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A Historical Overview and Detailed Explanation of Genetic Algorithms, Slides of Artificial Intelligence

A historical background of genetic algorithms (gas), from their origins in the works of charles darwin and gregor mendel to their modern applications. It also covers the key developments in ga research, including the works of holland, goldberg, rechenberg, fogel, owens, walsh, and koza. The principles of ga, including codifying the chromosome, defining the initial population, selection by the environment, chromosome recombination, mutation, and evolution. It also includes examples of ga applications and the use of gas in minimax functions.

Typology: Slides

2012/2013

Uploaded on 04/29/2013

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Definition
Genetic From Greek genno γεννώ= give birth)
Algorithm From Farsi, belonging to the a prominent Muslim
mathematician Al Khowarizmi (790-840). Advocates of the new
math system were called algorists as opposed to the abacists who
continued to use the abacus inherited from the Romans. The first use
of the word Algorithm is from Liebnitz in the late 1600 referring to
a method of solving problems my means of sequence of procedures
that loops and branches depending on what's coming up for them
thereby optimizing their chances of having a productive experience.
.
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Download A Historical Overview and Detailed Explanation of Genetic Algorithms and more Slides Artificial Intelligence in PDF only on Docsity!

Definition

Genetic From Greek genno γεννώ= give birth)

Algorithm From Farsi, belonging to the a prominent Muslim

mathematician Al Khowarizmi (790-840). Advocates of the new math system were called algorists as opposed to the abacists who continued to use the abacus inherited from the Romans. The first use of the word Algorithm is from Liebnitz in the late 1600 referring to a method of solving problems my means of sequence of procedures that loops and branches depending on what's coming up for them thereby optimizing their chances of having a productive experience.

.

History: The lighter side of it

2

So. What happened here ?????

Ga’s Detailed History

  • 1948 Turing proposed the search by means evolutionary or

genetics

  • 1962 Bremermann proposed optimization through recombination

and evolution

  • 1964 Rechenberg introduced the concepts of evolution strategies
  • 1965 Fogel, Owens and Walsh introduced evolutionary

programing

  • 1975 J. Holland the recognized father of GA
  • 1989 D. Goldberg big promoter of the use of GA for search and

learning

  • 1992 Koza introduces genetic programming

Genetic algorithms

  • GA represent a practical and no sweat approach

to finding a solution by letting the machine try different solutions in time until we get a good approximation to the best solution.

  • It is based on the belief that a solution is always

comprised by a set of elements and just recombining the elements will get us there.

  • Very much the way nature does it.

The Simple book of GA’s

  1. Determine the task to evaluate
  2. Codify the Chromosome and number of genes
  3. Define the initial population
  4. Criteria of selection by the environment
  5. Random selection of survivors
  6. Chromosome crossing
  7. Mutation
  8. Evolution

7

The knapsack

optimization

The Simple book of GA’s

  1. Determine the task to evaluate
    1. Optimization function definition (clear and unsolved)
    2. Value computation
    3. Example: Provide Optimal values for the function

F(x,y) = 21.5 + xSIN(4πx) + ySIN(20πy)

In the ranges of -3 < x < 12.1 and 4.1 < y < 5.

8

Source: Michalewicz Z. Genetic Algorithms Springer Verlag 1992

The Simple book of GA’s

  1. Example
    1. 18 bits for x and 15 bits for y (0101010010101010100,111000110101010) value = Initial + dec(Gene) * range / (2^GeneBits^ -1) x = -3 + DEC(genes(0,17)15.1/2^ 18 -1) y = 4.1 + DEC(genes(18,32)1.7/(2^ 15 -1)
  2. Define evolution parameters
  3. Population size 20 genes
  4. Number of crossings Chromosomes/
  5. Probability of crossing px = 1.
  6. Location of the crossing One crossing anywhere
  7. Substitution policy Population is added with no substitution
  8. Mutation probability pc = 0.
  9. Number of generations, time or stop criteria Ngen = 50

Source: Michalewicz Z. Genetic Algorithms Springer Verlag 1992 Docsity.com^10

The Simple book of GA’s

3. Define the initial population

1. Random process

2. Example

Chromosome 0 : (101010010101010101,111000110101010)

Chromosome 1 : (001111111110100101,111111110001101)

…..

Chromosome 18 : (001010010111111010,111000110111111)

Chromosome 19 : (011111010100101011,111000000001101)

The Simple book of GA’s

5. Random selection of survivors

1. Accumulative distribution

2. Random intervention to the distribution

3. Population size maintenance

4. Example

F(population) = f(c 0 )+ f(c 1 ) + f(c 2 ) + f(c 3 ) =

Chromosome Yields: c 0 = f(c 0 )/F(pop) , c 1 = f(c 1 )/F(pop), c (^) n = f(c (^) n)/F(pop)

With random intervention generate a

population from these selected chromosomes

Eliminate the other genes of the population

The Simple book of GA’s

6. Chromosome recombination(crossover)

  1. Number of crossover per generation
  2. Random selection of probability of crossover
  3. Random selection of crossover bit
  4. Random selection of genes to mate
  5. Crossing
  6. Substitution (or addition) into the population
  7. Example 1. Number of crossover per generation Chromosome/ 2. Probability of crossover if RAND > Th then Crossover 3. Random selection of crossover bit RAND in the bit range

4. Random selection of genes to mate 2 RAND in the range of

gene

population size

5. Crossover swap bits between genes 6. Substitution (or addition) into the population (^) 14

The Simple book of GA’s

8. Evolution

if generation = Limit of generations

(or any other stop criteria )

then Do step 4 and End Simulation

else Do repeat steps 4,5,6,7 y 8

GA’s for Minimax

  1. Determine the task to evaluate

The Evaluation Function

ef = ∑ciF pi = c 1 F 1 p1^ + c 2 F 2 p2^ for all i

In the ranges of -rmin < ci < rmx y pmin < p (^) i < p (^) mx

Code the doefficients of the function as parts of a chromosome

Play the game and determine the best genes

Cross the genes and so on …..

GA’s in minimax

  1. Example 1. If ∑ = Cr R + Cn N + Ca A + Cv V then : [01001,11111,01101,11101] Value Ci = r (^) min + DEC[genes(0,4)range/2^ 5 -1] ……… Value Ci = r (^) min + DEC[genes(0,4)range/2^ 5 -1]
  2. Define evolution parameters
  3. Population size 20 genes
  4. Number of crossings Chromosomes/
  5. Probability of crossing px = 1.
  6. Location of the crossing One crossing anywhere
  7. Substitution policy Population is added with no substitution
    1. MNumber of generations, time or stop criteriautation probability p (^) c = 0.0001 Ngen = 50

GA’s in minimax

  1. Define the initial population
    1. Random process
    2. Example

Chromosome 1 : (01010100101010101010)

Chromosome 2 : (01110101101110100010)

..........

Chromosome 19 : (11101101101110101111)

Chromosome20 : (10010111101110100110)