soft computing unit-5 by arun pratap singh

7/21/2019 Soft Computing Unit-5 by Arun Pratap Singh

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UNIT : V

SOFT COMPUTINGII SEMESTER (MCSE 205)

PREPARED BY ARUN PRATAP SINGH


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PREPARED BY ARUN PRATAP SINGH 2

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In a genetic algorithm, a population of candidate solutions (called individuals, creatures,

or phenotypes) to an optimization problem is evolved toward better solutions. Each candidate

solution has a set of properties (itschromosomes orgenotype)which can be mutated and altered;

traditionally, solutions are represented in binary as strings of 0s and 1s, but other encodings are

also possible.
http://en.wikipedia.org/wiki/Populationhttp://en.wikipedia.org/wiki/Candidate_solutionhttp://en.wikipedia.org/wiki/Phenotypehttp://en.wikipedia.org/wiki/Chromosomehttp://en.wikipedia.org/wiki/Genotypehttp://en.wikipedia.org/wiki/Genotypehttp://en.wikipedia.org/wiki/Chromosomehttp://en.wikipedia.org/wiki/Phenotypehttp://en.wikipedia.org/wiki/Candidate_solutionhttp://en.wikipedia.org/wiki/Population


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The evolution usually starts from a population of randomly generated individuals, and is

aniterative process,with the population in each iteration called a generation. In each generation,

the fitness of every individual in the population is evaluated; the fitness is usually the value of

the objective function in the optimization problem being solved. The more fit individuals

arestochastically selected from the current population, and each individual's genome is modified(recombined and possibly randomly mutated) to form a new generation. The new generation of

candidate solutions is then used in the next iteration of thealgorithm.Commonly, the algorithm

terminates when either a maximum number of generations has been produced, or a satisfactory

fitness level has been reached for the population.

A typical genetic algorithm requires:

1. agenetic representation of the solution domain,

2. afitness function to evaluate the solution domain.

A standard representation of each candidate solution is as anarray of bits.Arrays of other types

and structures can be used in essentially the same way. The main property that makes these

genetic representations convenient is that their parts are easily aligned due to their fixed size,

which facilitates simplecrossover operations. Variable length representations may also be used,

but crossover implementation is more complex in this case. Tree-like representations are explored

in genetic programming and graph-form representations are explored in evolutionary

programming; a mix of both linear chromosomes and trees is explored in gene expression

programming.

Once the genetic representation and the fitness function are defined, a GA proceeds to initialize

a population of solutions and then to improve it through repetitive application of the mutation,

crossover, inversion and selection operators.
http://en.wikipedia.org/wiki/Iterationhttp://en.wikipedia.org/wiki/Fitness_(biology)http://en.wikipedia.org/wiki/Objective_functionhttp://en.wikipedia.org/wiki/Stochasticshttp://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Genetic_representationhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Bit_arrayhttp://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Genetic_programminghttp://en.wikipedia.org/wiki/Evolutionary_programminghttp://en.wikipedia.org/wiki/Evolutionary_programminghttp://en.wikipedia.org/wiki/Gene_expression_programminghttp://en.wikipedia.org/wiki/Gene_expression_programminghttp://en.wikipedia.org/wiki/Gene_expression_programminghttp://en.wikipedia.org/wiki/Gene_expression_programminghttp://en.wikipedia.org/wiki/Evolutionary_programminghttp://en.wikipedia.org/wiki/Evolutionary_programminghttp://en.wikipedia.org/wiki/Genetic_programminghttp://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Bit_arrayhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Genetic_representationhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Stochasticshttp://en.wikipedia.org/wiki/Objective_functionhttp://en.wikipedia.org/wiki/Fitness_(biology)http://en.wikipedia.org/wiki/Iteration


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WORKING PRINCIPLE OF GENETIC ALGORITHMS:


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Genetic Algorithms are search algorithms that are based on concepts of natural selection andnatural genetics. Genetic algorithm was developed to simulate some of the processes observedin natural evolution, a process that operates on chromosomes (organic devices for encoding thestructure of living being). The genetic algorithm differs from other search methods in that itsearches among a population of points, and works with a coding of parameter set, rather than theparameter values themselves. It also uses objective function information without any gradient

information. The transition scheme of the genetic algorithm is probabilistic, whereas traditionalmethods use gradient information. Because of these features of genetic algorithm, they are usedas general purpose optimization algorithm. They also provide means to search irregular spaceand hence are applied to a variety of function optimization, parameter estimation and machinelearning applications.

