Genetic Algorithm
Made By-Garima Singhal
Introduction
• One of the central challenges of computer science
is to get a computer to do what needs to be done,
without telling it how to do it.
• Before looking forward to what actually is
GENETIC PROGRAMMING we shall first get
acquainted with Soft Computing.
Soft Computing
• It is another field of computer science.
• It is the fusion of methodologies that were designed to model
and enable solutions to real world problems, which are not
modeled, or too difficult to model, mathematically.
• It is associated with fuzzy, complex and dynamic system with
uncertain parameters.
• Quality of Service Networking is an example of the class of
complex, fuzzy and dynamic systems with uncertain
parameters, which soft computing is intended to model and
compute.
Difference between Soft computing And Conventional Computing
Hard Computing(Conventional)
Soft Computing
Requires precisely stated analytical model and a lot of computation time.
Tolerant of imprecision, uncertainty and approximation.
Based on binary logic, numerical analysis and crisp software.
Based on fuzzy logic, neural networks and probabilistic reasoning.
Requires programs to be written. Can evolve its own programs.
Deterministic. Incorporates stochasticity.
Strictly sequential. Allows parallel computations.
Current Applications of Soft Computing include
• Handwriting Recognition
• Image Processing and Data Compression
• Automotive Systems and Manufacturing
• Decision –Support Systems
• Neurofuzzy Systems
• Fuzzy Logic Control
Evolutionary Computation
• Evolutionary computation simulates evolution on a computer. The Evolutionary computation simulates evolution on a computer. The
result of such a simulation is a series of optimization algorithms, result of such a simulation is a series of optimization algorithms,
usually based on a simple set of rules. Optimizationusually based on a simple set of rules. Optimization iteratively iteratively
improves the quality of solutions until an optimal, or at improves the quality of solutions until an optimal, or at
least feasible, solution is found.least feasible, solution is found.
Contd…
• Evolutionary Computations can be studied under 2 categories:
Genetic Algorithm
Genetic programming
F inonacc i N ew ton
D irect m ethods Indirect m ethods
C alcu lus-based techn iques
Evolu tionary s trategies
C entra l ized D is tr ibuted
Para l le l
S teady-s ta te G enera tiona l
Sequentia l
G enetic a lgori thm s
Evolutionary a lgori thm s S im u lated annealing
G uided random search techniques
D ynam ic program m ing
Enum erative techn iques
Search techniques
Genetic Algorithm Terminologies
Now, before we start, we should understand some key terms :
Individual Any possible solution
Population Group of all individuals
Search Space
All possible solutions to the problem
Chromosome Blueprint for an individual
Trait Possible aspect of an individual
Allele Possible settings for a trait
Locus The position of a gene on the chromosome
Genome Collection of all chromosomes for an individual
Premise
Evolution works biologically so maybe it will work with
simulated environments.
Here each possible solution (good or bad) is represented
by a chromosome (i.e. a pattern of bits which is sort of
synonymous to DNA)
Determine the better solutions
Mate these solutions to produce new solutions which are
(hopefully!) occasionally better than the parents.
Do this for many generations.
Outline of the Genetic Algorithm
• Randomly generate a set of possible solutions to a problem,
representing each as a fixed length character string
• Test each possible solution against the problem using a
fitness function to evaluate each solution
• Keep the best solutions, and use them to generate new
possible solutions
• Repeat the previous two steps until either an acceptable
solution is found, or until the algorithm has iterated through a
given number of cycles (generations)
Basic Operators of Genetic Algorithm
• Reproduction: It is usually the first operator applied on population. Chromosomes are selected from the population of parents to cross over and produce offspring. It is based on Darwin’s evolution theory of “Survival of the fittest”. Therefore, this operator is also known as ‘Selection Operator’.
• Cross Over: After reproduction phase, population is enriched with better individuals. It makes clones of good strings but doesnot create new ones. Cross over operator is applied to the mating pool with a hope that it would create better strings.
• Mutation: After cross over, the strings are subjected to mutation. Mutation of a bit involves flipping it,changing 0 to 1 and vice-versa.
Basic genetic algorithmsBasic genetic algorithms
• Step 1Step 1: : Represent the problem variable domain as a chromosome of a Represent the problem variable domain as a chromosome of a fixed length, choose the size of a chromosome population fixed length, choose the size of a chromosome population NN, the , the crossover probability crossover probability ppcc and the mutation probability and the mutation probability ppmm..
• Step 2Step 2: : Define a fitness function to measure the performance, or Define a fitness function to measure the performance, or fitness, of an individual chromosome in the problem domain. The fitness fitness, of an individual chromosome in the problem domain. The fitness function establishes the basis for selecting chromosomes that will be function establishes the basis for selecting chromosomes that will be mated during reproduction.mated during reproduction.
