AT (2.88631, 1.82326) APPROX
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*20
      ENDIF
      ENDDO
      F1=DSIN((DCOS(X(1))+DCOS(X(2)))**2)**2
      F2=DCOS((DSIN(X(1))+DSIN(X(2)))**2)**2
      F3=-DLOG((F1-F2+X(1))**2 )
      F=F3+0.1D00*(X(1)-1.D00)**2+0.1D00*(X(2)-1.D00)**2
      RETURN
      ENDIF
C     ----------------------------------------------------------------
      IF(KF.EQ.5) THEN
C     QUINTIC FUNCTION:GLOBAL MINIMA,EXTREMELY DIFFICULT TO OPTIMIZE
C     MIN VALUE = 0 AT PERMUTATION OF (2, 2,..., 2, -1, -1, ..., -1,
C     -0.402627941) GIVES MIN F = 0.
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*20
      ENDIF
      ENDDO
      CALL QUINTIC(M,F,X)
      RETURN
      ENDIF
C     ----------------------------------------------------------------
      IF(KF.EQ.6) THEN
C     NEEDLE-EYE FUNCTION M=>1;
C     MIN = 1 IF ALL ABS(X) ARE SMALLER THAN THE EYE
C     SMALLER THE VALUE OF ZZ, MORE DIFFICULT TO ENTER THE EYE
C     LARGER THE VALUE OF M, MORE DIFFICULT TO FIND THE OPTIMUM
      F=0.D00
      EYE=0.000001D00
      FP=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.EYE) THEN
      FP=1.D00
       F=F+100.D00+DABS(X(I))
      ELSE
      F=F+1.D00
      ENDIF
      ENDDO
      IF(FP.EQ.0.D00) F=F/M
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.7) THEN
C     ZERO SUM FUNCTION : MIN  = 0 AT SUM(X(I))=0
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*20
      ENDIF
      ENDDO
      SUM=0.D00
      DO I=1,M
      SUM=SUM+X(I)
      ENDDO
      IF(SUM.NE.0.D00) F=1.D00+(10000*DABS(SUM))**0.5
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.8) THEN
C     CORANA FUNCTION : MIN = 0 AT (0, 0, 0, 0) APPROX
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.1000.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*2000
      ENDIF
      ENDDO
      DO J=1,M
        IF(J.EQ.1) DJ=1.D00
        IF(J.EQ.2) DJ=1000.D00
        IF(J.EQ.3) DJ=10.D00
        IF(J.EQ.4) DJ=100.D00
            ISGNXJ=1
            IF(X(J).LT.0.D00) ISGNXJ=-1
            ZJ=(DABS(X(J)/0.2D00)+0.49999)*ISGNXJ*0.2D00
            ISGNZJ=1
            IF(ZJ.LT.0.D00) ISGNZJ=-1
            IF(DABS(X(J)-ZJ).LT.0.05D00) THEN
            F=F+0.15D00*(ZJ-0.05D00*ISGNZJ)**2 * DJ
            ELSE
            F=F+DJ*X(J)**2
            ENDIF
      ENDDO
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.9) THEN
C     MODIFIED RCOS FUNCTION MIN=-0.179891 AT (-3.196989, 12.52626)APPRX
      F=0.D00
      IF(X(1).LT.-5.D00 .OR. X(1).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(1)=RAND*15.D00 -5.D00
      ENDIF
      IF(X(2).LT.0.D00 .OR. X(2).GT.15.D00) THEN
      CALL RANDOM(RAND)
      X(2)=RAND*15.D00
      ENDIF
      CA=1.D00
      CB=5.1/(4*PI**2)
      CC=5.D00/PI
      CD=6.D00
      CE=10.D00
      CF=1.0/(8*PI)
      F1=CA*(X(2)-CB*X(1)**2+CC*X(1)-CD)**2
      F2=CE*(1.D00-CF)*DCOS(X(1))*DCOS(X(2))
      F3=DLOG(X(1)**2+X(2)**2+1.D00)
      F=-1.0/(F1+F2+F3+CE)
      RETURN
      ENDIF
C     ----------------------------------------------------------------
      IF(KF.EQ.10) THEN
C     FREUDENSTEIN ROTH  FUNCTION : MIN  = 0 AT (5, 4)
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*20
      ENDIF
      ENDDO
      F1=(-13.D00+X(1)+((5.D00-X(2))*X(2)-2)*X(2))**2
      F2=(-29.D00+X(1)+((X(2)+1.D00)*X(2)-14.D00)*X(2))**2
      F=F1+F2
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.11) THEN
C     ANNS XOR FUNCTION (PARSOPOULOS, KE, PLAGIANAKOS, VP, MAGOULAS, GD
C     AND VRAHATIS, MN "STRETCHING TECHNIQUE FOR OBTAINING GLOBAL
C     MINIMIZERS THROUGH PARTICLE SWARM OPTIMIZATION")
C     MIN=0.9597588 FOR X=(1, -1, 1, -1, -1, 1, 1, -1, 0.421134) APPROX
C     OBTAINED BY DIFFERENTIAL EVOLUTION PROGRAM
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.1.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*2
      ENDIF
      ENDDO
      F11=X(7)/(1.D00+DEXP(-X(1)-X(2)-X(5)))
      F12=X(8)/(1.D00+DEXP(-X(3)-X(4)-X(6)))
      F1=(1.D00+DEXP(-F11-F12-X(9)))**(-2)
      F21=X(7)/(1.D00+DEXP(-X(5)))
      F22=X(8)/(1.D00+DEXP(-X(6)))
      F2=(1.D00+DEXP(-F21-F22-X(9)))**(-2)
      F31=X(7)/(1.D00+DEXP(-X(1)-X(5)))
      F32=X(8)/(1.D00+DEXP(-X(3)-X(6)))
      F3=(1.D00-(1.D00+DEXP(-F31-F32-X(9)))**(-1))**2
      F41=X(7)/(1.D00+DEXP(-X(2)-X(5)))
      F42=X(8)/(1.D00+DEXP(-X(4)-X(6)))
      F4=(1.D00-(1.D00+DEXP(-F41-F42-X(9)))**(-1))**2
      F=F1+F2+F3+F4
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.12) THEN
C     PERM FUNCTION #1 MIN = 0 AT (1, 2, 3, 4)
C     BETA => 0. CHANGE IF NEEDED. SMALLER BETA RAISES DIFFICULY
C     FOR BETA=0, EVERY PERMUTED SOLUTION IS A GLOBAL MINIMUM
      BETA=50.D00
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.M) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*2*M
      ENDIF
      ENDDO
      DO K=1,M
      SUM=0.D00
      DO I=1,M
      SUM=SUM+(I**K+BETA)*((X(I)/I)**K-1.D00)
      ENDDO
      F=F+SUM**2
      ENDDO
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.13) THEN
C     PERM FUNCTION #2 MIN = 0 AT (1/1, 1/2, 1/3, 1/4,..., 1/M)
C     BETA => 0. CHANGE IF NEEDED. SMALLER BETA RAISES DIFFICULY
C     FOR BETA=0, EVERY PERMUTED SOLUTION IS A GLOBAL MINIMUM
      BETA=10.D00
      DO I=1,M
      IF(DABS(X(I)).GT.1.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D00)*2
      ENDIF
      SGN=X(I)/DABS(X(I))
      ENDDO
      F=0.D00
      DO K=1,M
      SUM=0.D00
      DO I=1,M
      SUM=SUM+(I+BETA)*(X(I)**K-(1.D00/I)**K)
      ENDDO
      F=F+SUM**2
      ENDDO
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.14) THEN
C     POWER SUM FUNCTION; MIN = 0 AT PERM(1,2,2,3) FOR B=(8,18,44,114)
C     0 =< X <=4
      F=0.D00
      DO I=1,M
C     ANY PERMUTATION OF (1,2,2,3) WILL GIVE MIN = ZERO
      IF(X(I).LT.0.D00 .OR. X(I).GT.4.D00) THEN
      CALL RANDOM(RAND)
      X(I)=RAND*4
      ENDIF
      ENDDO
      DO K=1,M
      SUM=0.D00
      DO I=1,M
      SUM=SUM+X(I)**K
      ENDDO
      IF(K.EQ.1) B=8.D00
      IF(K.EQ.2) B=18.D00
      IF(K.EQ.3) B=44.D00
      IF(K.EQ.4) B=114.D00
      F=F+(SUM-B)**2
      ENDDO
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.15) THEN
C     GOLDSTEIN PRICE  FUNCTION  : MIN VALUE = 3 AT (0, -1)
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D00)*20
      ENDIF
      ENDDO
      F11=(X(1)+X(2)+1.D00)**2
      F12=(19.D00-14*X(1)+ 3*X(1)**2-14*X(2)+ 6*X(1)*X(2)+ 3*X(2)**2)
      F1=1.00+F11*F12
      F21=(2*X(1)-3*X(2))**2
      F22=(18.D00-32*X(1)+12*X(1)**2+48*X(2)-36*X(1)*X(2)+27*X(2)**2)
      F2=30.D00+F21*F22
      F= (F1*F2)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.16) THEN
C     BUKIN'S 6TH FUNCTION  MIN = 0 FOR (-10, 1)
C     -15. LE. X(1) .LE. -5 AND -3 .LE. X(2) .LE. 3
        IF(X(1).LT. -15.D00 .OR. X(1) .GT. -5.D00) THEN
        CALL RANDOM(RAND)
        X(1)=-(RAND*10+5.D00)
        ENDIF
        IF(DABS(X(2)).GT.3.D00) THEN
        CALL RANDOM(RAND)
        X(2)=(RAND-.5D00)*6
        ENDIF
      F=100.D0*DSQRT(DABS(X(2)-0.01D0*X(1)**2))+ 0.01D0*DABS(X(1)+10.D0)
       RETURN
       ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.17) THEN
C     NEW N#8 FUNCTION (MULTIPLE GLOBAL MINIMA)
C     MIN VALUE = -1 AT (AROUND .7 AROUND, 0.785 APPROX)
      F=0.D00
      DO I=1,M
      IF(X(I).LT.0.5D00 .OR. X(I).GT.1.D00) THEN
      CALL RANDOM(RAND)
      X(I)=RAND/2.D00
      ENDIF
      ENDDO
      F=-DEXP(-DABS(DLOG(.001D00+DABS((DSIN(X(1)+X(2))+DSIN(X(1)-X(2))+
     & (DCOS(X(1)+X(2))*DCOS(X(1)-X(2))+.001))**2)+
     & .01D00*(X(2)-X(1))**2)))
       RETURN
       ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.18) THEN
C     DEFLECTED CORRUGATED SPRING FUNCTION
C     MIN VALUE = -1 AT (5, 5, ..., 5) FOR ANY K AND ALPHA=5; M VARIABLE
      CALL DCS(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.19) THEN
C     FACTORIAL FUNCTION, MIN =0 AT X=(1,2,3,...,M)
      CALL FACTOR1(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.20) THEN
C     DECANOMIAL FUNCTION, MIN =0 AT X=(2, -3)
        DO I=1,M
        IF(DABS(X(I)).GT.4.D00) THEN
        CALL RANDOM(RAND)
        X(I)= (RAND-0.5D00)*8
        ENDIF
        ENDDO
      CALL DECANOM(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.21) THEN
C     JUDGE'S FUNCTION  F(0.864, 1.23) = 16.0817; M=2
      CALL JUDGE(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.22) THEN
C     DODECAL FUNCTION
      CALL DODECAL(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.23) THEN
C     WHEN X(1)*X(2)=X(1)*X(2) ? M=2
      CALL SEQP(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.24) THEN
C     WHEN ARITHMETIC MEAN = GEOMETRIC MEAN ? : M =>1
      CALL AMGM(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.25) THEN
C     M =>2
      CALL FUNCT2(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.26) THEN
