CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
C     This is an example call of MIDACO 6.0
C     -------------------------------------
C
C     MIDACO solves Multi-Objective Mixed-Integer Non-Linear Problems:
C
C
C      Minimize     F_1(X),... F_O(X)  where X(1,...N-NI)   is CONTINUOUS
C                                      and   X(N-NI+1,...N) is DISCRETE
C
C      subject to   G_j(X)  =  0   (j=1,...ME)      equality constraints
C                   G_j(X) >=  0   (j=ME+1,...M)  inequality constraints
C
C      and bounds   XL <= X <= XU
C
C
C     The problem statement of this example is given below. You can use 
C     this example as template to run your own problem. To do so: Replace 
C     the objective functions 'F' (and in case the constraints 'G') given 
C     here with your own problem and follow the below instruction steps.
C
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCC   MAIN PROGRAM   CCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      PROGRAM MAIN
      IMPLICIT NONE
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C     Dimensions of the optimization problem        
      INTEGER O, N, NI, M, ME
C     Lower and upper bounds ('XL' & 'XU') and optimization variable 'X'
      DOUBLE PRECISION XL(1000), XU(1000), X(1000)
C     Objectives 'F(X)' and constraints 'G(X)' 
      DOUBLE PRECISION F(10), G(1000)            
C     MIDACO information and stop flags
      INTEGER IFLAG, ISTOP
C     MIDACO parameter
      DOUBLE PRECISION PARAM(13)
C     MIDACO integer 'IW' and real'RW' workspace and pareto front 'PF'
      INTEGER LIW, LRW, LPF 
      PARAMETER (LIW = 50000, LRW = 50000, LPF = 50000)       
      INTEGER IW(LIW)
      DOUBLE PRECISION RW(LRW),PF(LPF)
C     Parameter for stopping criteria, printing and license
      INTEGER MAXTIME, MAXEVAL, PRINTEVAL, SAVE2FILE, I
      CHARACTER*60 KEY
      KEY='************************************************************'
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCC Step 1: Problem definition     CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
C     Step 1.A : Problem dimensions
C     CCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      O  = 1  ! Number of objectives
      N  = 37 ! Number of variables (in total)
      NI = 33 ! Number of integer variables (0 <= NI <= N)
      M  = 24 ! Number of constraints (in total)
      ME = 6  ! Number of equality constraints (0 <= ME <= M)
C
C     Step 1.B : Lower and upper bounds: 'XL' and 'XU'
C     CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      DO I = 1,4
         XL(I) = 1.0D0
         XU(I) = 1.0D2
      ENDDO
      DO I = 4+1,4+31
         XL(I) = 0.0D0
         XU(I) = 1.0D0
      ENDDO
      DO I = 4+31+1,N
         XL(I) = 5.0D0
         XU(I) = 1.0D2
      ENDDO
C         
C     Step 1.C : Starting point 'X'
C     CCCCCCCCCCCCCCCCCCCCCCCCCCCCC     
      DO I = 1,N          
          X(I) = XL(I) ! Here for example: starting point = lower bounds
      ENDDO
      
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCC Step 2: Choose stopping criteria and printing options    CCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C
C     Step 2.A : Stopping criteria
C     CCCCCCCCCCCCCCCCCCCCCCCCCCCC
      MAXEVAL = 999999999   ! Maximum evaluation budget (e.g. 1000000)
      MAXTIME = 60*60*24 ! Maximum time limit (e.g. 60*60*24 = 1 Day)
C
C     Step 2.B : Printing options
C     CCCCCCCCCCCCCCCCCCCCCCCCCCC
      PRINTEVAL = 50000 ! Print-Frequency for current best solution (e.g. 1000)
      SAVE2FILE = 1    ! Save SCREEN and SOLUTION to TXT-files [0=NO/1=YES]
      
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCC Step 3: Choose MIDACO parameters (FOR ADVANCED USERS)    CCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

      PARAM( 1) = 0.0D0  ! ACCURACY
      PARAM( 2) = 2.0D0  ! SEED
      PARAM( 3) = 5.3d0  ! FSTOP
      PARAM( 4) = 0.0D0  ! ALGOSTOP
      PARAM( 5) = 0.0D0  ! EVALSTOP
      PARAM( 6) = 0.0D0  ! FOCUS
      PARAM( 7) = 0.0D0  ! ANTS
      PARAM( 8) = 0.0D0  ! KERNEL
      PARAM( 9) = 0.0D0   ! ORACLE
      PARAM(10) = 0.0D0  ! PARETOMAX
      PARAM(11) = 0.0D0  ! EPSILON  
      PARAM(12) = 0.0D0  ! BALANCE
      PARAM(13) = 0.0D0  ! CHARACTER      

CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C         
C       Call MIDACO by Reverse Communication
C      
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
C     Print MIDACO headline with basic information
      CALL MIDACO_PRINT(1,PRINTEVAL,SAVE2FILE,IFLAG,ISTOP,F,G,X,XL,
     &         XU,O,N,NI,M,ME,RW,PF,MAXEVAL,MAXTIME,PARAM,1,0,KEY)             
      DO WHILE(ISTOP.EQ.0) !~~~Start~of~reverse~communication~loop  

C       Evaluate Objective F(X) and constraints G(X)
        CALL PROBLEM_FUNCTION( F, G , X)   
        
C       Call MIDACO
        CALL MIDACO(1,O,N,NI,M,ME,X,F,G,XL,XU,IFLAG,
     &              ISTOP,PARAM,RW,LRW,IW,LIW,PF,LPF,KEY)            
C       Call MIDACO printing routine
        CALL MIDACO_PRINT(2,PRINTEVAL,SAVE2FILE,IFLAG,ISTOP,F,G,X,
     &     XL,XU,O,N,NI,M,ME,RW,PF,MAXEVAL,MAXTIME,PARAM,1,0,KEY)     
      ENDDO !~~~~~~~~~~~~~~~~~~~~End~of~reverse~communication~loop  
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      ! PRINT*," Solution F(1) = ", F(1)
      ! PRINT*," Solution G(1) = ", G(1)
      ! PRINT*," Solution X(1) = ", X(1)            
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      END
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCC END OF MAIN CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC






CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCC   OPTIMIZATION PROBLEM   CCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      SUBROUTINE PROBLEM_FUNCTION(F,G,X)
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      IMPLICIT NONE
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      DOUBLE PRECISION F(*),G(*),X(*)
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC      
      double precision y(100),
     /        b1,  b2,  i3,  i4,  x5,  x6,  x7,  x8,  b9, b10,
     /       b11, b12, b13, b14, b15, b16, b17, b18, b19, b20,
     /       b21, b22, b23, b24, b25, b26, b27, b28, b29, b30,
     /       b31, b32, b33, b34, b35, b36, b37,
     /             e2,  e3,  e4,  e5,  e6,  e7,  e8,  e9, e10,
     /       e11, e12, e13, e14, e15, e16, e17, e18, e19, e20,
     /       e21, e22, e23, e24, e25
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
      INTEGER I,ncont,nint,nbin
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC

         ncont = 4
         nint  = 2
         nbin  = 31

      do i=1,nbin+nint
         y(i) = x(ncont+i)
      enddo  
       
      b1 = y(1)
      b2 = y(2)
      b9 = y(3)
      b10 = y(4)
      b11 = y(5)
      b12 = y(6)
      b13 = y(7)
      b14 = y(8)
      b15 = y(9)
      b16 = y(10)
      b17 = y(11)
      b18 = y(12)
      b19 = y(13)
      b20 = y(14)
      b21 = y(15)
      b22 = y(16)
      b23 = y(17)
      b24 = y(18)
      b25 = y(19)
      b26 = y(20)
      b27 = y(21)
      b28 = y(22)
      b29 = y(23)
      b30 = y(24)
      b31 = y(25)
      b32 = y(26)
      b33 = y(27)
      b34 = y(28)
      b35 = y(29)
      b36 = y(30)
      b37 = y(31)
      i3 = y(32)
      i4 = y(33)
      x5 = x(1)
      x6 = x(2)
      x7 = x(3)
      x8 = x(4)

      f(1)= 0.1d0*b1 + 0.2d0*b2 + b9 + 2.0d0*b10 + 3.0d0*b11 + 4.0d0*b12
     /     + 5.0d0*b13 + 6.0d0*b14 + 7.0d0*b15 + 8.0d0*b16 + b17 
     /     + 2.0d0*b18 + 3.0d0*b19 + 4.0d0*b20 + 5.0d0*b21 + 6.0d0*b22 
     /     + 7.0d0*b23                        
      
      e2 = 460.0d0*b24 + 920.0d0*b25 + 1380.0d0*b26 + 1840.0d0*b27
     /     + 570.0d0*b32 + 1140.0d0*b33 + 1710.0d0*b34 - 1900.0d0 

      e3 = 460.0d0*b28 + 920.0d0*b29 + 1380.0d0*b30 + 1840.0d0*b31 
     /     + 570.0d0*b35 + 1140.0d0*b36 + 1710.0d0*b37 - 1900.0d0 

      e4 = -460.0d0*b24 - 920.0d0*b25 - 1380.0d0*b26 - 1840.0d0*b27 
     /     - 570.0d0*b32 - 1140.0d0*b33 - 1710.0d0*b34 + 1700.0d0

      e5 = -460.0d0*b28 - 920.0d0*b29 - 1380.0d0*b30 - 1840.0d0*b31 
     /     - 570.0d0*b35 - 1140.0d0*b36 - 1710.0d0*b37 + 1700.0d0

