Minimal Genetic Algorithm

Minimal Genetic Algorithm preview image

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F1 Cosimo Leuci (Author)

Tags

arithmetic 

Tagged by Cosimo Leuci 11 days ago

genetic algorithms 

Tagged by Cosimo Leuci 25 days ago

Part of project 'Starfish_Planet' Parent of 1 model: Flibs'NLogo preview imageFlibs'NLogo
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## WHAT IS IT?

Genetic algorithms try to solve a computational problem following some priciples of the organic evolution.This model is able to give us an answer to the simple arithmetic problem how to find the highest number composed by a given number of digits. We approach the task using a genetic algorithm, where the possible answers to the problem are represented by agents that in logo programming environment are usually named "turtles".

## HOW IT WORKS

Every turtle owns a “chromosome” made up by a string of digits; chromosomes can mutate and exchange fragments with the chromosome carried by other turtles: we can see the mechanism as a mixture of eukaryotic crossing-over and prokaryotic conjugation, here we will refer to it as a genetic-shuffling. The sequence of digits in a chromosome can be read as a number and its value can be considered a turtles “phenotype”. A turtle will be as fit as the value expressed by its chromosome will be high. The best fitness can be easily matematically established as the nearest to the result of a simple formula. If n is the number of digits in a string, the higher number having n digits is: (10 ^ n) - 1, that is a sequence of n 9s; on the contrary 10 ^ (n - 1) will give the lower number composed by n digits.

Only the fittest turtle can conjugate with another turle giving part of its chromosome. So the best answer is searched foundamentally in two steps: mutation and selective reproduction of (part of) the fittest chromosome by genetic-shuffling.

Mutations happen randomly with a given frequency on just one chromosomal digit place.

Genetic-shuffling takes place between a randomly choosen turtle (recipient) and the most performing one (donor) that offers a fragment of its chromosome to the first one; the two turtles involved in this process will be highlighted by a link. Genetic-shuffling leads to the formation of a new hybrid chromosome made up by the chromosome of the recipient turtle in which a fragmet of digits included between two randomly choosen positions are replaced by the corresponding digits of one of the donor turtles' chromosome.

## HOW TO USE IT

SETUP button creates the selected number of turtles having a chromosome constituted by a string long till 20 digits, as choosen by the user. Initially, all chromosomes show the lowest suitability.

GO buttons launch a block of instructions that after the detecion of the current best and worst chromosomes, recall the genetic-shuffling and mutation routines.

Four displays show some data concerning the last processed genetic-shuffling: the starting point (a-split) and the ending point (b-split) of the donor's fragment insertion (the first extreme is included into the fragment but not the second one) and the number of "genes" replaced; the resulting hybridized chromosome is reported, as well.

Step by step the less and the most suitable phenotypes (the numerical value of the chromosomal string) are monitored.

## THINGS TO NOTICE

1. During genetic-shuffling, the replaced chromosomal fragment can have random lenght, so sometimes it can have null extension or it could cover the entire chromosom but a gene (the fragment's final digit).

2. Because the strict correspondence between genotype and phenotype, this model doesn't need a routine selecting from the population an individual carrying the nearest traits to the desired ones, such a routine is usually required in a genetic algorithm.

## THINGS TO TRY

Search a possible statistical relationship between the number of cycles required to obtain the right answer to the problem and the the single parameter adjustable by sliders.

## EXTENDING THE MODEL

Minimal Genetic Algorithm is preliminary for Flibs'NLogo project, but it can be considered as self-standing and can be furtherly extended by adding new routines: e.g. it would be interesting to introduce a routine evaluating the genotypes diversity dinamic during the search.

## CREDITS, REFERENCES AND RELATED MODELS

- A nice introduction to genetic algoritm could be the chapter nine of the book "Complexity - A guided tour" by Melanie Mitchel (2009 - Oxford University Press) where the GA "Robby the Robot" is described; see also Mitchell, M., Tisue, S. and Wilensky, U. (2012). NetLogo Robby the Robot model. http://ccl.northwestern.edu/netlogo/models/RobbytheRobot. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

- Stonedahl, F. and Wilensky, U. (2008). NetLogo Simple Genetic Algorithm model. http://ccl.northwestern.edu/netlogo/models/SimpleGeneticAlgorithm. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

- Cosimo Leuci (2018) Flibs'NLogo http://modelingcommons.org/browse/one_model/5754