C     M =>2
      CALL FUNCT3(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.27) THEN
C     M =>2
      CALL FUNCT4(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.28) THEN
C     M =>2
      CALL FUNCT6(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.29) THEN
C     M =>2
      CALL FUNCT7(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.30) THEN
C     M =>2
      CALL FUNCT12(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.31) THEN
C     M =>2
      CALL FUNCT13(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.32) THEN
C     M =2
      CALL FUNCT14(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.33) THEN
C     M =4
      CALL FUNCT15(M,F,X)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.34) THEN
C     WOOD FUNCTION : F MIN  : M=4
      CALL WOOD(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.35) THEN
C     FENTON & EASON FUNCTION :   : M=2
      CALL FENTONEASON(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.36) THEN
C     HOUGEN FUNCTION 5 VARIABLES : M =3
      CALL HOUGEN(X,M,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.37) THEN
C     GIUNTA FUNCTION 2 VARIABLES  :M =2
      CALL GIUNTA(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.38) THEN
C     EGGHOLDER FUNCTION M VARIABLES
      CALL EGGHOLD(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.39) THEN
C     TRID FUNCTION M VARIABLES
      CALL TRID(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.40) THEN
C     GRIEWANK FUNCTION M VARIABLES
      CALL GRIEWANK(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.41) THEN
C     WEIERSTRASS FUNCTION M VARIABLES
      CALL WEIERSTRASS(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.42) THEN
C     LEVY-3 FUNCTION 2 VARIABLES
      CALL LEVY3(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.43) THEN
C     LEVY-5 FUNCTION 2 VARIABLES
      CALL LEVY5(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.44) THEN
C     LEVY-8 FUNCTION 3 VARIABLES
      CALL LEVY8(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.45) THEN
C     RASTRIGIN FUNCTION M VARIABLES
      CALL RASTRIGIN(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.46) THEN
C     ACKLEY FUNCTION M VARIABLES
      CALL ACKLEY(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.47) THEN
C     MICHALEWICZ FUNCTION M VARIABLES
      CALL MICHALEWICZ(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.48) THEN
C     SCHWEFEL FUNCTION M VARIABLES
      CALL SCHWEFEL(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.49) THEN
C     SHUBERT FUNCTION 2 VARIABLES
      CALL SHUBERT(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.50) THEN
C     DIXON AND PRICE FUNCTION M VARIABLES
      CALL DIXPRICE(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.51) THEN
C     SHEKEL FUNCTION 4 VARIABLES
      CALL SHEKEL(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.52) THEN
C     PAVIANI FUNCTION 10 VARIABLES
      CALL PAVIANI(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.53) THEN
C     BRANIN FUNCTION#1 2 VARIABLES
      CALL BRANIN1(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.54) THEN
C     BRANIN FUNCTION#2 2 VARIABLES
      CALL BRANIN2(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.55) THEN
C     BOHACHEVSKY FUNCTION#1 2 VARIABLES
      CALL BOHACHEVSKY1(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.56) THEN
C     BOHACHEVSKY FUNCTION#2 2 VARIABLES
      CALL BOHACHEVSKY2(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.57) THEN
C     BOHACHEVSKY FUNCTION#3 2 VARIABLES
      CALL BOHACHEVSKY3(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.58) THEN
C     EASOM FUNCTION#3 2 VARIABLES
      CALL EASOM(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.59) THEN
C     ROSENBROCK FUNCTION  M VARIABLES
      CALL ROSENBROCK(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.60) THEN
C     CROSS-LEGGED TABLE FUNCTION : 2 VARIABLES
      CALL CROSSLEG(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.61) THEN
C     CROSS FUNCTION : 2 VARIABLES
      CALL CROSS(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.62) THEN
C     CROSS-IN-TRAY FUNCTION : 2 VARIABLES
      CALL CROSSINTRAY(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.63) THEN
C     CROWNED-CROSS FUNCTION : 2 VARIABLES
      CALL CROWNEDCROSS(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.64) THEN
C     TT-HOLDER FUNCTION : 2 VARIABLES, MIN F([+/-]1.5706, 0)= -10.8723
      CALL TTHOLDER(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.65) THEN
C     HOLDER-TABLE FUNCTION : 2 VARIABLES
C     MIN F ([+/-] 9.64617, [+/-] 9.64617) APPROX = -26.92034 APPROX
      CALL HOLDERTABLE(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.66) THEN
C     CARROM-TABLE FUNCTION : 2 VARIABLES
C     MIN F ([+/-] 9.64617, [+/-] 9.64617) APPROX = -24.15682 APPROX
      CALL CARROMTABLE(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.67) THEN
C     PEN-HOLDER FUNCTION : 2 VARIABLES
C     MIN F ([+/-] 9.64617, [+/-] 9.64617) APPROX = -0.963535 APPROX
      CALL PENHOLDER(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.68) THEN
C     BIRD FUNCTION : 2 VARIABLES
C     MIN F (4.70104, 3.15294) APPROX = -106.764537 APPROX  OR
C     MIN F (-1.58214, -3.13024) APPROX = -106.764537 APPROX
      CALL BIRD(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.69) THEN
C     CHICHINADZE FUNCTION :  -30 <=X(I)<= 30;  M=2
C     MIN F (5.901329, 0.5) = -43.3158621
      CALL CHICHINADZE(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.70) THEN
C     MCCORMICK FUNCTION : -1.5<= X(1)<=4; -3<=X(2)<=4 ; M=2
C     MIN F (-0.54719755, -1.54719755) = -1.913223 APPROX
      CALL MCCORMICK(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.71) THEN
C     GLANKWAHMDEE FUNCTION:
      CALL GLANKWAHMDEE(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.72) THEN
C     FLETCHER-POWELL FUNCTION
      CALL FLETCHER(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.73) THEN
C     POWELL FUNCTION
      CALL POWELL(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.74) THEN
C     HARTMANN FUNCTION
      CALL HARTMANN(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.75) THEN
C     COVILLE FUNCTION
      CALL COLVILLE(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
      IF(KF.EQ.76) THEN
C     HIMMELBLAU FUNCTION
      CALL HIMMELBLAU(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.77) THEN
C     BEALE FUNCTION
      CALL BEALE(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.78) THEN
C     BOOTH FUNCTION
      CALL BOOTH(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.79) THEN
C     HUMP FUNCTION
      CALL HUMP(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.80) THEN
C     MATYAS FUNCTION
      CALL MATYAS(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.81) THEN
C     MISHRA_1 FUNCTION
      CALL MISHRA_1(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.82) THEN
C     MISHRA_2 FUNCTION
      CALL MISHRA_2(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.83) THEN
C     ZAKHAROV FUNCTION
      CALL ZAKHAROV(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.84) THEN
C     MULTOMOD FUNCTION
      CALL MULTIMOD(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.85) THEN
C     NONLINEAR  FUNCTION
      CALL NONLIN(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.86) THEN
C     QUADRATIC  FUNCTION
      CALL QUADRATIC(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.87) THEN
C     TRIGON FUNCTION
      CALL TRIGON(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.88) THEN
C     WAVY-1 FUNCTION
      CALL  WAVY1(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.89) THEN
C     WAVY-2 FUNCTION
      CALL  WAVY2(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.90) THEN
C     TREFETHEN FUNCTION
      CALL  TREFETHEN(M,X,F)
      RETURN
      ENDIF
C     ------------------------------------------------------------------
      IF(KF.EQ.91) THEN
C     ALPINE FUNCTION
      CALL  ALPINE(M,X,F)
      RETURN
      ENDIF
C     -----------------------------------------------------------------
C      IF(KF.EQ.99) THEN
C     *****  FUNCTION
C      CALL SUBROUTINE(M,X,F)
C      RETURN
C      ENDIF
C     =================================================================
      WRITE(*,*)'FUNCTION NOT DEFINED. PROGRAM ABORTED'
      STOP
      END
C     >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
      SUBROUTINE DCS(M,F,X)
C     FOR DEFLECTED CORRUGATED SPRING FUNCTION
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*),C(100)
C     OPTIMAL VALUES OF (ALL) X ARE ALPHA , AND K IS ONLY FOR SCALING
C     OPTIMAL VALUE OF F IS -1. DIFFICULT TO OPTIMIZE FOR LARGER M.
