GA_POPULATION Function

PV-WAVE Advantage > IMSL Statistics Reference Guide > Data Mining > GA_POPULATION Function

Creates a population data structure from user supplied individuals.

Usage

result = GA_POPULATION (chromosome, individual)

Input Parameters

chromosome—A chromosome data structure created by GA_CHROMOSOME describing the chromosome encoding for individuals.

individual—An array of size n, which is the number of individuals in the population, of individuals.

Returned Value

result—GA_POPULATION returns a population data structure, which is required input to GENETIC_ALGORITHM Function.

Input Keywords

Print—If present and nonzero, this option turns on printing of intermediate results. By default, intermediate results are not printed.

Gray_encoding—If present and nonzero, specifies alleles are encoded using Gray encoding for integer and real phenotypes. If undefined or zero, specifies alleles are encoded using Base-2 encoding for integer and real phenotypes. Default: Base-2 encoding.

Fitness—An array of length n containing the fitness values for the individuals in the population. Fitness(i) is the fitness for the ith individual.

Fit_fcn—User-supplied function to calculate fitness for individual. If this is supplied, fitness values are calculated for each individual and included within the expanded population data structure. Otherwise they are set to zero.

Double—If present and nonzero, then double precision is used.

Discussion

The GENETIC_ALGORITHM Function operates on a population of individuals. GA_POPULATION allows users to systematically create an initial population by adding individuals to that population. It takes the individuals created using GA_INDIVIDUAL Function and encapsulates them into a population data structure.

Example

This example creates a population of 40 individuals each with one binary, two nominal, three integer and two real phenotypes. The Print keyword is used to print a description of the population. A simple fitness function calculation is used to illustrate how fitness values can be used to initialize a population with the Fitness keyword. If fitness is not initialized, the fitness array in the data structure is set to null. It can be initialized using a keyword with GENETIC_ALGORITHM Function.

PRO ga_population_ex1

   ; number of phenotypes by category

   n_binary  = 1

   n_nominal = 2

   n_integer = 3

   n_real    = 2

   n = 40                      ; population size

   binaryPhenotype  = [1]    ; binary phenotype

   ; Number of categories for nomial phenotypes

   n_categories     = [2, 3]

   ; Nominal phenotype values

   nominalPhenotype = [1, 2]

   ; Number of intervals and boundaries for integer

   ; phenotypes

   i_intervals      = [16, 16, 16]

   i_bounds         = [0, 1000, -10, 10, -20, 0]

   ; Integer phenotype values

   integerPhenotype = [200, -5, -5]

   ; Number of intervals and boundaries for real

   ; phenotypes

   r_intervals      = [512, 1024]

   r_bounds         = [0.0, 20.0, -20.0, 20.0]

   ; Real phenotype values

   realPhenotype    = [19.9, 19.9]

   ; Fitness array for individuals

   fitness = FLTARR(40)

   ; The individuals in the population

   individuals = LISTARR(n)

  chromosome = GA_CHROMOSOME( $

             N_binary=n_binary, $

           N_nominal=n_nominal, $

     N_categories=n_categories, $

           N_integer=n_integer, $

       I_intervals=i_intervals, $

             I_bounds=i_bounds, $

                 N_real=n_real, $

       R_intervals=r_intervals, $

             R_bounds=r_bounds)

   ; Create reproducible results

   RANDOMOPT,set=12345

   ; Create individuals

   PRINT,"Creating 40 Individuals"

   FOR i=0L, n-1 DO BEGIN

      ;;;;;;;;;;;;;;

      ; Generate random values for phenotypes

      ;;;;;;;;;;;;;;

      binaryPhenotype = RANDOM(1,$

                            /Binomial, $

                   Parameters=[0.5, 1])

      irandom = RANDOM(1, /Discrete_unif, $

                       Param=n_categories(0))

      nominalPhenotype(0) = irandom(0)-1

      irandom = RANDOM(1, /Discrete_unif, $

                       Param=n_categories(1))

      nominalPhenotype(1) = irandom(0)-1

      irandom = RANDOM(1, /Discrete_unif, $

                      Param=i_bounds(1)-i_bounds(0))

      integerPhenotype(0) = irandom(0)-1

      irandom = RANDOM(1, /Discrete_unif, $

                      Param=i_bounds(3)-i_bounds(2))

      integerPhenotype(1) = irandom(0)-1+i_bounds(2)

      irandom = RANDOM(1, /Discrete_unif, $

                      Param=i_bounds(5)-i_bounds(4))

      integerPhenotype(2) = irandom(0)-1+i_bounds(4)

      rrandom = RANDOM(1, /Uniform)

      realPhenotype(0) = $

         rrandom(0) * (r_bounds(1)-r_bounds(0)) + r_bounds(0)

      rrandom = RANDOM(1, /Uniform)

      realPhenotype(1) = $

         rrandom(0)*(r_bounds(3)-r_bounds(2)) + r_bounds(2)

      ; Create individual from these phenotypes

      individuals(i) = GA_INDIVIDUAL(chromosome, $

           Binary_phenotype=binaryPhenotype, $

         Nominal_phenotype=nominalPhenotype, $

         Integer_phenotype=integerPhenotype, $

               Real_phenotype=realPhenotype)

      ; Calculate fitness for this individual

      fitness(i)  = 100.0 + 10*binaryPhenotype(0)

      fitness(i) = fitness(i)+ $

               2*nominalPhenotype(1) - 4*nominalPhenotype(0)

      fitness(i) = fitness(i) +$

                   0.0001*integerPhenotype(0) + $

            ABS(integerPhenotype(1)+integerPhenotype(2))*0.1

      fitness(i) = fitness(i) + 0.1*realPhenotype(0)

      IF realPhenotype(1) GT 0 THEN BEGIN

            fitness(i) = fitness(i) + 0.2*realPhenotype(1)

      ENDIF ELSE  fitness(i) = $

                  fitness(i) - 0.2*realPhenotype(1)

   ENDFOR

   PRINT,"Creating Population from 40 Individuals"

   population = GA_POPULATION(individuals, $

                  Fitness=fitness, /Print)

END

Output

The Print option produced the following description of the population. A summary of the population chromosome structure and fitness are printed followed by detailed information for the first 5 individuals in the population.

