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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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History: The lighter side of it
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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
- Determine the task to evaluate
- Codify the Chromosome and number of genes
- Define the initial population
- Criteria of selection by the environment
- Random selection of survivors
- Chromosome crossing
- Mutation
- Evolution
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The knapsack
optimization
The Simple book of GA’s
- Determine the task to evaluate
- Optimization function definition (clear and unsolved)
- Value computation
- 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.
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Source: Michalewicz Z. Genetic Algorithms Springer Verlag 1992
The Simple book of GA’s
- Example
- 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)
- Define evolution parameters
- Population size 20 genes
- Number of crossings Chromosomes/
- Probability of crossing px = 1.
- Location of the crossing One crossing anywhere
- Substitution policy Population is added with no substitution
- Mutation probability pc = 0.
- 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)
- Number of crossover per generation
- Random selection of probability of crossover
- Random selection of crossover bit
- Random selection of genes to mate
- Crossing
- Substitution (or addition) into the population
- 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
- 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
- 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]
- Define evolution parameters
- Population size 20 genes
- Number of crossings Chromosomes/
- Probability of crossing px = 1.
- Location of the crossing One crossing anywhere
- Substitution policy Population is added with no substitution
- MNumber of generations, time or stop criteriautation probability p (^) c = 0.0001 Ngen = 50
GA’s in minimax
- Define the initial population
- Random process
- Example
Chromosome 1 : (01010100101010101010)
Chromosome 2 : (01110101101110100010)
..........
Chromosome 19 : (11101101101110101111)
Chromosome20 : (10010111101110100110)