      DATA K,ALPHA/5,5.D00/ ! K AND ALPHA COULD TAKE ON ANY OTHER VALUES
      R2=0.D00
      DO I=1,M
      C(I)=ALPHA
      R2=R2+(X(I)-C(I))**2
      ENDDO
      R=DSQRT(R2)
      F=-DCOS(K*R)+0.1D00*R2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE QUINTIC(M,F,X)
C     QUINTIC FUNCTION: GLOBAL MINIMA,EXTREMELY DIFFICULT TO OPTIMIZE
C     MIN VALUE = 0 AT PERM( -1, -0.402627941, 2)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      F=0.D00
      DO I=1,M
      F=F+DABS(X(I)**5-3*X(I)**4+4*X(I)**3+2*X(I)**2-10*X(I)-4.D00)
      ENDDO
      F=1000*F
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FACTOR1(M,F,X)
C     FACTORIAL FUNCTION; MIN (1, 2, 3, ...., M) = 0
C     FACT = FACTORIAL(M) = 1 X 2 X 3 X 4 X .... X M
C     FIND X(I), I=1,2,...,M SUCH THAT THEIR PRODUCT IS EQUAL TO FACT.
C     LARGER THE VALUE OF M (=>8) OR SO, HARDER IS THE PROBLEM
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      F=0.D00
      FACT=1.D00
      P=1.D00
      DO I=1,M
      FACT=FACT*I
      P=P*X(I)
      F=F+DABS(P-FACT)**2
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE DECANOM(M,F,X)
C     DECANOMIAL FUNCTION; MIN (2, -3) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      F1= DABS(X(1)**10-20*X(1)**9+180*X(1)**8-960*X(1)**7+
     & 3360*X(1)**6-8064*X(1)**5+13340*X(1)**4-15360*X(1)**3+
     & 11520*X(1)**2-5120*X(1)+2624.D00)
      F2= DABS(X(2)**4+12*X(2)**3+54*X(2)**2+108*X(2)+81.D00)
      F=0.001D00*(F1+F2)**2
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE JUDGE(M,X,F)
      PARAMETER (N=20)
C     THIS SUBROUTINE IS FROM THE EXAMPLE IN JUDGE ET AL., THE THEORY
C     AND PRACTICE OF ECONOMETRICS, 2ND ED., PP. 956-7. THERE ARE TWO
C     OPTIMA: F(0.86479,1.2357)=16.0817307 (WHICH IS THE GLOBAL MINUMUM)
C     AND F(2.35,-0.319)=20.9805 (WHICH IS LOCAL). ADAPTED FROM BILL
C     GOFFE'S SIMMAN (SIMULATED ANNEALING) PROGRAM
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION Y(N), X2(N), X3(N), X(*)
       DATA (Y(I),I=1,N)/4.284,4.149,3.877,0.533,2.211,2.389,2.145,
     & 3.231,1.998,1.379,2.106,1.428,1.011,2.179,2.858,1.388,1.651,
     & 1.593,1.046,2.152/
       DATA (X2(I),I=1,N)/.286,.973,.384,.276,.973,.543,.957,.948,.543,
     & .797,.936,.889,.006,.828,.399,.617,.939,.784,.072,.889/
      DATA (X3(I),I=1,N)/.645,.585,.310,.058,.455,.779,.259,.202,.028,
     & .099,.142,.296,.175,.180,.842,.039,.103,.620,.158,.704/

      F=0.D00
      DO I=1,N
      F=F+(X(1) + X(2)*X2(I) + (X(2)**2)*X3(I) - Y(I))**2
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE DODECAL(M,F,X)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     DODECAL POLYNOMIAL MIN F(1,2,3)=0
      DO I=1,M
      IF(DABS(X(I)).GT.5.D0) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*10
      ENDIF
      ENDDO
      F=0.D00
      F1=2*X(1)**3+5*X(1)*X(2)+4*X(3)-2*X(1)**2*X(3)-18.D00
      F2=X(1)+X(2)**3+X(1)*X(2)**2+X(1)*X(3)**2-22.D00
      F3=8*X(1)**2+2*X(2)*X(3)+2*X(2)**2+3*X(2)**3-52.D00
      F=(F1*F3*F2**2+F1*F2*F3**2+F2**2+(X(1)+X(2)-X(3))**2)**2
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE SEQP(M,F,X)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     FOR WHAT VALUES X(1)+X(2)=X(1)*X(2) ? ANSWER: FOR (0,0) AND (2,2)
C     WHILE X(1), X(2) ARE INTEGERS.
      X(1)=INT(X(1)) ! X(1) CONVERTED TO INTEGER
      X(2)=INT(X(2)) ! X(2) CONVERTED TO INTEGER

      F1=X(1)+X(2)
      F2=X(1)*X(2)
      F=(F1-F2)**2    ! TURN ALIVE THIS  XOR
C      F=DABS(F1-F2)   ! TURN ALIVE THIS  - BUT NOT BOTH --------------
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE AMGM(M,F,X)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     FOR WHAT VALUES ARITHMETIC MEAN = GEOMETRIC MEAN ? THE ANSWER IS:
C     IF X(1)=X(2)=....=X(M) AND ALL X ARE NON-NEGATIVE
C     TAKE ONLY THE ABSOLUTE VALUES OF X
      SUM=0.D00
      DO I=1,M
      X(I)=DABS(X(I))
      ENDDO
C     SET SUM = SOME POSITIVE NUMBER. THIS MAKES THE FUNCTION UNIMODAL
      SUM= 100.D00 ! TURNED  ALIVE FOR UNIQUE MINIMUM AND SET SUM TO
C     SOME POSITIVE NUMBER. HERE IT IS 100; IT COULD BE ANYTHING ELSE.
      F1=0.D00
      F2=1.D00
      DO I=1,M
      F1=F1+X(I)
      F2=F2*X(I)
      ENDDO
      XSUM=F1
      F1=F1/M ! SUM DIVIDED BY M = ARITHMETIC MEAN
      F2=F2**(1.D00/M) ! MTH ROOT OF THE PRODUCT = GEOMETRIC MEAN
      F=(F1-F2)**2
      IF(SUM.GT.0.D00) F=F+(SUM-XSUM)**2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FUNCT2(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
C     IN FOGEL, L.J., ANGELIN, P.J. AND BACK, T. (ED) PROCEEDINGS OF THE
C     FIFTH ANNUAL CONFERENCE ON EVOLUTIONARY PROGRAMMING, PP. 451-460,
C     MIT PRESS, CAMBRIDGE, MASS.