• Step 3Step 3: : Randomly generate an initial population of chromosomes of size Randomly generate an initial population of chromosomes of size NN::xx11, , xx22 , . . . , , . . . , xxNN
• Step 4Step 4: : Calculate the fitness of each individual chromosome:Calculate the fitness of each individual chromosome: f f ((xx11), ), f f ((xx22), . . . , ), . . . , f f ((xxNN))
• Step 5Step 5: : Select a pair of chromosomes for mating from the current Select a pair of chromosomes for mating from the current population. Parent`chromosomes are selected with a probability related population. Parent`chromosomes are selected with a probability related to their fitness.to their fitness.
• Step 6Step 6:: Create a pair of offspring chromosomes by applying the genetic Create a pair of offspring chromosomes by applying the genetic operators operators - - crossovercrossover and mand mutationutation..
• Step 7Step 7:: Place the created offspring chromosomes in the new Place the created offspring chromosomes in the new population.population.
• Step 8Step 8:: RepeatRepeat Step 5 Step 5 until the size of the new chromosome population until the size of the new chromosome population becomes equal to the size of the initial population, becomes equal to the size of the initial population, NN..
• Step 9Step 9:: Replace the initial (parent) chromosom population with the Replace the initial (parent) chromosom population with the new (offspring) population.new (offspring) population.
• Step 10Step 10:: Go to Go to Step 4Step 4, and repeat the process until the termination , and repeat the process until the termination criterion is satisfied.criterion is satisfied.
Working Principle of Genetic Algorithm
Genetic Algorithms: Case StudyGenetic Algorithms: Case Study
• A simple example will help us to understand how a GA works. Let A simple example will help us to understand how a GA works. Let us find the maximum value of the function (15us find the maximum value of the function (15x x - - xx22) where ) where parameter parameter xx varies between 0 and 15. For simplicity, we may varies between 0 and 15. For simplicity, we may assume that assume that x x takes only integer values. Thus, chromosomes can be takes only integer values. Thus, chromosomes can be built with only four genes:built with only four genes:
Integer Binary code Integer Binary code Integer Binary code1 112 7 123 8 134 9 145 10 15
6 1 0 1 11 1 0 01 1 0 11 1 1 01 1 1 1
0 1 1 00 1 1 11 0 0 01 0 0 11 0 1 0
0 0 0 10 0 1 00 0 1 10 1 0 00 1 0 1
• Suppose that the size of the chromosome population NSuppose that the size of the chromosome population N is 6, the is 6, the
crossover probability crossover probability ppcc equals 0.7, and the mutation probability equals 0.7, and the mutation probability ppmm
equals 0.001. The fitness function in our example is definedequals 0.001. The fitness function in our example is defined byby
ff((xx) = ) = 15 15 x x – – xx22
The fitness function and chromosome The fitness function and chromosome locationslocations
Chromosomelabel
Chromosomestring
Decodedinteger
Chromosomefitness
Fitnessratio, %
X1 1 1 0 0 12 36 16.5X2 0 1 0 0 4 44 20.2X3 0 0 0 1 1 14 6.4X4 1 1 1 0 14 14 6.4X5 0 1 1 1 7 56 25.7X6 1 0 0 1 9 54 24.8
x
50
40
30
20
60
10
00 5 10 15
f(x)
(a) Chromosome initial locations.
x
50
40
30
20
60
10
00 5 10 15
(b) Chromosome final locations.
• The last column in Table shows the ratio of the individual The last column in Table shows the ratio of the individual
chromosome’s fitness to the population’s total fitness. This ratio chromosome’s fitness to the population’s total fitness. This ratio
determines the chromosome’s chance of being selected for mating. The determines the chromosome’s chance of being selected for mating. The
chromosome’s average fitness improves from one generation to the chromosome’s average fitness improves from one generation to the
next.next.
Roulette wheel selectionRoulette wheel selection
• The most commonly used chromosome selection techniques is the The most commonly used chromosome selection techniques is the roulette wheel selectionroulette wheel selection..
100 0
36.743.149.5
75.2
X1: 16.5%X2: 20.2%X3: 6.4%X4: 6.4%X5: 25.3%X6: 24.8%
Crossover operatorCrossover operator
• In our example, we have an initial population of 6 chromosomes. In our example, we have an initial population of 6 chromosomes. Thus, to establish the same population in the next generation, the Thus, to establish the same population in the next generation, the roulette wheel would be spun six times.roulette wheel would be spun six times.
• Once a pair of parent chromosomes is selected, the Once a pair of parent chromosomes is selected, the crossovercrossover operator is applied.operator is applied.
• First, the crossover operator randomly chooses a crossover point First, the crossover operator randomly chooses a crossover point where two parent chromosomes “break”, and then exchanges the where two parent chromosomes “break”, and then exchanges the chromosome parts after that point. As a result, two new offspring chromosome parts after that point. As a result, two new offspring are created.are created.
• If a pair of chromosomes does not cross over, then the chromosome If a pair of chromosomes does not cross over, then the chromosome cloning takes place, and the offspring are created as exact copies of cloning takes place, and the offspring are created as exact copies of each parent.each parent.
X6i 1 00 0 01 0 X2i
0 01 0X2i 0 11 1 X5i
0X1i 0 11 1 X5i1 01 0
0 10 0
11 101 0
Mutation operatorMutation operator
• Mutation represents a change inMutation represents a change in the gene.the gene.
• Mutation is a background operator. Its role is to provide a guarantee Mutation is a background operator. Its role is to provide a guarantee
that the search algorithm is not trapped on a local optimum.that the search algorithm is not trapped on a local optimum.
• The mutation operator flips a randomly selected gene in a The mutation operator flips a randomly selected gene in a
chromosome.chromosome.
• The mutation probability is quite small in nature, and is kept low for The mutation probability is quite small in nature, and is kept low for
GAs, typically in the range between 0.001 and 0.01.GAs, typically in the range between 0.001 and 0.01.
0 11 1X5'i 01 0
X6'i 1 00
0 01 0X2'i 0 1
0 0
0 1 111X5i
1 1 1 X1"i1 1
X2"i0 1 0
0X1'i 1 1 1
0 1 0X2i
1 01 0X1i
Generation i
0 01 0X2i
0 00 1X3i
1 11 0X4i
0 11 1X5i f = 56
1 00 1X6i f = 54
f = 36
f = 44
f = 14
f = 14
1 00 0X1i+1
Generation (i + 1)
0 01 1X2i+1
1 10 1X3i+1
0 01 0X4i+1
0 11 0X5i+1 f = 54
0 11 1X6i+1 f = 56
f = 56
f = 50
f = 44
f = 44
Crossover
X6i 1 00 0 01 0 X2i
0 01 0X2i 0 11 1 X5i
0X1i 0 11 1 X5i1 01 0
0 10 0
11 101 0
Mutation
0 11 1X5'i 01 0
X6'i 1 00
0 01 0X2'i 0 1
0 0
0 1 111X5i
1 1 1 X1"i1 1
X2"i0 1 0
0X1'i 1 1 1
0 1 0X2i
Example Checkboard
• We are given an n by n checkboard in which every field can have a different colour from a set of four colours.
• Goal is to achieve a checkboard in a way that there are no neighbours with the same colour (not diagonal).
1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
1 2 3 4 5 6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
• Chromosomes represent the way the checkboard is coloured.
• Chromosomes are not represented by bitstrings but by bitmatrices
• The bits in the bitmatrix can have one of the four values 0, 1, 2 or 3, depending on the colour
• Crossing-over involves matrix manipulation instead of point wise operating. Crossing-over can be combining the parential matrices in a horizontal, vertical, triangular or square way
• Mutation remains bitwise changing bits in either one of the other numbers
• Fitness curve for the checkboard example
• This problem can be seen as a graph with n nodes and (n-1) edges, so the fitness f(x) is easily defined as: f(x) = 2 · (n-1) ·n
0 100 200 300 400 500 600130
135
140
145
150
155
160
165
170
175
180
Generations
Fitn
ess
Best FitnessMean Fitness
0 100 200 300 400 500130
140
150
160
170
180
Fitne
ss
Lower-Triangular Crossing Over
0 200 400 600 800130
140
150
160
170
180Square Crossing Over
0 200 400 600 800130
140
150
160
170
180
Generations
Fitne
ss
Horizontal Cutting Crossing Over
0 500 1000 1500130
140
150
160
170
180
Generations
Verical Cutting Crossing Over
Fitnesscurves for different cross-over rules
The GA Cycle of Reproduction
Population
Fitness EvaluationGenetic Operators
Selection(Mating Pool)
Parents
Offspring
New Generation
Manipulation Reproduction
Decoded Strings
Issues for Genetic Algorithm practitioners
• Choosing basic implementation issues such as
Representation
Population size and mutation rate
Selection, deletion policies
Cross over and mutation operators
• Termination criterion
• Performance and scalability
• Solution is only as good as evaluation functions.
Benefits Of Genetic Algorithms
• Easy to understand
• Supports multi-objective optimisation
• Good for noisy environment
• We always get answer and answer gets better with time
• Inherently parallel and easily distributed
• Easy to exploit for precious or alternate solutions
• Flexible in forming building blocks for hybrid applications
• Has substantial history and range of use
Genetic Algorithm Applications
Domains Application Types
Control Gas pipeline, pole balancing, missile evasion, pursuit
Robotics Trajectory planning
Signal Processing Filter design
Game Playing Poker, checker, prisoner’s dilemma
Scheduling Manufacturing facility, scheduling, resource allocation
Design Semiconductor layout, aircraft design, keyboard configuration, communication networks
Combinatorial Optimisation
Set covering, travelling salesmen, routing, bin packing, graph coloring and partitioning
Any Questions
Bibliography
• www.softcomputing.net/gpsystems.pdf
• http://cs.mwsu.edu/~simpson/
• http://geneticalgorithms.ai-depot.com/Tutorial/Overview.html
• Neural Networks, Fuzzy Logic, And Genetic Algorithm:Synthesis And Application
• S.Rajasekaran• G.A.Vijayalakshmi Pai
• http://c2.com/cgi/wiki?GeneticAlgorithm