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turtles-own [chromosome  ;; a string of digits representing a possible answer to the problem
             fitness     ;; the numerical value of the chromosomal string
             ]

globals [best            ;; the numerical value of the chromosome  closer to the goal
         worst           ;; the numerical value of the chromosome more distant from the goal
         donor           ;; the agent having the best chromosome
         recipient       ;; an agent not having the best chromosome
         chromcopy       ;; the copy of the best chromosome
         a-split         ;; the position of one extreme of a chromosome's fragment
         b-split         ;; the position of the second extreme of a chromosome's fragment
         counter         ;; a conter usefull in different blocks
         ]



;;  SETUP PROCEDURES
;;  _________________________________________________________________________________________________

to setup                 ;; reset parameters and create a number of agents given by the user
  clear-all
  set counter 0
  reset-ticks
  create-turtles turtles-number [
    set shape "circle 2"
    set size 1.8
    fd 7
    genotype/fenotype-construction
   ]
end 

to genotype/fenotype-construction
  ;; the genotype (chromosome) and the corresponding fenotype (fitness) of the agent
  ;; is initially equal to the worst response to the problem; it is shown as label
  set fitness 10 ^ (chromosome-digits - 1)
  ;; lowest fitness value is converted into string:
  ;; it will be the initial chromosome structure
  set chromosome word fitness ""
  ;; chromosome is displayed as label
  set label chromosome
end 



;;  RUNTIME PROCEDURES
;;  _________________________________________________________________________________________________

to go
  ;; worse and best fitness value are detected
  set worst min [fitness] of turtles
  set best max [fitness] of turtles
  ;; the problem is resolved when an agent gain the higher value of fitness having a user
  ;; specified number of digits
  if best = 10 ^ chromosome-digits - 1 [show "DONE!!!" stop]
  ;; when  diversity between chromosomes is null, genetic-shuffling is skipped
  if best != worst [genetic-shuffling]
  if random-float 1 < mutation-rate [mutate]
  tick
end 

to genetic-shuffling
  ;; hybridization occur between the chromosome of a randomly choosen turtle (recipient)
  ;; and the chromosome of the most performing one (donor) that offer a fragment of its
  ;; chromosome to first turtle; the two involved agents are highlighted by a link
  clear-links
  set donor [who] of one-of turtles with [fitness = best]
  set recipient [who] of one-of turtles with [fitness != best]
  ask turtle donor [create-link-with turtle recipient ]
  set counter 0
  set a-split random chromosome-digits
  set b-split random chromosome-digits
  set chromcopy [chromosome] of turtle donor
  ask turtle recipient [
     hybridization
     set fitness read-from-string chromosome
     set label fitness
    ]
end 

to hybridization
  ;; the two selected chromosomosomal strings give place to hybridization with a mechanism inspired both
  ;; to crossing-over and bacterial conjugation: the recipient string will be hybridized with a fragment
  ;; of the donor one; strings are treated as circular, as occur in bacterial chromosomes or plasmids
  ifelse a-split < b-split [set chromosome
            replace-item (a-split + counter) chromosome (item (a-split + counter) chromcopy)
            set counter (counter + 1)
            if counter < b-split - a-split [hybridization]]
       [if b-split < a-split [set chromosome
              replace-item ((a-split + counter) mod chromosome-digits)
                  chromosome (item ((a-split + counter) mod chromosome-digits) chromcopy)
              set counter (counter + 1)
              if counter < chromosome-digits - a-split + b-split [hybridization]]
    ]
  if length chromosome != chromosome-digits [show "Invalid chromosome length"]
end 

to mutate
  ;; mutations happen randomly with a given frequency on just one digit place
  ask turtle random turtles-number
       [set chromosome replace-item random chromosome-digits chromosome word random 10 ""
        set fitness read-from-string chromosome
        set label fitness
        if length chromosome != chromosome-digits [show "Invalid chromosome length"]
    ]
end 

There are 9 versions of this model.

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Cosimo Leuci 4 days ago simplifications Download this version
Cosimo Leuci 4 days ago simplifications Download this version
Cosimo Leuci 5 days ago flux bug fixed Download this version
Cosimo Leuci 12 days ago Info tab new revision Download this version
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Cosimo Leuci 21 days ago Info tab new revision Download this version
Cosimo Leuci 24 days ago user interface and info tab update Download this version
Cosimo Leuci 24 days ago Info tab revised Download this version
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