dna.hlp

{smcl}
{* 24oct2008}{...}
{hline}
help for {hi:dna}
{hline}

{title:Genetic Algorithm}

{p 8}{cmd:dna {ul:f}unction} {it:function_name}

{p 8}{cmd:dna {ul:l}ength} {it:#}

{p 8}{cmd:dna {ul:p}opulation} {it:#}

{p 8}{cmd:dna {ul:o}ffspring} {it:#}

{p 8}{cmd:dna {ul:sel}ection} {it:#}

{p 8}{cmd:dna {ul:m}utation} {it:#} [{it:#}]

{p 8}{cmd:dna {ul:r}adiation} {it:#} [{it:#}]

{p 8}{cmd:dna {ul:de}fine} {it:#} {it:#} {it:#}

{p 8}{cmd:dna {ul:gr}oup} {it:#} {it:#}

{p 8}{cmd:dna {ul:ge}nerations} {it:#}

{p 8}{cmd:dna {ul:st}agnation} {it:#}

{p 8}{cmd:dna {ul:a}uto}

{p 8}{cmd:dna {ul:ma}nual}

{p 8}{cmd:dna {ul:i}nfo}

{p 8}{cmd:dna {ul:di}splay}

{p 8}{cmd:dna {ul:e}xport}

{p 8}{cmd:dna {ul:c}lear}

{p 8}{cmd:dna {ul:go}}

{title:Description}

{p}{cmd:dna} executes a genetic algorithm based optimization. The
population of potential solutions resides in the matrix {hi:pop}.
The row vector {hi:dna} contains the active solution. This vector is the interface to
the fitness function. Each column corresponds to a parameter of the function. 
The fitness is saved in an additional column on the rightmost position of
both matrixes.{break}
The parametrization of the genetic algorithm is achieved over multiple calls of the 
command {cmd:{ul:dna}} followed by an option and its parameters separated by blanks.
All settings are saved in global macros starting with the letters {hi:DNA}.
If a macro does not exist it will be generated with a default setting.

{title:Options}

{p 0 4}{cmd:{ul:f}unction} {it:function_name} specifies the fitness function.
A potential solution is copied into the row vector {hi:dna} to be evaluated by this function.
Each element of the row vector {hi:dna} represents a parameter of the function.
They can be addressed by using the following syntax: {cmd:dna[}1{cmd:,}{it:#}{cmd:]}, where {hi:#} is the number
of the parameter. The fitness is returned in the last element of the {hi:dna} vector.
The global macro {hi:DNAFIT} contains the column index of this element.
The iteration process can be manually stopped if something is put into the global
macro {hi:DNASTOP}. The generation number is saved in the global macro {hi:DNAITER}.
The actual mutation parameters are saved in the macros {hi:DNAMUTX} and {hi:DNARADX}
(see options {hi:manual} and {hi:auto}).
The name of the function is saved in the global macro {hi:DNAFUN}.

{p 0 4}{cmd:{ul:l}ength} {it:#} defines the number of parameters used
in the fitness function. The length is saved in the global macro {hi:DNALEN} (range: [1,...]).
A row in the population matrix {hi:pop} has {hi:DNALEN}+1 rows because of the additional
column for the fitness.

{p 0 4}{cmd:{ul:p}opulation} {it:#} defines the size of the population.
The population size is saved in the global macro {hi:DNAPOP} (range: [2,...], default: 100).
The population matrix {hi:pop} has {hi:DNAPOP} rows and {hi:DNALEN}+1 columns.

{p 0 4}{cmd:{ul:o}ffspring} {it:#} defines the number of offspring vectors to
be created during each iteration. An intermediate population consists of
all the parent vectors in {hi:pop} and the offspring vectors. Only the best {hi:DNAPOP}
candidates as evaluated by the fitness function of this intermediate population
remain in the base population {hi:pop} as the next generation.
The offspring number is saved in the global macro {hi:DNAOFF} (range: [1,...], default: DNAPOP).

{p 0 4}{cmd:{ul:sel}ection} {it:#} defines the influence of the fitness on the
selection probabilty of a parent vector. If the selection value is zero the choice of partner
is a complete random process. The importance of the fitness as a weight of the selection
probabilty increases with the selection value. The selection value is
saved in the global macro {hi:DNASEL} (range: [0,1], default: 1.0).

{p 0 4}{cmd:{ul:m}utation} {it:#} [{it:#}] specifies the probability of a mutation for
any element of an offsping vector. The offspring can have multiple mutations. The second
parameter defines the half-life of the mutation in generations (this value can be negative for
growing mutation rates). The mutation and its half-life are saved in the global macros {hi:DNAMUT}
(range: [0,1], default: 0.25) and {hi:DNAMHL} (default: 0, resulting in a contant mutation rate).

{p 0 4}{cmd:{ul:r}adiation} {it:#} [{it:#}] specifies the effect of a mutation. The value
of an offspring element will be shifted by a random factor which ranges from the negative radiation number to the
positive radiation number. The second parameter defines the half-life of the radiation in generations
(this value can be negative for growing radiation levels).
The radiation and its half-life are saved in the global macros {hi:DNARAD} (default: 4) and {hi:DNARHL} (default: 0).