Basic Principle

The working principle of a canonical GA is illustrated in Fig.1.The major steps involved are thegeneration of a population of solutions, finding the objective function and fitness function and theapplication of genetic operators. These aspects are described briefly below. They are describedin detail in the following subsection.

1:The Working Principle of a Simple Genetic Algorithm
http://www.civil.iitb.ac.in/tvm/2701_dga/2701-ga-notes/gadoc/gadoc.html#qf_ga_wphttp://www.civil.iitb.ac.in/tvm/2701_dga/2701-ga-notes/gadoc/gadoc.html#qf_ga_wphttp://www.civil.iitb.ac.in/tvm/2701_dga/2701-ga-notes/gadoc/gadoc.html#qf_ga_wphttp://www.civil.iitb.ac.in/tvm/2701_dga/2701-ga-notes/gadoc/gadoc.html#qf_ga_wp


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2: The basic GA operations: One generation is broken down into a selection phase and

recombination phase. Strings are assigned into adjacent slots during selection.

An important characteristic of genetic algorithm is the coding of variables that describes theproblem. The most common coding method is to transform the variables to a binary string orvector; GAs perform best when solution vectors are binary. If the problem has more than onevariable, a multi-variable coding is constructed by concatenating as many single variables codingas the number of variables in the problem. Genetic Algorithm processes a number of solutionssimultaneously. Hence, in the first step a population having P individuals is generated by pseudorandom generators whose individuals represent a feasible solution. This is a representation ofsolution vector in a solution space and is called initial solution. This ensures the search to berobust and unbiased, as it starts from wide range of points in the solution space.

In the next step, individual members of the population are evaluated to find the objective function

value. In this step, the exterior penalty function method is utilized to transform a constrainedoptimization problem to an unconstrained one. This is exclusively problem specific. In the thirdstep, the objective function is mapped into a fitness function that computes a fitness value foreach member of the population. This is followed by the application of GA operators.


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Working Principle

To illustrate the working principles of GAs, an unconstrained optimization problem is considered.Let us consider following maximization problem,

(1)

where, and are the lower and upper bound the variable can take. Although a

maximization problem is considered here, a maximization problem can also be handled using

GAs. The working of GAs is completed by performing the following tasks.

OPERATORS OF GENETIC ALGORITHM :

A genetic operatoris anoperator used ingenetic algorithms to maintaingenetic diversity,known

as mutation and to combine existing solutions into others, crossover. The main difference

between them is that the mutation operators operate on one chromosome, that is, they are unary,

while the crossover operators are binary operators.

Genetic variation is a necessity for the process ofevolution.Genetic operators used in genetic

algorithms are analogous to those in the natural world: survival of the fittest, or selection;

reproduction (crossover,also called recombination); andmutation.
http://en.wikipedia.org/wiki/Operator_(programming)http://en.wikipedia.org/wiki/Genetic_algorithmshttp://en.wikipedia.org/wiki/Genetic_diversityhttp://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)http://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Survival_of_the_fittesthttp://en.wikipedia.org/wiki/Selection_(genetic_algorithm)http://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)http://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)http://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Selection_(genetic_algorithm)http://en.wikipedia.org/wiki/Survival_of_the_fittesthttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)http://en.wikipedia.org/wiki/Genetic_diversityhttp://en.wikipedia.org/wiki/Genetic_algorithmshttp://en.wikipedia.org/wiki/Operator_(programming)


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DELETION AND INVERSION :


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FITNESS FUNCTION:

A fitness function is a particular type of objective function that is used to summarise, as a

singlefigure of merit,how close a given design solution is to achieving the set aims.

In particular, in the fields ofgenetic programming andgenetic algorithms,each design solution is

represented as a string of numbers (referred to as achromosome). After each round of testing,

or simulation, the idea is to delete the 'n' worst design solutions, and tobreed 'n' new ones from

the best design solutions. Each design solution, therefore, needs to be awarded a figure of merit,

to indicate how close it came to meeting the overall specification, and this is generated by applying

the fitness function to the test, or simulation, results obtained from that solution.