C     MIN F (0, 0, ..., 0) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      F=0.D00
      F1=1.D00
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D00)*20
      ENDIF
      ENDDO
      DO I=1,M
      F=F+DABS(X(I))
      F1=F1*DABS(X(I))
      ENDDO
      F=F+F1
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FUNCT3(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
C     MIN F (0, 0, ... , 0) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      F=0.D00
      F1=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D00)*200
      ENDIF
      ENDDO
      DO I=1,M
      F1=0.D00
      DO J=1,I
      F1=F1+X(J)**2
      ENDDO
      F=F+F1
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FUNCT4(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
C     MIN F (0, 0, ..., 0) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      F=0.D00
      DO I=1,M
      IF(X(I).LT.0.D00 .OR. X(I).GE.M) THEN
      CALL RANDOM(RAND)
      X(I)=RAND*2*M
      ENDIF
      ENDDO
C     FIND MAX(X(I))=MAX(ABS(X(I))) NOTE: HERE X(I) CAN BE ONLY POSITIVE
      XMAX=X(1)
      DO I=1,M
      IF(XMAX.LT.X(I)) XMAX=X(I)
      ENDDO
      F=XMAX
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE FUNCT6(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
C     MIN F (-.5, -.5, ..., -.5) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D00)*200
      ENDIF
      ENDDO
      DO I=1,M
       F=F+(X(I)+0.5D00)**2
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FUNCT7(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
C     MIN F(0, 0, ..., 0) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
      F=0.D00
        DO I=1,M
        IF(DABS(X(I)).GT.1.28D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*2.56D00
        ENDIF
        ENDDO
      DO I=1,M
      CALL RANDOM(RAND)
      F=F+(I*X(I)**4)
      ENDDO
       CALL RANDOM(RAND)
       F=F+RAND
      RETURN
      END
C     ---------------------------------------------------------------
      SUBROUTINE FUNCT12(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(100),Y(100)
      DATA A,B,C /10.D00,100.D00,4.D00/
      PI=4.D00*DATAN(1.D00)
      F=0.D00
C     MIN F (-1, -1, -1, ..., -1) = 0
C       X(I)=-1.D00  ! TO CHECK, TURN IT ALIVE
       DO I=1,M
        IF(DABS(X(I)).GT.50.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*100.D00
        ENDIF
        ENDDO
      F1=0.D00
      DO I=1,M
      XX=DABS(X(I))
      U=0.D00
      IF(XX.GT.A) U=B*(XX-A)**C
      F1=F1+U
      ENDDO
      F2=0.D00
      DO I=1,M-1
      Y(I)=1.D00+.25D00*(X(I)+1.D00)
      F2=F2+ (Y(I)-1.D00)**2 * (1.D00+10.D00*(DSIN(PI*X(I+1))**2))
      ENDDO
      Y(M)=1.D00+.25D00*(X(M)+1.D00)
      F3=(Y(M)-1.D00)**2
      Y(1)=1.D00+.25D00*(X(1)+1.D00)
      F4=10.D00*(DSIN(PI*Y(1)))**2
      F=(PI/M)*(F4+F2+F3)+F1
      RETURN
      END
C     ---------------------------------------------------------------
      SUBROUTINE FUNCT13(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(100)
      DATA A,B,C /5.D00,100.D00,4.D00/
      PI=4*DATAN(1.D00)
      F=0.D00
C     MIN F (1, 1, 1, ..., 4.7544 APPROX) = -1.15044 APPROX
C        X(I)=1.D00  ! TO CHECK, TURN IT ALIVE
C        X(M)=-4.7544  ! TO CHECK, TURN IT ALIVE
      DO I=1,M
      IF(DABS(X(I)).GT.50.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D00)*100.D00
      ENDIF
      ENDDO
      F1=0.D00
      DO I=1,M
      XX=DABS(X(I))
      U=0.D00
      IF(XX.GT.A) U=B*(XX-A)**C
      F1=F1+U
      ENDDO
      F2=0.D00
      DO I=1,M-1
      F2=F2+ (X(I)-1.D00)**2 * (1.D00+(DSIN(3*PI*X(I+1))**2))
      ENDDO
      F3=(X(M)-1.D00)*  (1.D00+(DSIN(2*PI*X(M)))**2)
      F4=(DSIN(3*PI*X(1)))**2
      F=0.1*(F4+F2+F3)+F1
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FUNCT14(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
C     MIN F (-31.98, 31.98) = 0.998
      PARAMETER (N=25,NN=2)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(2), A(NN,N)
      DATA (A(1,J),J=1,N) /-32.D00,-16.D00,0.D00,16.D00,32.D00,-32.D00,
     & -16.D00,0.D00,16.D00,32.D00,-32.D00,-16.D00,0.D00,16.D00,32.D00,
     & -32.D0,-16.D0,0.D0,16.D0,32.D0,-32.D0,-16.D0,0.D0,16.D0,32.D0/
      DATA (A(2,J),J=1,N) /-32.D00,-32.D00,-32.D00,-32.D00,-32.D00,
     & -16.D00,-16.D00,-16.D00,-16.D00,-16.D00,0.D00,0.D00,0.D00,0.D00,
     & 0.D00,16.D00,16.D00,16.D00,16.D00,16.D00,32.D00,32.D00,
     & 32.D00,32.D00,32.D00/

      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D00)*200.D00
      ENDIF
      ENDDO
      F1=0.D00
      DO J=1,N
      F2=0.D00
      DO I=1,2
      F2=F2+(X(I)-A(I,J))**6
      ENDDO
      F2=1.D00/(J+F2)
      F1=F1+F2
      ENDDO
      F=1.D00/(0.002D00+F1)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FUNCT15(M,F,X)
C     REF: YAO, X. AND LIU, Y. (1996): FAST EVOLUTIONARY PROGRAMMING
C     MIN F(.19, .19, .12, .14) = 0.3075
      PARAMETER (N=11)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*), A(N),B(N)
      DATA (A(I),I=1,N) /.1957D00,.1947D00,.1735D00,.16D00,.0844D00,
     & .0627D00,.0456D00,.0342D00,.0323D00,.0235D00,.0246D00/
      DATA (B(I),I=1,N) /0.25D00,0.5D00,1.D00,2.D00,4.D00,6.D00,8.D00,
     & 10.D00,12.D00,14.D00,16.D00/
      DO I=1,N
      B(I)=1.D00/B(I)
      ENDDO
      F=0.D00
      DO I=1,M
      IF(DABS(X(I)).GT.5.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D00)*10.D00
      ENDIF
      ENDDO
      DO I=1,N
      F1=X(1)*(B(I)**2+B(I)*X(2))
      F2=B(I)**2+B(I)*X(3)+X(4)
      F=F+(A(I)-F1/F2)**2
      ENDDO
      F=F*1000
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE LINPROG1(M,F,X)
C     LINEAR PROGRAMMING : MINIMIZATION PROBLEM
C     IN THIS PROBLEM : M = NO. OF DECISION VARIABLES = 2
C     MIN F (2.390, 2.033) = -19.7253 APPROX
C     MIN F = OVER J=1, M : DO SUM(A(1,J)*X(J))  SUBJECT TO CONSTRAINTS
C     OVER  J=1, M : DO SUM(A(I,J)*X(J)) <= C(I) ; I=2
C     . . .         . . .          . . .       . . .
C     OVER  J=1, M : DO SUM(A(I,J)*X(J)) <= C(I) ; I=N
C     ALL X(I) => 0
      PARAMETER (N=3) ! N IS THE NO. OF CONSTRAINTS + 1
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*),A(20,10),C(20),FF(20)
      DATA (A(1,J),J=1,2),C(1)/4.D0,5.D0,0.0D0/!COEFF OF OBJ FUNCTION
      DATA (A(2,J),J=1,2),C(2)/10.D0,3.D0,30D0/!COEFF OF 1ST CONSTRAINT
      DATA (A(3,J),J=1,2),C(3)/6.D0,20.D0,55.D0/!COEFF OF 2ND CONSTRAINT
C     ------------------------------------------------------------------
C     USING ONLY NON-NEGATIVE VALUES OF X(I)
      DO I=1,M
      X(I)=DABS(X(I))
      ENDDO
C     EVALUATION OF OBJ FUNCTION AND CONSTRAINTS
      DO I=1,N
      FF(I)=0.D00
      DO J=1,M
      FF(I)=FF(I)+A(I,J)*X(J)
      ENDDO
      ENDDO
      F=-FF(1) ! CHANGE OF SIGN FOR MINIMIZATION
C     CHECK FOR SATISFYING OR VIOLATING THE CONSTRAINTS
      DO I=2,N
      FF(I)=FF(I)-C(I) ! SLACK
C     PENALTY FOR CROSSING LIMITS
      IF(FF(I).GT.0) F=F+(10+FF(I))**2
      ENDDO
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE LINPROG2(M,F,X)
C     LINEAR PROGRAMMING : MINIMIZATION PROBLEM
C     IN THIS PROBLEM : M = NO. OF DECISION VARIABLES = 3
C     MIN F (250, 625, 0) = -3250
C     MIN F = OVER J=1, M : DO SUM(A(1,J)*X(J))   SUBJECT TO CONSTRAINTS
C     OVER  J=1, M : DO SUM(A(I,J)*X(J)) <= C(I) ; I=2
C     . . .         . . .          . . .       . . .
C     OVER  J=1, M : DO SUM(A(I,J)*X(J)) <= C(I) ; I=N
C     ALL X(I) => 0
      PARAMETER (N=4) ! N IS THE NO. OF CONSTRAINTS + 1
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*),A(20,10),C(20),FF(20)
      DATA (A(1,J),J=1,3),C(1)/30.D0,40.D0,20.D0,0.0D0/! COEFF OF OBJ FUNCTION
      DATA (A(2,J),J=1,3),C(2)/10.D0,12.D0,7.D0,10000.0D0/!COEFF OF 1ST CONSTRAINT
      DATA (A(3,J),J=1,3),C(3)/7.D0,10.D0,8.D0,8000.D0/! COEFF OF 2ND CONSTRAINT
      DATA (A(4,J),J=1,3),C(4)/1.D0,1.D0,1.D0,1000.D0/! COEFF OF 3RD CONSTRAINT
C     ------------------------------------------------------------------
C     USING ONLY NON-NEGATIVE VALUES OF X(I)
      DO I=1,M
      X(I)=DABS(X(I))
      ENDDO
C     EVALUATION OF OBJ FUNCTION AND CONSTRAINTS
      DO I=1,N
      FF(I)=0.D00
      DO J=1,M
      FF(I)=FF(I)+A(I,J)*X(J)
      ENDDO
      ENDDO
      F=-FF(1) ! CHANGE OF SIGN FOR MINIMIZATION
C     CHECK FOR SATISFYING OR VIOLATING THE CONSTRAINTS
      DO I=2,N
      FF(I)=FF(I)-C(I) ! SLACK
C     PENALTY FOR CROSSING LIMITS
      IF(FF(I).GT.0.D00) F=F+(100.D00+FF(I))**2
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE HOUGEN(A,M,F)
      PARAMETER(N=13,K=3)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(N,K),RATE(N),A(*)
C     ----------------------------------------------------------------
C     HOUGEN FUNCTION (HOUGEN-WATSON MODEL FOR REACTION KINATICS)
C     NO. OF PARAMETERS (A) TO ESTIMATE = 5 = M

C     BEST RESULTS ARE:
C     A(1)=1.253031; A(2)=1.190943; A(3)=0.062798; A(4)=0.040063
C     A(5)=0.112453  ARE BEST ESTIMATES OBTAINED BY ROSENBROCK &
C     QUASI-NEWTON METHOD WITH SUM OF SQUARES OF DEVIATION =0.298900994
C     AND R=0.99945.

C     THE NEXT BEST RESULTS GIVEN BY HOOKE-JEEVES & QUASI-NEWTON
C     A(1)=2.475221;A(2)=0.599177; A(3)=0.124172; A(4)=0.083517
C     A(5)=0.217886; SUM OF SQUARES OF DEVIATION = 0.318593458
C     R=0.99941
C     MOST OF THE OTHER METHODS DO NOT PERFORM WELL
C     -----------------------------------------------------------------
      DATA X(1,1),X(1,2),X(1,3),RATE(1) /470,300,10,8.55/
      DATA X(2,1),X(2,2),X(2,3),RATE(2) /285,80,10,3.79/
      DATA X(3,1),X(3,2),X(3,3),RATE(3) /470,300,120,4.82/
      DATA X(4,1),X(4,2),X(4,3),RATE(4) /470,80,120,0.02/
      DATA X(5,1),X(5,2),X(5,3),RATE(5) /470,80,10,2.75/
      DATA X(6,1),X(6,2),X(6,3),RATE(6) /100,190,10,14.39/
      DATA X(7,1),X(7,2),X(7,3),RATE(7) /100,80,65,2.54/
      DATA X(8,1),X(8,2),X(8,3),RATE(8) /470,190,65,4.35/
      DATA X(9,1),X(9,2),X(9,3),RATE(9) /100,300,54,13/
      DATA X(10,1),X(10,2),X(10,3),RATE(10) /100,300,120,8.5/
      DATA X(11,1),X(11,2),X(11,3),RATE(11) /100,80,120,0.05/
      DATA X(12,1),X(12,2),X(12,3),RATE(12) /285,300,10,11.32/
      DATA X(13,1),X(13,2),X(13,3),RATE(13) /285,190,120,3.13/
C     WRITE(*,1)((X(I,J),J=1,K),RATE(I),I=1,N)
C   1 FORMAT(4F8.2)
      DO J=1,M
      IF(DABS(A(J)).GT.5.D00) THEN
      CALL RANDOM(RAND)
      A(J)=(RAND-0.5D00)*10.D00
      ENDIF
      ENDDO
      F=0.D00
      DO I=1,N
      D=1.D00
         DO J=1,K
         D=D+A(J+1)*X(I,J)
         ENDDO
      FX=(A(1)*X(I,2)-X(I,3)/A(M))/D
C     FX=(A(1)*X(I,2)-X(I,3)/A(5))/(1.D00+A(2)*X(I,1)+A(3)*X(I,2)+
C     A(4)*X(I,3))
      F=F+(RATE(I)-FX)**2
      ENDDO
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE GIUNTA(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     GIUNTA FUNCTION
C     X(I) = -1 TO 1;  M=2
        DO I=1,M
        IF(DABS(X(I)).GT.1.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*2.D00
        ENDIF
        ENDDO
      C=16.D00/15.D00
      F=DSIN(C*X(1)-1.D0)+DSIN(C*X(1)-1.D0)**2+DSIN(4*(C*X(1)-1.D0))/50+
     &DSIN(C*X(2)-1.D0)+DSIN(C*X(2)-1.D0)**2+DSIN(4*(C*X(2)-1.D0))/50+.6
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE EGGHOLD(M,X,F)
C     EGG HOLDER FUNCTION
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      DO I=1,M
       IF(DABS(X(I)).GT.512.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*1024.D00
       ENDIF
       ENDDO
       F=0.D00
      DO I=1,M-1
      F1=-(X(I+1)+47.D00)
      F2=DSIN(  DSQRT(  DABS(  X(I+1)+X(I)/2+47.D00  )  )  )
      F3=DSIN(  DSQRT(  DABS(  X(I)-(X(I+1)+47.D00) ) ))
      F4=-X(I)
      F=F+ F1*F2+F3*F4
      ENDDO
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE TRID(M,X,F)
C     TRID FUNCTION
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      F1=0.D00
      F2=0.D00
      DO I=1, M
      F1=F1+(X(I)-1.D00)**2
      ENDDO
      DO I=2, M
      F2=F2+X(I)*X(I-1)
      ENDDO
      F=F1-F2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE GRIEWANK(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     GRIEWANK FUNCTION
      F1=0.D00
      F2=1.0D00
      DO I=1,M
      F1=F1+X(I)**2
      FI=DFLOAT(I)
      F2=F2*DCOS(X(I)/DSQRT(FI))
      ENDDO
      F=F1/4000.D00-F2+1.0D00
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE WEIERSTRASS(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
C     WEIERSTRASS FUNCTION ------------------------------------
      DATA AX,BX,KMAX/0.5D00,3.D00,20/
      F1=0.D00
      F2=0.D00

        DO I=1,M
        IF(DABS(X(I)).GT.0.5D00) THEN
        CALL RANDOM(RAND)
        X(I)=RAND-0.5D00
        ENDIF
        ENDDO

      DO I=1,M
      S=0.D00
          DO KK=1,KMAX+1
          K=KK-1
          S=S+(AX**K*DCOS(2*PI*BX**K*(X(I)+0.5D00)))
          ENDDO
      F1=F1+S
      ENDDO

      DO KK=1,KMAX+1
      K=KK-1
      F2=F2+(AX**K*DCOS(2*PI*BX**K*0.5D00))
      ENDDO
      F=F1-M*F2
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE LEVY3(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     LEVY # 3 (LEVY ET AL. 1981) ------------------------------------
         DO I=1,M
         IF(DABS(X(I)).GT.10.D00) THEN
         CALL RANDOM(RAND)
         X(I)=(RAND-0.5D00)*20
         ENDIF
         ENDDO
          F1=0.0D+00
          F2=0.0D+00
          DO I=1,5
          F1=F1+(I*DCOS((I-1)*X(1)+I))
          F2=F2+(I*DCOS((I+1)*X(2)+I))
          ENDDO
         F=F1*F2
         RETURN
         END
C     -----------------------------------------------------------------
      SUBROUTINE LEVY5(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
            F1=0.0D+00
          F2=0.0D+00
        DO I=1,5
       F1=F1+(I*DCOS((I-1)*X(1)+I))
          F2=F2+(I*DCOS((I+1)*X(2)+I))
          ENDDO
          F3=(X(1)+1.42513D+00)**2
         F4=(X(2)+0.80032D+00)**2
         F=(F1*F2) + (F3+F4)
         RETURN
         END
C     ----------------------------------------------------------------
      SUBROUTINE LEVY8(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*),Y(3)
      PI=4*DATAN(1.D00)
C     LEVY # 8 FUNCTION ----------------------------------------------
         DO I=1,3
         Y(I)=1.D+00+(X(I)-1.D+00)/4.D+00
         ENDDO
         F1=DSIN(PI*Y(1))**2
        F3=(Y(3)-1.D+00)**2
       F2=0.D+00
        DO I=1,2
         F2=F2+((Y(I)-1.D+00)**2)*(1.D+00+10.D+00*(DSIN(PI*Y(I+1)))**2)
         ENDDO
       F=F1+F2+F3
       RETURN
       END
C     -----------------------------------------------------------------
      SUBROUTINE RASTRIGIN(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
C     RASTRIGIN'S FUNCTION
      F=0.D00
      DO I=1,M
      F=F+ X(I)**2 -10*DCOS(2*PI*X(I)) + 10.D00
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE ACKLEY(M,X,F)
C     ACKLEY FUNCTION
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
      F=20.D00+DEXP(1.D00)
      DO I=1,M
      IF(X(I).LT. -15.D00 .OR. X(I).GT.30.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*90 -15.D00
      ENDIF
      ENDDO
      F1=0.D00
      F2=0.D00
        DO I=1,M
         F1=F1+X(I)**2
         F2=F2+DCOS(2*PI*X(I))
        ENDDO
      F1=-20*DEXP(-0.2D00*DSQRT(F1/M))
      F2=-DEXP(F2/M)
      F=F+F1+F2
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE MICHALEWICZ(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     MICHALEWICZ FUNCTION   [ 0 <= X(I) <= PI ] MP IS A PARAMETER
      MP=10  ! SET IT TO THE DESIRED VALUE
      PI=4*DATAN(1.D00)
      DO I=1,M
      IF(X(I).LT.0.D00 .OR. X(I).GT.PI)THEN
      CALL RANDOM(RAND)
      X(I)=RAND*PI
      ENDIF
      ENDDO
      F=0.D00
      DO I=1,M
      F=F-DSIN(X(I))*(DSIN(I*X(I)**2/PI))**(2*MP)
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE SCHWEFEL(M,X,F)
C     SCHWEFEL FUNCTION
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      DO I=1,M
      IF(DABS(X(I)).GT.500) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*1000
      ENDIF
      ENDDO
      F=0.D00
      DO I=1,M
      F=F+ X(I)*DSIN(DSQRT(DABS(X(I))))
      ENDDO
      F=418.9829D00*M - F
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE SHUBERT(M,X,F)
C     SHUBERT FUNCTION
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
         DO I=1,M
         IF(DABS(X(I)).GT.10.D00) THEN
         CALL RANDOM(RAND)
         X(I)=(RAND-0.5D00)*20
         ENDIF
         ENDDO
      F1=0.D00
      F2=0.D00
      DO I=1,5
      F1=F1+I*DCOS((I+1.D00)*X(1)+I)
      F2=F2+I*DCOS((I+1.D00)*X(2)+I)
      ENDDO
      F=F1*F2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE DIXPRICE(M,X,F)
C     DIXON & PRICE FUNCTION
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
       DO I=1,M
         IF(DABS(X(I)).GT.10.D00) THEN
         CALL RANDOM(RAND)
         X(I)=(RAND-0.5D00)*20
         ENDIF
       ENDDO
      F=0.D00
      DO I=2, M
      F=F + I*(2*X(I)**2-X(I-1))**2
      ENDDO
      F=F+(X(1)-1.D00)**2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE SHEKEL(M,X,F)
C     SHEKEL FUNCTION FOR TEST OF GLOBAL OPTIMIZATION METHODS
      PARAMETER(NROW=10,NCOL=4, NR=9)! NR MAY BE 2 TO 10
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION A(NROW,NCOL),C(NROW),X(*)
      DATA ((A(I,J),J=1,NCOL),I=1,NROW)/4.,4.,4.,4.,1.,1.,1.,1.,8.,8.,
     & 8.,8.,6.,6.,6.,6.,3.,7.,3.,7.,2.,9.,2.,9.,5.,5.,3.,3.,8.,1.,8.,
     & 1.,6.,2.,6.,2.,7.,3.6D00,7.,3.6D00/
      DATA (C(I),I=1,NROW)/0.1D00,0.2D00,0.2D00,0.4D00,0.4D00,0.6D00,
     & 0.3D00,0.7D00,0.5D00,0.5D00/
      F=0.D00
      DO I=1,NR
        S=0.D00
        DO J=1,M
        S=S+(X(J)-A(I,J))**2
        ENDDO
      F=F-1.D00/(S+C(I))
      ENDDO
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE PAVIANI(M,X,F)
C     PAVIANI FUNCTION : MIN F(9.3502,...,9.3502)=45.77847 APPROX
C     IN THE DOMAIN 2<= X(I) <= 10 FOR I=1,2,...,10.
