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

GA_POPULATION Function (PV-WAVE Advantage)
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 (PV-WAVE Advantage).
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 (PV-WAVE Advantage) 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 (PV-WAVE Advantage) 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 (PV-WAVE Advantage).
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
***************************************************************

Version 2017.0
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