      e6 = b24 + 2.0d0*b25 + 3.0d0*b26 + 4.0d0*b27 + b32 + 2.0d0*b33 
     /     + 3.0d0*b34 - 5.0d0

      e7 = b28 + 2.0d0*b29 + 3.0d0*b30 + 4.0d0*b31 + b35 + 2.0d0*b36 
     /    + 3.0d0*b37 - 5.0d0

      e8 = b1 - b9 - 2.0d0*b10 - 3.0d0*b11 - 4.0d0*b12 - 5.0d0*b13 
     /     - 6.0d0*b14 - 7.0d0*b15 - 8.0d0*b16      

      e9 = b2 - b17 - 2.0d0*b18 - 3.0d0*b19 - 4.0d0*b20 - 5.0d0*b21 
     /     - 6.0d0*b22 - 7.0d0*b23     

      e10 = -8.0d0*b1 + b9 + 2.0d0*b10 + 3.0d0*b11 + 4.0d0*b12
     /      + 5.0d0*b13 + 6.0d0*b14 + 7.0d0*b15 + 8.0d0*b16  

      e11 = -7.0d0*b2 + b17 + 2.0d0*b18 + 3.0d0*b19 + 4.0d0*b20 
     /      + 5.0d0*b21 + 6.0d0*b22 + 7.0d0*b23   

      e12 = i3 - 3.0d0*b9 - 8.0d0*b10 - 15.0d0*b11 - 24.0d0*b12 
     /      - 35.0d0*b13 - 48.0d0*b14 - 63.0d0*b15  
     /       - 80.0d0*b16 - 1                   

      e13 = i4 - 3.0d0*b17 - 8.0d0*b18 - 15.0d0*b19 - 24.0d0*b20
     /      - 35.0d0*b21 - 48.0d0*b22 - 63.0d0*b23 - 1.0d0

      e14 = b9 + b10 + b11 + b12 + b13 + b14 + b15 + b16 - 1.0d0 

      e15 = b17 + b18 + b19 + b20 + b21 + b22 + b23 - 1.0d0

      e16 = x5 - 3.0d0*b24 - 8.0d0*b25 - 15.0d0*b26 - 24.0d0*b27 - 1.0d0

      e17 = x6 - 3.0d0*b28 - 8.0d0*b29 - 15.0d0*b30 - 24.0d0*b31 - 1.0d0

      e18 = x7 - 3.0d0*b32 - 8.0d0*b33 - 15.0d0*b34 - 1.0d0 

      e19 = x8 - 3.0d0*b35 - 8.0d0*b36 - 15.0d0*b37 - 1.0d0         

      e20 = b24 + b25 + b26 + b27 - 1.0d0

      e21 = b28 + b29 + b30 + b31 - 1.0d0

      e22 = b32 + b33 + b34 - 1.0d0

      e23 = b35 + b36 + b37 - 1.0d0      

      e24 = -(dsqrt(i3*x5) + dsqrt(i4*x6)) + b9 + 2.0d0*b10 + 3.0d0*b11
     /      + 4.0d0*b12 + 5.0d0*b13 + 6.0d0*b14 + 7.0d0*b15 + 8.0d0*b16
     /      + b17 + 2.0d0*b18 + 3.0d0*b19 + 4.0d0*b20 + 5.0d0*b21 
     /      + 6.0d0*b22 + 7.0d0*b23 + b24 + 2.0d0*b25 + 3.0d0*b26 
     /      + 4.0d0*b27 + b28 + 2.0d0*b29 + 3.0d0*b30 + 4.0d0*b31 
     /      + 10.0d0 

      e25 = -(dsqrt(i3*x7) + dsqrt(i4*x8)) + b9 + 2.0d0*b10 + 3.0d0*b11
     /      + 4.0d0*b12 + 5.0d0*b13 + 6.0d0*b14 + 7.0d0*b15 + 8.0d0*b16
     /      + b17 + 2.0d0*b18 + 3.0d0*b19 + 4.0d0*b20 + 5.0d0*b21 
     /      + 6.0d0*b22 + 7.0d0*b23 + b32 + 2.0d0*b33 + 3.0d0*b34 + b35 
     /      + 2.0d0*b36 + 3.0d0*b37 + 9.0d0

      g(1) = e12
      g(2) = e13
      g(3) = e16
      g(4) = e17
      g(5) = e18
      g(6) = e19
      g(7) = -e2
      g(8) = -e3
      g(9) = -e4
      g(10) = -e5
      g(11) = -e6
      g(12) = -e7
      g(13) = -e8
      g(14) = -e9
      g(15) = -e10
      g(16) = -e11
      g(17) = -e14
      g(18) = -e15
      g(19) = -e20
      g(20) = -e21
      g(21) = -e22
      g(22) = -e23
      g(23) = -e24
      g(24) = -e25

      END
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCC END OF FILE CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC