Genetic algorithms start by generating a set of random feasible solutions. The best of these solutions are permitted to "mate" and produce offspring and mutations are occasionally introduced. The worst solutions in every generation are discarded and the process continues until either an iteration limit is reached or convergence takes place. See R. L. Haupt and S. E. Haupt, Practical Genetic Algorithms, Wiley, 1998 and D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley, 1989.

Suitable parameters for the algorithm should be determined by experimentation, since good values are problem dependent. This implementation is a continuous parameter (thus not a binary encoded) version of genetic algorithms.

In the MAIN program you must include

        CALL DFLT
        OPEN (UNIT=nfile,file='filename')

where NFILE is initialized by DFLT to 8 and will be the output file.

The call to GENALG is



  MX      = 1 to maximize, = 2 to minimize
  NP      = the number of parameters
  NIPOP   = the initial population (a power of 2; 128 is
            often suitable)
  NPOP    = the "working size" of the population (a power of 2, 64
            is often suitable)
  NGOOD   = the subpopulation that is permitted to mate (a power
            of 2; 32 is often suitable)
  XL      = a DOUBLE PRECISION vector dimensioned XL(NP)
            containing the lower bounds of the search area
  XH      = a DOUBLE PRECISION vector dimensioned XH(NP)
            containing the upper bounds of the search area
  CC,PP,CPP = DOUBLE PRECISION work arrays, each dimensioned
            NP, i.e., CC(NP), PP(NP), CPP(NP)
  MATES   = a work array dimensioned MATES(2,NGOOD/2)
  X       = a DOUBLE PRECISION work array dimensioned X(NP)
  POP     = an INTEGER array dimensioned POP(NIPOP,NP) containing
            the initial and subsequent populations; after
            convergence POP(1,.) contains the parameter values
            for the best solution
  U       = DOUBLE PRECISION work array dimensioned U((NIPOP,NP)
  FVAL    = DOUBLE PRECISION array which will contain the function
            values corresponding to the population members; after
            convergence, FVAL(1) contains the best function value
  FUNC    = the name of the function subroutine to be minimized or
            maximized; must be declared in an EXTERNAL statement
            in the MAIN program. See Section 1.1 for the conventions
            concerning FUNC subroutines.
  ITERC   = the iteration (generation) count
  IVAL    = the number of function evaluations
  IER     = error return; =-1 iteration limit exceeded, =-3 input
            error, =-5 continual straying into a forbidden region
  NCONT   = an integer value which causes the computations to be
            repeated if > 1. The repetition is as follows: after
            the first "pass" has converged, the best parameter
            values (in POP(1,.)) are retained, the feasible search
            area is shrunk (except in directions in which the
            optimum value is near the original boundary, in which
            case the search area is expanded in that direction), a
            new set of NIPOP-1 points are generated and the
            algorithm resumes. See also SHRINK1 and EXPAND below.
            A value of NCONT > 1 is useful to refine the location
            of a local optimum, but may hurt the chances of
            finding  a global optimum.
  IHOWMAN = the number of consecutive generations (iterations)
            in which either the optimal function value or the mean
            function value is allowed to remain unchanged without
            terminationg the computations; must be <=9.

The following parameters, communicated to GENALG through labelled COMMON, are also important.



   NC       = 1 should not be altered; this is a provision for
              future modifications
   INITGEN  = 2 initial population is generated randomly;
              3 no initial population is generated; user is
              responsible for filling the NIPOP rows of POP;
              4 one half of the population is generated randomly;
              from the ith row of POP (i=1,nipop/2) the remaining
              rows are generated by POP(nipop/2+i,j)=XH(j)-POP(i,j)
   IPAIR    = 1 parents are selected for pairing as follows: the
              lowest-cost parent mates with the second-lowest
              cost parent, the third-lowest with the
              fourth-lowest, and so on;
            = 2 pairing by rank-weighting (See Haupt and Haupt,
              p. 39);
            = 3 pairing by cost weighting (See Haupt and Haupt,
              pp. 39-40) (default=3);
            = 4 random pairing
   IMATE    = 1 each parent pair creates four potential offspring
              which differ in that for two the ic-th parameter of
              the offspring being a (BET1,1-BET1) and a
              (1-BET1,BET1) convex combination of the parents and
              for another two a (1+ALPH1,-ALPH1) and a (-ALPH1,
              ALPH1) combination, with the best two selected;
            = 2 each parent produces three potential offspring,
              the first of which is for the ic-th parameter
              a (u,1-u) combination of the parents (where u
              is a U(0,1) deviate), and the remaining two as
              immediately above, with the best two chosen;
   KTERL    = iteration limit (default=99)
   IMUTE    = 1 mutation rate remains constant;
            = 2 mutation rate decays 10% each generation;
            = 3 mutation is given by POP(I,.)*(1.5-u) where
              u is distributed as U(0,1);
   ITEST    = 1 if testing for convergence should be based on the
              optimal value achieved in a population (default=1);
            = 2 if testing should be based on the mean value of the
              population (this latter is likely to give a better
              optimum, but may take a great deal more
   IHOWMAN  = the number of consecutive generations (iterations)
              in which either the optimal function value or the mean
              function value is allowed to remain unchanged without
              terminationg the computations; must be <=9.


   YMUTE   = DOUBLE PRECISION constant defining the mutation rate;
             the number of mutations in a population will be
             (NPOP+NGOOD)*NP*YMUTE. The required number of
             individuals in the population will be chosen at random
             (except the best element in the population will not
             be subject to mutation) and then two randomly
             chosen city pairs will be exchanged (default=0.06)
   BACC    = DOUBLE PRECISION required relative accuracy (default=
   ALPH1   = extrapolation factor for mating (see IMATE above)
             (default =0.1)
   BET1    = convex combination factor for mating (see (IMATE
             above (default = 0.5)
   PM4     = used internally; user should not alter this
   SHRINK1 = Shrinkage factor for region of exploration in
             successive passes. XL and XH for each parameter are
             reset as XL = XL + SHRINK1*(POP(1,.)-XL) and
             XH = XH + SHRINK1*(POP(1,.)-XH) (default=0.95)
   EXPAND  = Expansion factor for region of exploration in
             successive passes. XL and XH for each parameter are
             reset as XL = XL - EXPAND*(XH-XL) and
             XH = XH + EXPAND*(XH-XL) (default=0.05)

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