Genetic Algorithms for optimization
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GENETIC ALGORITHM FOR OPTIMIZATION
FETHİ CANDAN ANIL ERDİNÇ TÜFEKÇİ
İSMAİL HANCI
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NUMERICAL METHODS IN OPTIMIZATION
OUTLINE
▸ What are the Genetic Algorithms (GA)
▸ Characteristics of GA
▸ Darwin’s Principle of Natural Selection
▸ Working of GA
▸ Components of GA
▸ Uniqueness of GA
▸ Procedure of GA
▸ Example
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WHAT ARE THE GENETIC ALGORITHMS
Genetic Algorithms are search and optimization techniques based on Darwin’s Principle of Natural Selection.
NUMERICAL METHODS IN OPTIMIZATION
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HISTORY OF GA
▸ 1950 : Alan Turing proposed a “Learning Machine”
▸ 1957 : Alex Fraser published simulation of artificial selection of organisms
▸ 1960 : Hans-Joachim Bremermann published a series of papers in the 1960s that also adopted a population of solution to optimization problems, undergoing recombination, mutation, and selection. Bremermann's research also included the elements of modern genetic algorithms.
▸ 1975 : J.H.Holland, Adaptive in Natural and Artificial Systems.
NUMERICAL METHODS IN OPTIMIZATION
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CHARACTERISTICS OF GA
▸ Stochastic in nature and less likely to get caught in local minima, so mostly used for global optimization problems
▸ Applies to both continuous and discrete optimization problems
▸ Parallel-Search procedure that can be implemented on parallel processing machines for speeding operations
▸ Heuristic method based on ‘Survival of the fittest’
▸ Useful when search space very large or too complex for analytic treatment
NUMERICAL METHODS IN OPTIMIZATION
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DARWIN’S PRINCIPLE OF NATURAL SELECTION
The basic principles formulated by Darwin:
1.The strongest survive and tips die (Natural Selection)
2.The new individual is obtained by crossing and there is mutation
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WORKING GA
▸ GA encodes each point in a parameter space into a binary bit called chromosome
▸ Each point is associated with a fitness function
▸ Gene pool is a population of all such points
▸ In each generation GA constructs a new population using genetic operators
Crossover
Mutation
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COMPONENTS OF GA
Encoding Schemes
Crossover Operators
Mutation Operators
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STOCHASTIC OPERATORS
▸ Selection : Replicates the most successful solutions found in a population at a rate proportional to their relative quality.
▸ Recombination : Decomposes two distinct solution and then randomly mixes their parts to form new solutions.
▸ Mutation : Randomly pertubs a candidate solution.
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UNIQUENESS OF GA
▸ Works with a coding of the parameter set, not the parameter themselves
▸ Search for a population of point and not single point
▸ Use objective function information and not derivatives or other auxiliary knowledge
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PROCEDURE OF GA
FlowChart
SELECT THE BEST, DISCARD THE RESTSTART
GENERATE INITIAL POPULATION
CALCULATE THE COST FUNCTION
ALGORITHM END?
SELECTION
RECOMBINATION
MUTATION
NEXT GENERATION RESULT
END
N
N-n
n
N-n
N
YES
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EXAMPLE
• A simple GA application
• Problem : Reach a target value with simple mathematical calculations.
• We have a target value such as 5, 37, 72.8, 231.38, etc.
• We have numbers { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }.
• We have operators { +, -, *, / }
• Totally we have 14 (10 + 4) different elements.
• We call each of one as GENE.
• A combination of GENEs, becomes a CHROMOSOME.
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▸ We have to encode all of these different genes
▸ As a general attitude, we use binary bits
▸ Binary bits string
▸ The number of different elements that can be encoded:
▸ We have to chose bit number n so as to have enough space for encoding all our different
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We can encode our elements as such:
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▸ Problem (Mathematical Calculations) can be formulated differently
▸ Prob1 : use each number ones
▸ Prob2 : use each operator ones
▸ Prob3 : use each number ones, but there is no restriction about operators
▸ Prob4 : use operator ones, but there is no restriction about numbers
▸ There may be Restrictions on number of elements or Gene. It defines the length of chromosomes.
▸ Chromosome Length = Gene Length x Number of Genes
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TargetGenes
Chromosome
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‣We need to decide some parameters beforehand.
‣ Later according to performance, we have to change these parameters to improve the performance considering our restrictions such as
‣ Convergence ratio
‣ Computation number
‣ Computation types
‣ Storage, RAM, time, error tolerance (fitness score and target)…
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GA DESIGN PARAMETERS
‣Number of POPULATION
‣ Length of CHROMOSOME
‣Value and type of CROSSOVER
‣Value of MUTATION RATE
‣Number of GENERATIONS (stop criteria)
‣ Type of SELECTION
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‣Population (parents, fathers and mothers)
‣Population number can be 500, 20.000, or 1.000.000
‣We create randomly
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‣We test each population member for a possible solution to the problem.
‣We decode each gene with the order.
‣Calculate the result mathematically ( 8 + 5 – 3 / 2 *4 / 7 = 2.857)
‣We need to define a Fitness Score for each member of population in every generation.
‣ It is normalized to [0 , 1].
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▸ Fitness Score Calculation or Fitness Function
▸ There can be different calculations
▸ One of them is
|Target Value - Result|1_____________________
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‣After assigning a Fitness Score to each population, we have to eliminate weak ones as nature does due to Darwin’s Natural Selection Principle
‣We need a Selection Pattern
‣One method is Roulette Wheel
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‣ We define a crossover pattern.
‣ In nature, we have dominant and recessive genes.
‣ We model with random numbers.
‣ The aim of crossover is to sustain different members, chormosomes or solution variables.
‣ If the same population we cannot find the solution.
‣ We have to mix population by Crossover
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‣We define a mutatation pattern
‣As it is also rare in nature, we have low mutation ratio
‣ The aim of mutation is sustain different members as well
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THANKS FOR LISTENING… ANY QUESTIONS ?
NUMERICAL METHODS IN OPTIMIZATION