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      DO I=1,M
      IF(X(I).LE.2.D00.OR.X(I).GE.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=RAND*8+2.D00
      ENDIF
      ENDDO
      F1=0.D00
      F2=1.D00
      DO I=1,M
      F1=F1+ DLOG(X(I)-2.D00)**2+DLOG(10.D00-X(I))**2
      F2=F2*X(I)
      ENDDO
      F=F1-F2**0.2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE BRANIN1(M,X,F)
C     BRANIN FUNCTION #1  MIN F (1, 0) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
      DO I=1,M
      IF(DABS(X(I)).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*20
      ENDIF
      ENDDO
      F=(1.D00-2*X(2)+DSIN(4*PI*X(2))/2.D00-X(1))**2+(X(2)-
     & DSIN(2*PI*X(1))/2.D00)**2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE BRANIN2(M,X,F)
C     BRANIN FUNCTION #2 MIN F (3.1416, 2.25)= 0.397887 APPROX
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
      IF(X(1).LT.-5.D00 .OR. X(1).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(1)=RAND*15-5.D00
      ENDIF
      IF(X(2).LT.0.D00 .OR. X(2).GT.15.D00) THEN
      CALL RANDOM(RAND)
      X(2)=RAND*15
      ENDIF
      F=(X(2)-5.D00*X(1)**2/(4*PI**2)+5*X(1)/PI-6.D00)**2 +
     &   10*(1.D00-1.D00/(8*PI))*DCOS(X(1))+10.D00
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE BOHACHEVSKY1(M,X,F)
C     BOHACHEVSKY FUNCTION #1 : MIN F (0, 0) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*200
      ENDIF
      ENDDO
      F=X(1)**2+2*X(2)**2-0.3D00*DCOS(3*PI*X(1))-0.4D00*DCOS(4*PI*X(2))
     & +0.7D00
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE BOHACHEVSKY2(M,X,F)
C     BOHACHEVSKY FUNCTION #2  : MIN F (0, 0) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*200
      ENDIF
      ENDDO
      F=X(1)**2+2*X(2)**2-0.3D00*DCOS(3*PI*X(1))*DCOS(4*PI*X(2))+0.3D00
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE BOHACHEVSKY3(M,X,F)
C     BOHACHEVSKY FUNCTION #3   : MIN F (0, 0) = 0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*200
      ENDIF
      ENDDO
      F=X(1)**2+2*X(2)**2-0.3D00*DCOS(3*PI*X(1)+4*PI*X(2))+0.3D00
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE EASOM(M,X,F)
C     EASOM FUNCTION : 2-VARIABLES, MIN F (PI, PI) = -1.
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      PI=4*DATAN(1.D00)
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*200
      ENDIF
      ENDDO
      F=-DCOS(X(1))*DCOS(X(2))*DEXP(-(X(1)-PI)**2 -(X(2)-PI)**2)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE ROSENBROCK(M,X,F)
C     ROSENBROCK FUNCTION : M VARIABLE; MIN F (1, 1,...,1)=0
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      DO I=1,M
      IF(X(I).LT.-5.D00 .OR. X(I).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=RAND*15-5.D00
      ENDIF
      ENDDO
      F=0.D00
      DO I=1,M-1
      F=F+ (100.D00*(X(I+1)-X(I)**2)**2 + (X(I)-1.D00)**2)
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE CROSSLEG(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     CROSS-LEGGED TABLE FUNCTION ; -10<= X(I) <=10; M=2
C     MIN F(0 , X ) OR F(X, 0) = -1.
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
      F=-(DABS(DSIN(X(1))*DSIN(X(2))*DEXP(DABS(100.D00-(DSQRT
     & (X(1)**2+X(2)**2)/PI))))+1.D00)**(-.1)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE CROSS(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     CROSS FUNCTION ; -10<= X(I) <=10; M=2;
C     MIN F(A, B)=0 APPROX; A, B=1.3494 APPROX OF EITHER SIGN (+ OR -)
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
      F=(DABS(DSIN(X(1))*DSIN(X(2))*DEXP(DABS(100.D00-(DSQRT
     & (X(1)**2+X(2)**2)/PI))))+1.D00)**(-.1)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE CROSSINTRAY(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     CROSS IN TRAY FUNCTION ; -10<= X(I) <=10; M=2;
C     MIN F(A, B)=-20626.1218 APPROX; A, B=1.3494 APPROX OF EITHER SIGN
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
      F=-(DABS(DSIN(X(1))*DSIN(X(2))*DEXP(DABS(100.D00-(DSQRT
     & (X(1)**2+X(2)**2)/PI))))+1.D00)**(.1)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE CROWNEDCROSS(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     CROWNED CROSS FUNCTION ; -10<= X(I) <=10; M=2; MIN F = 1
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
      F=(DABS(DSIN(X(1))*DSIN(X(2))*DEXP(DABS(100.D00-
     & (DSQRT(X(1)**2+X(2)**2)/PI))))+1.D00)**(.1)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE TTHOLDER(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     TEST-TUBE HOLDER FUNCTION ; -10<= X(I) <=10; M=2;
C     MIN F([+/-]1.5706, 0)= -10.8723
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
      F=-4*DABS(DSIN(X(1))*DCOS(X(2))*DEXP(DABS(DCOS((X(1)**2+X(2)**2)/
     & 200))))
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE HOLDERTABLE(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     HOLDER-TABLE FUNCTION  ; -10<= X(I) <=10; M=2;
C     MIN F ([+/-] 9.64617, [+/-] 9.64617) APPROX = -26.92034 APPROX
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
      F=-DABS(DCOS(X(1))*DCOS(X(2))*DEXP(DABS(1.D00-(DSQRT(X(1)**2+
     & X(2)**2)/PI))))
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE CARROMTABLE(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     CARROM-TABLE FUNCTION  ; -10<= X(I) <=10; M=2;
C     MIN F ([+/-] 9.64617, [+/-] 9.64617) APPROX = -24.15682 APPROX
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
      F=-1.D00/30*(DCOS(X(1))*DCOS(X(2))*DEXP(DABS(1.D00-
     & (DSQRT(X(1)**2 + X(2)**2)/PI))))**2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE PENHOLDER(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     PENHOLDER FUNCTION  ; -11<= X(I) <=11; M=2;
C     MIN F ([+/-] 9.64617, [+/-] 9.64617) APPROX = -0.963535 APPROX
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.11.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*22
        ENDIF
        ENDDO
      F=-DEXP(-(DABS(DCOS(X(1))*DCOS(X(2))*DEXP(DABS(1.D0-(DSQRT
     & (X(1)**2+X(2)**2)/PI))))**(-1)))
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE BIRD(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     BIRD FUNCTION ; -2PI<= X(I) <=2PI; M=2;
C     MIN F (4.70104, 3.15294) APPROX = -106.764537 APPROX  OR
C     MIN F (-1.58214, -3.13024) APPROX = -106.764537 APPROX
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.2*PI) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*4*PI
        ENDIF
        ENDDO
      F=(DSIN(X(1))*DEXP((1.D00-DCOS(X(2)))**2) +