The reason that genetic algorithms cannot be considered to be a lazy way of performing design

work is precisely because of the effort involved in designing a workable fitness function. Even

though it is no longer the human designer, but the computer, that comes up with the final design,

it is the human designer who has to design the fitness function. If this is designed badly, the

algorithm will either converge on an inappropriate solution, or will have difficulty converging at all.

Moreover, the fitness function must not only correlate closely with the designer's goal, it must also

be computed quickly. Speed of execution is very important, as a typical genetic algorithm must

be iterated many times in order to produce a usable result for a non-trivial problem.

Fitness approximation may be appropriate, especially in the following cases:

Fitness computation time of a single solution is extremely high

Precise model for fitness computation is missing The fitness function is uncertain or noisy.

Two main classes of fitness functions exist: one where the fitness function does not change, as

in optimizing a fixed function or testing with a fixed set of test cases; and one where the fitness

function is mutable, as inniche differentiation orco-evolving the set of test cases.

Another way of looking at fitness functions is in terms of a fitness landscape,which shows the

fitness for each possible chromosome.

Definition of the fitness function is not straightforward in many cases and often is performed

iteratively if the fittest solutions produced by GA are not what is desired. In some cases, it is veryhard or impossible to come up even with a guess of what fitness function definition might

be. Interactive genetic algorithms address this difficulty by outsourcing evaluation to external

agents (normally humans).
http://en.wikipedia.org/wiki/Objective_functionhttp://en.wikipedia.org/wiki/Figure_of_merithttp://en.wikipedia.org/wiki/Genetic_programminghttp://en.wikipedia.org/wiki/Genetic_algorithmhttp://en.wikipedia.org/wiki/Chromosome_(genetic_algorithm)http://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Fitness_approximationhttp://en.wikipedia.org/wiki/Niche_differentiationhttp://en.wikipedia.org/wiki/Co-evolutionhttp://en.wikipedia.org/wiki/Fitness_landscapehttp://en.wikipedia.org/wiki/Interactive_genetic_algorithmshttp://en.wikipedia.org/wiki/Interactive_genetic_algorithmshttp://en.wikipedia.org/wiki/Fitness_landscapehttp://en.wikipedia.org/wiki/Co-evolutionhttp://en.wikipedia.org/wiki/Niche_differentiationhttp://en.wikipedia.org/wiki/Fitness_approximationhttp://en.wikipedia.org/wiki/Crossover_(genetic_algorithm)http://en.wikipedia.org/wiki/Chromosome_(genetic_algorithm)http://en.wikipedia.org/wiki/Genetic_algorithmhttp://en.wikipedia.org/wiki/Genetic_programminghttp://en.wikipedia.org/wiki/Figure_of_merithttp://en.wikipedia.org/wiki/Objective_function


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As mentioned earlier, GAs mimic the survival-of-the-fittest principle of nature to make

a search process. Therefore, GAs are naturally suitable for solving maximization

problems. Maximization problems are usually transformed into maximization problem

by suitable transformation. In general, a fitness function is first derived from the

objective function and used in successive genetic operations. Fitness in biological sense

is a quality value which is a measure of the reproductive efficiency of chromosomes. In

genetic algorithm, fitness is used to allocate reproductive traits to the individuals in the

population and thus act as some measure of goodness to be maximized. This means that

individuals with higher fitness value will have higher probability of being selected as

candidates for further examination. Certain genetic operators require that the fitness

function be non-negative, although certain operators need not have this requirement.

For maximization problems, the fitness function can be considered to be the same as

the objective function or . For minimization problems, to generate non-

negative values in all the cases and to reflect the relative fitness of individual string, it

is necessary to map the underlying natural objective function to fitness function form.

A number of such transformations is possible. Two commonly adopted fitness

mappings is presented below.

(4)

This transformation does not alter the location of the minimum, but converts aminimization problem to an equivalent maximization problem. An alternate function

to transform the objective function to get the fitness value as below.

(5)

where, is the objective function value of individual, is the population

size and is a large value to ensure non-negative fitness values. The value of V

adopted in this work is the maximum value of the second term of equation5so that

the fitness value corresponding to maximum value of the objective function is zero.

