select: Select - Runs a Genetic Algorithm

In AndrewM1130/GA: On Multivariate Feature Selection with Genetic Algorithms

Select - Runs a Genetic Algorithm

Description

This function optimizes a linear regression using a genetic algorithm. User can enter a custom function or select a metric from (AIC, BIC, AICC, R2) to optimize features to include in the linear regression. This function has a broad range of genetic algorithm features including multiple parent section methods, crossover options, mutation options and other features such as elitism, minimizing-inbreeding, using more than two parents and selecting from a range of early termination options. See below for details)

Usage

select(
  total_number_generations,
  number_of_parents = 2,
  pop,
  gene_length,
  response_vec,
  independent_vars,
  prob = 0.05,
  user_genes = NULL,
  metric = "AIC",
  family = "gaussian",
  method = "roulette",
  susN = 1,
  tourn_size = 2,
  mutation = "fixed",
  mutation_rate = 0.02,
  minimize_inbreeding = FALSE,
  crossover = "uniform",
  number_of_crossovers = 1,
  elitism = TRUE,
  elite_prop = 0.05,
  ad_max_mutate = 0.1,
  ad_min_mutate = 0.01,
  ad_inflection = 0.3,
  ad_curve = 15,
  custom_function = NULL,
  estimator = NULL,
  pause_length = NULL,
  percent_converge = NULL,
  score_threshold = NULL,
  fittest = "high"
)

Arguments

total_number_generations	an integer representing the maximum number of iterations
number_of_parents	an integer defining the number of parents per offspring
pop	an integer defining the number of creatures per a generation
gene_length	an integer representing the number of genes per a creature
response_vec	a numeric vector without infinite or NA values
independent_vars	a matrix or dataframe with ncol equal to number of genes and nrow with the same length as the response_vec
prob	a number 0-1 representing the chance that an individual has any given gene
user_genes	a matrix consisting of 1s and 0s without any rows with all zeros ncol equal to gene_length and nrow less than or equal to pop
metric	a character from the following 'R2', 'AIC', 'BIC', or 'AICc', the statistic LM or GLM is returning
family	the GLM family of distributions (must have the same support as the data for instance exponential cannot have negative numbers)
method	the method of choosing parents, 'roulette', 'rank', 'tournament', and 'sus'
susN	if sus is selected how many parents are chosen scholastically
tourn_size	if tournament is chosen how many candidates are in the tournament
mutation	a character either 'fixed' or 'adaptive' indicating the type of mutation
mutation_rate	a numeric between 0 and 1 indicating how often a creature is selected for mutation.
minimize_inbreeding	a logical indicating whether or not we minimize inbreeding.
crossover	a character that can be 'uniform', 'fitness', or ‘k_point’ indicating how to carry out crossover.
number_of_crossovers	number of k_point crossovers, needs to be less than gene_length
elitism	a logical representing whether elitism is requested
elite_prop	the proportion of each generation that is selected for elitism
ad_max_mutate	max mutation rate for adaptive mutation, numeric between 0 and 1 and more than ad_min
ad_min_mutate	min mutation rate for adaptive mutation, numeric between 0 and 1 and less than ad_max
ad_inflection	percentage of diversity in population where adaptive mutation begins to increase rapidly
ad_curve	rate that influence how intensely adaptive mutation changes
custom_function	user defined custom mast take vector representing a single creatures genes, data, and return a single numeric
estimator	character string from 'Min.','1st Qu.','Median','Mean','3rd Qu.', or 'Max.'. This term controls termination conditions for instance, terminating after the Mean AIC is above a certain threshold
pause_length	a numeric indicating how many iterations without improvement in the estimator before you terminate
percent_converge	percentage of diversity when algorithm terminates for instance .1 will terminate if there are only .90 of the population is represented by the same genes
score_threshold	a numeric indicating a threshold to cutoff if the estimator reaches that value
fittest	a character either 'high' or 'low' defining whether a custom functions

Details

user_genes allows the user specific genes to the initial generation provided that the matrix consist only of 1s and 0s has no all-zero rows, ncol = gene_length, and has nrow less than or equal the total population pop

custom_function allows the user to specify a custom function instead of lm() or glm(). User-provided function must have its first two arguments be (1) generation_matrix and (2) data. Function needs to take a single row of a generation_matrix and return a single numeric without NAs or infinities.