{p 0 4}{cmd:{ul:a}uto} sets the mutation mode to {hi:auto}. The program executes the
mutation according to its parameters. The mode is saved in the global macro {hi:DNAMOD} (default: auto).

{p 0 4}{cmd:{ul:ma}nual} sets the mutation mode to {hi:manual}. The program assumes that
the fitness function executes the mutation. The algorithm changes the actual
values of the mutation ({hi:DNAMUTX}) and radiation ({hi:DNARADX}) as normal
without entering the automatic mutation procedure.
With this option it is possible to implement specific mutation methods.
The mode is saved in the global macro {hi:DNAMOD} (default: auto).

{p 0 4}{cmd:{ul:de}fine} {it:#} {it:#} {it:#} defines the initialization
range of the parameters. The first number is the parameter number. The
second and third number specifies the low and the high value of the
parameter. The low ranges are saved in the global macros {hi:DNAL}#
(default: -1) and the high ranges are saved in the global macros
{hi:DNAH}# (default: 1).

{p 0 4}{cmd:{ul:gr}oup} {it:#} {it:#} defines groups of parameters. The
first number is the parameter number. The second number specifies a
group. A group must be a positive integer number. The group number 0
declares free parameters (default). During the crossover and mutation process the
corresponding elements of grouped parameters will be regarded as one
element. Random weights, multiplier and decisions will be the same for
all elements of a group.
The group numbers are saved in the global macros {hi:DNAG}# (default: 0).

{p 0 4}{cmd:{ul:ge}nerations} {it:#} defines the maximum number of generations.
A generation limit of 0 deactivates this method to stop the algotithm.
The generation limit is saved in the global macro {hi:DNAGEN} (range: [0,...], default: 50).

{p 0 4}{cmd:{ul:s}tagnation} {it:#} defines the maximum number of subsequent stagnations in the
population. A stagnant population consists completely of vectors from the previous generation.
This happens when no offspring survives the intermediate phase between generations, because the parent generation
is dominating the fitness charts. The genetic algorithm stops if this number is reached.
A stagnation limit of 0 deactivates this method to stop the algotithm.
The stagnation limit is saved in the global macro {hi:DNASTA} (range: [0,...], default: 10).

{p 0 4}{cmd:{ul:di}splay} sets the display mode to a viewable format.
The display mode is saved in the global macro {hi:DNADIS} (default: display).

{p 0 4}{cmd:{ul:e}xport} sets the display mode to an exportable, comma-separated format.
The display mode is saved in the global macro {hi:DNADIS} (default: display).

{p 0 4}{cmd:{ul:i}nfo} lists all parameters of the genetic algorithm.

{p 0 4}{cmd:{ul:c}lear} clears all {cmd:dna} related global macros.

{p 0 4}{cmd:{ul:go}} starts the genetic algorithm.

{title:Example 1: Least Squares Method}

The fitness function:{inp}

    cap program drop lsm
    program define lsm
        tempvar xb d
        qui gen `xb' = x1*dna[1,1] + x2*dna[1,2] + x3*dna[1,3] + x4*dna[1,4] + dna[1,5]
        qui egen `d' = sum((y - `xb')^2)
        matrix dna[1,$DNAFIT] = -`d'[1]
    end

{text}The parametrization of the genetic algorithm:{inp}

    dna clear
    dna fun lsm
    dna len 5
    dna pop 50
    dna off 100
    dna mut 1 20
    dna rad 4 20
    dna gen 200
    dna sta 20
    forvalue i = 1/5 {
        dna `i' -10 10
    }
    dna go
{text}

{title:Example 2: Censored Least Absolute Deviation (CLAD)}

First we create simulated data using a skewed error term {hi:e}.
Variable {hi:y} is censored to the left.{inp}

    set obs 1000
    gen x1 = invnorm(uniform())
    gen x2 = uniform()
    gen e = exp(invnorm(uniform()))
    sum e, d
    replace e = e - r(p50)
    gen y = x1 + x2 + 1 + e
    replace y = 0 if y < 0

{text}The fitness function:{inp}

    cap program drop clad
    program define clad
        tempvar score xb
        qui gen double `xb' = x1*dna[1,1] + x2*dna[1,2] + dna[1,3]
        qui egen double `score' = sum(abs(y - max(`xb',0)))
        qui matrix dna[1,$DNAFIT] = _N/`score'[1]
    end

{text}The parametrization of the genetic algorithm:
{inp}
    dna clear
    dna fun clad
    dna len 3
    dna pop 50
    dna off 100
    dna mut 1 40
    dna rad 1 40
    dna gen 200
    dna sta 20
    dna 1 -2 2
    dna 2 -2 2
    dna 3 -2 2
    dna go
{text}

{title:Author}

{p 4 4}Thorsten Doherr{break}
Centre for European Economic Research{break}
L7,1{break}
68161 Mannheim{break}
Germany{break}
Phone: +49 621 1235 291{break}
Fax: +49 621 1235 170{break}
E-Mail: doherr@zew.de{break}
Internet: www.zew.de

{title:Reference}

{p 4 4}Dirk Czarnitzki and Thorsten Doherr (2002/2008), Genetic algorithms: A tool for optimization
in econometrics - Basic concept and an example for empirical applications, ZEW Discussion Paper 02-41, Mannheim.