     & DCOS(X(2))*DEXP((1.D00-DSIN(X(1)))**2))+(X(1)-X(2))**2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE CHICHINADZE(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     CHICHINADZE FUNCTION :  -30 <=X(I)<= 30;  M=2
C     MIN F (5.901329, 0.5) = -43.3158621
        PI=4*DATAN(1.D00)
        DO I=1,M
        IF( DABS(X(I)).GT.30) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*60
        ENDIF
        ENDDO
      F=X(1)**2-12*X(1)+11.D00+10*DCOS(PI*X(1)/2)+8*DSIN(5*PI*X(1))-
     & (1.D00/DSQRT(5.D00))*DEXP(-(X(2)-0.5D00)**2/2)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE MCCORMICK(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     MCCORMICK FUNCTION : -1.5<= X(1)<=4; -3<=X(2)<=4 ; M=2
C     MIN F (-0.54719755, -1.54719755) = -1.913223 APPROX
        IF(X(1).LT. -1.5D00 .OR. X(1) .GT. 4.D00) THEN
        CALL RANDOM(RAND)
        X(1)=RAND*5.5D00-1.5D00
        ENDIF
        IF(X(2).LT. -3.D00 .OR. X(2) .GT. 4.D00) THEN
        CALL RANDOM(RAND)
        X(2)=RAND*7.D00-3.D00
        ENDIF
      F=DSIN(X(1)+X(2))+(X(1)-X(2))**2-1.5*X(1)+2.5*X(2)+1.D00
      RETURN
      END
C     ----------------------------------------------------------------
      SUBROUTINE FENTONEASON(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     FENTON & EASON FUNCTION  FMIN(1.74345, -2.029695) = 1.744152
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*200
      ENDIF
      ENDDO
      F=1.2D00+0.1*X(1)**2 +(0.1D00+0.1*X(2)**2)/X(1)**2+
     & (.1*X(1)**2*X(2)**2+10.D00)/((X(1)*X(2))**4)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE WOOD(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     WOOD FUNCTION:FMIN(0.443546,-0.194607,1.466077,2.15115)=1.09485393
      DO I=1,M
      IF(DABS(X(I)).GT.5.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*10
      ENDIF
      ENDDO
      F1=100*(X(2)+X(1)**2)**2 + (1.D0-X(1))**2 +90*(X(4)-X(3)**2)**2
      F2=(1.D0-X(3))**2 +10.1*((X(2)-1.D0)**2+(X(4)-1.D0)**2)
      F3=19.8*(X(2)-1.D0)*(X(4)-1.D0)
      F=F1+F2+F3
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE GLANKWAHMDEE(M,X,F)
      PARAMETER (N=5)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*),A(N,N), B(N)
C     ------------------ GLANKWAHMDEE FUNCTION ------------------------
C     GLANKWAHMDEE A, LIEBMAN JS AND HOGG GL (1979) "UNCONSTRAINED
C     DISCRETE NONLINEAR PROGRAMMING. ENGINEERING OPTIMIZATION 4: 95-107
C     PARSOPOULOS, KE AND VRAHATIS, MN (2002) RECENT APPROACHES TO
C     GLOBAL OPTIMIZATION PROBLEMS THROUGH PARTICLE SWARM OPTIMIZATION,
C     NATURAL COMPUTING 1: 235-306, 2002.  REPORT THE BEST OBTAINED
C     FMIN (0,12,23,17,6)= -737 OR  MIN F(0, 11,22,16,6)= -737
C     WE GET FMIN(-.232, 11.489, 22.273, 16.540, 6.115) = -739.822991
C     ------------------------------------------------------------------
      DATA ((A(I,J),J=1,N),I=1,N) /35,-20,-10,32,-10,-20, 40,-6,-31,32,
     & -10,-6,11,-6,-10,32,-31,-6,38,-20,-10,32,-10,-20,31/
      DATA (B(J),J=1,N) /-15,-27,-36,-18,-12/
C     -----------------------------------------------------------------
      DO I=1,M
      IF(DABS(X(I)).GT.100.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*200
      ENDIF
      ENDDO
      F=0.D0
      DO J=1,M
      F=F+B(J)*X(J)
      ENDDO
      DO I=1,M
      C=0.D0
      DO J=1,M
      C=C+X(J)*A(J,I)
      ENDDO
      F=F+C*X(I)
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE FLETCHER(M,X,F)
C     FLETCHER-POWELL FUNCTION, M <= 10, ELSE IT IS VERY MUCH SLOW
C     SOLUTION: MIN F = 0 FOR X=(C1, C2, C3,...,CM)
      PARAMETER(N=10) ! FOR DIMENSION OF DIFFERENT MATRICES AND VECTORS
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*),A(N,N),B(N,N),AA(N),BB(N),AL(N),C(N),C1(N)
      PI=4*DATAN(1.D00)
C     GENERATE A(I,J) AND B(I,J) BETWEEN (-100, 100) RANDOMLY.
C     C(I) = BETWEEN (-PI, PI) IS EITHER GIVEN OR RANDOMLY GENERATED.
C     DATA (C(I),I=1,10)/1,2,3,-3,-2,-1,0,1,2,3/ ! BETWEEN -PI AND PI
      DATA (C1(I),I=1,N)/-3,-3.02,-3.01,1,1.03,1.02,1.03,-.08,.001,3/
C     DATA (C1(I),I=1,N)/0,0,0,0,0,0,0,0,0,0/ ! ANOTHER EXAMPLE C1 = 0
      NC=0  ! DEFINE NC HERE 0 OR 1 OR 2
C     IF NC=0, C1 FROM DATA IS USED (THAT IS FIXED C);
C     IF NC=1, C IS MADE FROM C1 BY ADDING RANDOM PART - THAT IS C=C1+R
C     IF NC=2 THEN C IS PURELY RANDOM THAT IS C= 0 + R
C     IN ANY CASE C LIES BETWEEN -PI AND PI.
C     ----------------------------------------------------------------
C     FIND THE MAX MAGNITUDE ELEMENT IN C1 VECTOR (UPTO M ELEMENTS)
       CMAX=DABS(C1(1))
       DO J=2,M
       IF(DABS(C1(J)).GT.CMAX) CMAX=DABS(C1(J))
       ENDDO
       RANGE=PI-CMAX
C     -----------------------------------------------------------------
      DO J=1,M
      DO I=1,M
      CALL RANDOM(RAND)
      A(I,J)=(RAND-0.5D00)*200.D00
      CALL RANDOM(RAND)
      B(I,J)=(RAND-0.5D00)*200.D00
      ENDDO
      IF(NC.EQ.0) AL(J)=C1(J) ! FIXED OR NON-STOCHASTIC C
      IF(NC.EQ.1) THEN
      CALL RANDOM(RAND)
      AL(J)=C1(J)+(RAND-0.5D0)*2*RANGE ! A PART FIXED, OTHER STOCHASTIC
      ENDIF
      IF(NC.EQ.2) THEN
      CALL RANDOM(RAND)
      AL(J)=(RAND-0.5D00)*2*PI ! PURELY STOCHASTIC
      ENDIF
      ENDDO
      DO I=1,M
      AA(I)=0.D00
      DO J=1,M
      AA(I)=AA(I)+A(I,J)*DSIN(AL(J))+B(I,J)*DCOS(AL(J))
      ENDDO
      ENDDO
C     -----------------------------------------------------------------
      DO I=1,M
      IF(DABS(X(I)).GT.PI) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-0.5D00)*2*PI
      ENDIF
      ENDDO
      DO I=1,M
      BB(I)=0.D00
      DO J=1,M
      BB(I)=BB(I)+A(I,J)*DSIN(X(J))+B(I,J)*DCOS(X(J))
      ENDDO
      ENDDO
      F=0.D00
      DO I=1,M
      F=F+(AA(I)-BB(I))**2
      ENDDO
      RETURN
      END
C----------------------------------------------------------------------
      SUBROUTINE POWELL(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     POWELL FUNCTION  ; -4<= X(I) <=5; M=A MULTIPLE OF 4;
C     MIN F  =  0.0
        DO I=1,M
        IF(X(I).LT.-4.D00 .OR. X(I).GT.5.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*9+.5D00
        ENDIF
        ENDDO
      M4=M/4
      F=0.D00
      DO I=1,M4
      J=4*I
      F=F+(X(J-3)+10*X(J-2))**2+5*(X(J-1)-X(J))**2+(X(J-2)-X(J-1))**4 +
     & 10*(X(J-3)-X(J))**4
      ENDDO
      RETURN
      END
C----------------------------------------------------------------------
      SUBROUTINE HARTMANN(M,X,F)
      PARAMETER (N=4)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*),P(N,3),A(N,3),C(N)
C     HARTMANN FUNCTION
C     MIN F  =  -3.86278 APPROX  : 0 < X < 1.