Otherwise, user should specify a metric from R2, AIC, BIC, or AICC. The underlying fitness function for R2 is lm() and the underlying fitness function for AIC, BIC, and AICc is glm(). AIC, BIC, and AICC has the option to specify a specific family of functions however, the data needs to be defined across the support for the given family for instance exponential must be greater than 0.

Parents are selected via a number of methods: #'Roulette Method selects parents randomly with a probability proportional to their fitness

Rank Method selects parents randomly with a probability proportional to the rank of their fitness

Tournament uses tourn_size to randomly group that many creatures together. The most fit in that group becomes a parent.

Stochastic Universal Sampling works like roulette but also selects a number (susN) more candidates at a fixed width from the first draw to increase diversity

crossover Methods Uniform - each gene is randomly selected from 2 or more parents from a PMF proportional to the number of parents.

Fitness - each gene is randomly selected from 2 or more parents from a PMF proportional to the parent's fitness.

K-Point - parents genes are broken into k+1 segments, then the offspring inherits portions randomly from the parents. Takes the parameter number_of_crossovers which must be less than 1/2 gene_length.

For all methods candidate offspring are accepted / rejected so that they don't have completely 0-vector genes.

mutation Fixed - Each offspring has a mutation_rate chance of being selected for mutation. Once selected one gene is switched form one to zero or zero to one.

Adaptive - the overall population is measured for diversity. As diversity becomes lower, the mutation rate increases. Once selected for mutation a single gene is switched from one to zero or zero to one. The adaptive function is controlled by a simple logistic function with parameters ad_min and ad_max describing the minimum and maximum mutation rates. ad_inflection controls where the logistics point pivots, and ad_curve controls how rapidly the logistics curve increase.

For all mutation methods, candidate offspring are accepted / rejected so that they don't have completely 0-vector genes.

Minimize inbreeding. his option reduces (though does not remove) the chance of similar creatures creating offspring together. Each parent is assigned new partner(s) randomly from a PMF proportional to how different their genes are. Parents are drawn without replacement so that if they were selected to become parents, they will still remain parents.

Elitism preserves the most-fit creatures from each generation. by selecting a number of most fit creatures equal to the ceiling(pop * elite_prop) and guarantees that they make it to the next generation. Additionally, this features makes a copy of each most-fit creature and conducts one gene mutation randomly on each creature. If the copy is more fit than the original, it is returned instead of the original so that the final returned matrix of elite creatures are at least as fit as the incoming elite creatures.

Early Termination Conditions: User can define early termination criteria to include a percentage_convergence such that when diversity falls below a specific threshold the program terminates. User can identify a estimate (from the standard summary() function that if the estimate reaches a specific threshold the program terminates or if the estimate pauses for a certain number of iterations terminates.

estimator - cam be nominated from the summary() function aka Min., 1st Qu., Median, Mean, 3rd Qu., or Max. so for instance estimator=Max. metric = 'AIC' and score_threshold = 500 would terminate when the Max. AIC falls below 500.

diversity is defined as sum(unique(genes))/total_genes

Value

returns a list consisting of [[1]] the fittest gene, [[2]] the fittest gene's score, [[3]] the most fit score by generation, [[4]] the summary data by generation and [[5]] the final generation's genes.

Examples

pop <- 50
gene_length <- 10
response_vec <-rnorm(100)
independent_vars <- matrix(rnorm(100*10),ncol=10)
total_number_generations <-15
select(pop = pop,gene_length = gene_length,
response_vec = response_vec,independent_vars = independent_vars,
total_number_generations = total_number_generations)

response_vec <-rnorm(100)
independent_vars <- matrix(rnorm(100*50),ncol=50)
pop <- 50
gene_length <-50
elitism <- TRUE
elite_prop <- .05
mutation_rate <- .1
crossover <- 'k_point'
method <-"rank"
number_generations <-50

select(pop = pop,gene_length = gene_length,
response_vec = response_vec,independent_vars = independent_vars,
total_number_generations = total_number_generations,
elitism = elitism,mutation_rate = mutation_rate,crossover = crossover,
method = method)

AndrewM1130/GA documentation built on July 9, 2022, 11:43 a.m.