This example also illustrates the bit ordering within chromosomes. Nominal phenotypes are placed in the first bits followed by binary and encoded integers and real phenotypes.

Creating 40 Individuals

Creating Population from 40 Individuals

Population Size: 40

Average   Fitness: 109.472527

Std. Dev. Fitness: 5.927261

Maximum Fitness: 120.244392

Minimum Fitness: 98.221916

Chromosome:

*******************************

**** CHROMOSOME STRUCTURE *****

Chromosome length:       34 Bits

*****BIT ASSIGNMENTS***********

Binary:    2 -   2 n_binary = 1

Nominal:   1 -   2 n_nominal= 2

Integer:   3 -  14 n_integer= 3

Real:     15 -  33 n_real   = 2

*******************************

NOMINAL CATEGORIES*************

   Variable  0:    2 categories

   Variable  1:    3 categories

*******************************

INTEGER BOUNDS*****************

   Variable  0: [    0,  1000]

   Variable  1: [  -10,    10]

   Variable  2: [  -20,     0]

*******************************

INTEGER BITS*******************

   Variable  0:    4 bits

   Variable  1:    4 bits

   Variable  2:    4 bits

*******************************

INTEGER DISCRETE INTERVALS*****

   Variable  0:   16 intervals

   Variable  1:   16 intervals

   Variable  2:   16 intervals

*******************************

REAL BOUNDS********************

   Variable  0: [0,20]

   Variable  1: [-20,20]

*******************************

REAL BITS**********************

   Variable  0:    9 bits

   Variable  1:   10 bits

*******************************

REAL DISCRETE INTERVALS********

   Variable  0:  512 intervals

   Variable  1: 1024 intervals

*******************************

First 5 Individuals

****** INDIVIDUAL 0 ********************************************

   Number of Parents: 2

   Encoding: BASE-2

   Fitness: 105.114510

           PHENOTYPES

*************BINARY************

   Variable  0: 0

************NOMINAL************

   Variable  0: 1

   Variable  1: 2

************INTEGER************

   Variable  0: 35

   Variable  1: -10

   Variable  2: -19

**************REAL*************

   Variable  0: 15.3157

   Variable  1: 3.39719

**********CHROMOSOME*******************************************

1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 0

***************************************************************

****** INDIVIDUAL 1 ********************************************

   Number of Parents: 2

   Encoding: BASE-2

   Fitness: 111.796173

           PHENOTYPES

*************BINARY************

   Variable  0: 1

************NOMINAL************

   Variable  0: 1

   Variable  1: 0

************INTEGER************

   Variable  0: 195

   Variable  1: -5

   Variable  2: -5

**************REAL*************

   Variable  0: 19.6777

   Variable  1: -14.0445

**********CHROMOSOME*******************************************

1 0 1 0 0 1 1 0 1 0 0 1 1 0 0 1 1 1 1 1 0 1 1 1 0 0 1 0 0 1 1 0 0 0

***************************************************************

****** INDIVIDUAL 2 ********************************************

   Number of Parents: 2

   Encoding: BASE-2

   Fitness: 104.841797

           PHENOTYPES

*************BINARY************

   Variable  0: 0

************NOMINAL************

   Variable  0: 0

   Variable  1: 0

************INTEGER************

   Variable  0: 167

   Variable  1: 7

   Variable  2: -16

**************REAL*************

   Variable  0: 18.3331

   Variable  1: -10.4589

**********CHROMOSOME*******************************************

0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 0 0

***************************************************************

****** INDIVIDUAL 3 ********************************************

   Number of Parents: 2

   Encoding: BASE-2

   Fitness: 110.905807

           PHENOTYPES

*************BINARY************

   Variable  0: 1

************NOMINAL************

   Variable  0: 1

   Variable  1: 0

************INTEGER************

   Variable  0: 629

   Variable  1: 0

   Variable  2: -17

**************REAL*************

   Variable  0: 18.213

   Variable  1: -6.608

**********CHROMOSOME*******************************************

1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 1 0 1 1 0

***************************************************************

****** INDIVIDUAL 4 ********************************************

   Number of Parents: 2

   Encoding: BASE-2

   Fitness: 114.371025

           PHENOTYPES

*************BINARY************

   Variable  0: 1

************NOMINAL************

   Variable  0: 1

   Variable  1: 2

************INTEGER************

   Variable  0: 51

   Variable  1: 8

   Variable  2: -3

**************REAL*************

   Variable  0: 7.13049

   Variable  1: -15.7644

**********CHROMOSOME*******************************************

1 2 1 0 0 0 0 1 1 1 0 1 1 0 1 0 1 0 1 1 0 1 1 0 0 0 0 1 1 0 1 1 0 0

***************************************************************