      DATA ((P(I,J),J=1,3),I=1,4) /0.6890,0.1170,0.2673,0.4699,0.4387,
     &  0.7470,0.1091,0.8732,0.5547,0.0381,0.5743,0.8828/
      DATA ((A(I,J),J=1,3),I=1,4) /3.0,10.0,30.0,0.1,10.0,35.0,3.0,
     &  10.0,30.0,0.1,10.0,35.0/
      DATA (C(J),J=1,4) /1.0,1.2,3.0,3.2/
        DO I=1,M
        IF(X(I).LE.0.D00 .OR. X(I).GE.1.D00) THEN
        CALL RANDOM(RAND)
        X(I)=RAND
        ENDIF
        ENDDO
      F=0.D00
      DO I=1,N
      S=0.D00
      DO J=1,M
      S=S+A(I,J)*(X(J)-P(I,J))**2
      ENDDO
      F=F+C(I)*DEXP(-S)
      ENDDO
      F=-F
      RETURN
      END
C----------------------------------------------------------------------
      SUBROUTINE COLVILLE(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
C     COLVILLE FUNCTION  ; -10<= X(I) <=10; M= 4;
C     MINF(1,1,1,1)= 0.0
        DO I=1,M
        IF(X(I).LT.-10.D00 .OR. X(I).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
      F=100*(X(1)**2-X(2))**2 + (X(1)-1.D00)**2 +(X(3)-1.D00)**2+
     & 90*(X(3)**2-X(4))**2+10.1*((X(2)-1.D0)**2+(X(4)-1.D00)**2)+
     & 19.8*(X(2)-1.D00)*(X(4)-1.D00)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE HIMMELBLAU(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
      NF=0   ! SET NF = 0 MULTIPLE OPTIMA NF=1 SINGLE OPTIMUM
        DO I=1,M
        IF(X(I).LT.-10.D00 .OR. X(I).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
C     HIMMELBLAU FUNCTION. IT HAS MULTIPLE (4) GLOBAL OPTIMA : MINF=0
C     (3, 2); (-2.8051, 3.1313); (3.5744, -1.8481); (-3.779, -3.283)
      IF(NF.EQ.0) THEN
      F= (X(1)**2+X(2)-11)**2+  (X(1)+X(2)**2-7)**2
      RETURN
      ENDIF
      IF(NF.EQ.1) THEN
C     MODIFIED HIMMELBLAU FUNCTION. IT HAS ONLY ONE GLOBAL OPTIMUM
C     MINF=0 AT (3,2)
      F= (X(1)**2+X(2)-11)**2+(X(1)+X(2)**2-7)**2+0.1D00*((X(1)-3)**2 +
     1  (X(2)-2)**2)
      ENDIF
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE BEALE(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
        DO I=1,M
        IF(X(I).LT.-4.500 .OR. X(I).GT.4.500) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*9
        ENDIF
        ENDDO
C     BEALE FUNCTION  : MINF =0 AT (3, 0.5)
      F1=(1.5D00-X(1)+X(1)*X(2))**2
      F2=(2.25D00-X(1)+X(1)*X(2)**2)**2
      F3=(2.625D00-X(1)+X(1)*X(2)**3)**2
      F=F1+F2+F3
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE BOOTH(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
        DO I=1,M
        IF(X(I).LT.-10.D00 .OR. X(I).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
C     BOOTH FUNCTION  MINF (1,3)=0
      F=(X(1)+2*X(2)-7.0D00)**2+(2*X(1)+X(2)-5.0D00)**2
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE HUMP(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
        DO I=1,M
        IF(X(I).LT.-5.D00 .OR. X(I).GT.5.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*10
        ENDIF
        ENDDO
C     HUMP FUNCTION  MINF (0.0898, -0.7127) = -1.0316
      F=4*X(1)**2 - 2.1D00*X(1)**4 + (X(1)**6)/3.D00 + X(1)*X(2) -
     & 4*X(2)**2 + 4*X(2)**4
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE MATYAS(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H, O-Z)
      DIMENSION X(*)
        DO I=1,M
        IF(X(I).LT.-10.D00 .OR. X(I).GT.10.D00) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-0.5D00)*20
        ENDIF
        ENDDO
C     MATYAS FUNCTION  MIN F (0, 0) = 0
      F=0.26D00*(X(1)**2 + X(2)**2) - 0.48D00*X(1)*X(2)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE MISHRA_1(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     MIN F (1, 1, ..., 1) =2
      DO I=1,M
      IF(X(I).LT.0.D00 .OR. X(I).GT.1.D00) THEN
      CALL RANDOM(RAND)
      X(I)=RAND
      ENDIF
      ENDDO
      S=0.D00
      DO I=1,M-1
      S=S+X(I)
      ENDDO
      X(M)=(M-S)
      F=(1.D00+X(M))**X(M)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE MISHRA_2(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     MIN F (1, 1, ..., 1) =2
      DO I=1,M
      IF(X(I).LT.0.D00 .OR. X(I).GT.1.D00) THEN
      CALL RANDOM(RAND)
      X(I)=RAND
      ENDIF
      ENDDO
      S=0.D00
      DO I=1,M-1
      S=S+(X(I)+X(I+1))/2.D00
      ENDDO
      X(M)=(M-S)
      F=(1.D00+X(M))**X(M)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE ZAKHAROV(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     ZAKHAROV FUNCTIONMIN MINF = (0, 0, ..., 0) =0
      DO I=1,M
      IF(X(I).LT.-5.D00 .OR. X(I).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D0)*15 + 2.5D0
      ENDIF
      ENDDO
      F1=0.D00
      F2=0.D00
      DO I=1, M
      F1=F1+ X(I)**2
      F2=F2 + I*X(I)/2.D00
      ENDDO
      F=F1+F2**2+F2**4
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE MULTIMOD(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     MULTIMODAL  FUNCTION  MINF = (0,0)= -1  : M=2
      DO I=1,M
      IF(X(I).LT.-10.D00 .OR. X(I).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D0)*20
      ENDIF
      ENDDO
C     A TYPICAL MULTIMODAL FUNCTION
      F=-DCOS(X(1))*DCOS(X(2))*DEXP(-(X(1)**2 + X(2)**2)**2/4.D00)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE NONLIN(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     NONLINEAR  MULTIMODAL FUNCTION  MINF = 0
      DO I=1,M
      IF(X(I).LT.-10.D00 .OR. X(I).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D0)*20
      ENDIF
      ENDDO
      F=0.D0
      DO I=2,M
      F=F+DCOS(DABS(X(I)-X(I-1)) / DABS(X(I-1)+X(I)))
      ENDDO
      F=F+(M-1.D00)
C     IF 0.001*X(1) IS ADDED TO F, IT BECOMES UNIMODAL
C     F=F+0.001*X(1)
      RETURN
      END
C     ------------------------------------------------------------------
      SUBROUTINE QUADRATIC(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     QUADRATIC FUNCTION  MINF (0.19388, 0.48513) = -3873.7243 (M=2)
      DO I=1,M
      IF(X(I).LT.-10.D00 .OR. X(I).GT.10.D00) THEN
      CALL RANDOM(RAND)
      X(I)=(RAND-.5D0)*200
      ENDIF
      ENDDO
      F=-3803.84-138.08*X(1)-232.92*X(2)+128.08*X(1)**2+203.64*X(2)**2+
     & 182.25*X(1)*X(2)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE TRIGON(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     TRIGON FUNCTION F MIN (0, 0, 0,..., 0) OR (PI, 0, 0, ...,0) =0
      PI=4*DATAN(1.D00)
        DO I=1,M
        IF(X(I).LT.0.D00 .OR. X(I).GT.PI) THEN
        CALL RANDOM(RAND)
        X(I)=RAND*PI
        ENDIF
        ENDDO
      F=0.D00
      DO I=2,M
      F=F+(DCOS(I+0.D00)*DSIN(X(I)-X(I-1))**2 +
     & (I-1.D00)*(1.D0-DCOS(X(I))))**2
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE WAVY1(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     WAVY-1 FUNCTION F MIN (24, 24,...,24)=0
        DO I=1,M
        IF(X(I).LT.-100.D00 .OR. X(I).GT.100.D0) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-.5D0)*200
        ENDIF
        ENDDO
      F=0.D00
      DO I=1,M
      F=F+DABS(2*(X(I)-24.D0)+(X(I)-24.D0)*DSIN(X(I)-24.D0))
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE WAVY2(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     WAVY-2 FUNCTION F MIN (0,0,...,0)=0
        DO I=1,M
        IF(X(I).LT.-100.D00 .OR. X(I).GT.100.D0) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-.5D0)*200
        ENDIF
        ENDDO
      F=0.D00
      DO I=1,M
      F=F+X(I)**6*(2.D0+DSIN(1.D0/X(I)))
      ENDDO
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE TREFETHEN(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     TREFETHEN FUNCTION:FMIN(-0.02440307923,0.2106124261)=-3.3068686475
        DO I=1,M
        IF(X(I).LT.-10.D00 .OR. X(I).GT.10.D0) THEN
        CALL RANDOM(RAND)
        X(I)=(RAND-.5D0)*20
        ENDIF
        ENDDO
      F=0.D00
C     THE JAN-FEB 2002 ISSUE OF SIAM NEWS CONTAINED THE FOLLOWING
C     CHALLENGE FROM L. N. TREFETHEN OF OXFORD UNIVERSITY.
C     FMIN = F(-0.02440307923, 0.2106124261)= -3.3068686475
      F=DEXP(DSIN(50*X(1))) + DSIN(60*DEXP(X(2))) + DSIN(70*DSIN(X(1)))
     &  + DSIN(DSIN(80*X(2))) - DSIN(10*(X(1)+X(2))) +
     & 1.D0/4*(X(1)**2 + X(2)**2)
      RETURN
      END
C     -----------------------------------------------------------------
      SUBROUTINE ALPINE(M,X,F)
      IMPLICIT DOUBLE PRECISION (A-H,O-Z)
      COMMON /RNDM/IU,IV
      INTEGER IU,IV
      DIMENSION X(*)
C     ALPINE FUNCTION F MIN (7.917, 7.917, ..., 7.917)= -2.808131 APPROX
C     THE DOMAIN : X IN [-10, 10].
C     NOTE: IN THE ORIGINAL FUNCTION MIN F = -(2.808131)^M
        DO I=1,M
        IF(X(I).LT.0.D00 .OR. X(I).GT.10.D0) THEN
        CALL RANDOM(RAND)
        X(I)=RAND*10.D0
        ENDIF
        ENDDO
      F1=1.D0
      F2=1.D0
      DO I=1,M
      F1=F1*DSIN(X(I))
      F2=F2*X(I)
      ENDDO
      F=-DEXP(DLOG(F1*DSQRT(F2))/M)
      RETURN
      END