This transformation also does not alter the location of the solution, but converts a

minimization problem to an equivalent maximization problem. The fitness function

value of a string is known as the string fitness.
http://www.civil.iitb.ac.in/tvm/2701_dga/2701-ga-notes/gadoc/gadoc.html#qe_trf_fun_2http://www.civil.iitb.ac.in/tvm/2701_dga/2701-ga-notes/gadoc/gadoc.html#qe_trf_fun_2http://www.civil.iitb.ac.in/tvm/2701_dga/2701-ga-notes/gadoc/gadoc.html#qe_trf_fun_2http://www.civil.iitb.ac.in/tvm/2701_dga/2701-ga-notes/gadoc/gadoc.html#qe_trf_fun_2


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ENCODING IN GENETIC ALGORITHM :


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OPTIMIZATION :


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GENETIC MODELING :


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JOB-SHOP SCHEDULING PROBLEM (JSSP):

Job shop scheduling (or job-shop problem) is an optimization problem in computer

science andoperations research in which ideal jobs are assigned to resources at particular times.

The most basic version is as follows:

We are given n jobs J1, J2, ..., Jnof varying sizes, which need to be scheduled on m identical

machines, while trying to minimize the makespan. The makespan is the total length of the

schedule (that is, when all the jobs have finished processing). Nowadays, the problem is

presented as an online problem (dynamic scheduling), that is, each job is presented, and

theonline algorithm needs to make a decision about that job before the next job is presented.

This problem is one of the best known online problems, and was the first problem forwhichcompetitive analysis was presented, by Graham in 1966.[1]Best problem instances for basic

model with makespan objective are due to Taillard.
http://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Operations_Researchhttp://en.wikipedia.org/wiki/Online_problemhttp://en.wikipedia.org/wiki/Online_algorithmhttp://en.wikipedia.org/wiki/Competitive_analysis_(online_algorithm)http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-graham1966-1http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-graham1966-1http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-graham1966-1http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-graham1966-1http://en.wikipedia.org/wiki/Competitive_analysis_(online_algorithm)http://en.wikipedia.org/wiki/Online_algorithmhttp://en.wikipedia.org/wiki/Online_problemhttp://en.wikipedia.org/wiki/Operations_Researchhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Computer_science


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Problem variations:

Many variations of the problem exist, including the following:

Machines can be related, independent, equal

Machines can require a certain gap between jobs or no idle-time

Machines can havesequence-dependent setups

Objective function can be to minimize the make span, the Lp norm, tardiness, maximum

lateness etc. It can also be multi-objective optimization problem

Jobs may have constraints, for example a job ineeds to finish before job jcan be started

(seeworkflow). Also, the objective function can be multi-criteria.

Jobs and machines have mutual constraints, for example, certain jobs can be scheduled on

some machines only
http://en.wikipedia.org/wiki/Sequence-dependent_setuphttp://en.wikipedia.org/wiki/Lp_spacehttp://en.wikipedia.org/wiki/Lp_spacehttp://en.wikipedia.org/wiki/Lp_spacehttp://en.wikipedia.org/wiki/Workflowhttp://en.wikipedia.org/wiki/Workflowhttp://en.wikipedia.org/wiki/Lp_spacehttp://en.wikipedia.org/wiki/Sequence-dependent_setup


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Set of jobs can relate to different set of machines

Deterministic (fixed) processing times or probabilistic processing times

There may also be some other side constraints

NP-hardness:

If one already knows that thetravelling salesman problem is NP-hard (as it is), then the job-shop

problem is clearly also NP-hard, since the TSP is special case of the JSP with (the

salesman is the machine and the cities are the jobs).

Problem representation:

Thedisjunctive graph[4]is one of the popular models used for describing the job shop scheduling

problem instances.[5]

A mathematical statement of the problem can be made as follows:

Let and be twofinitesets.On account

of the industrial origins of the problem, the are called machinesand the are calledjobs.

Let denote the set of all sequential assignments of jobs to machines, such that every job is

done by every machine exactly once; elements may be written as matrices, in

which column lists the jobs that machine will do, in order. For example, the matrix

means that machine will do the three jobs in the order , while

machine will do the jobs in the order .

Suppose also that there is some cost function . The cost function may

be interpreted as a "total processing time", and may have some expression in terms of

times , the cost/time for machine to do job .

The job-shop problem is to find an assignment of jobs such that is a

minimum, that is, there is no such that .

The problem of infinite cost :

One of the first problems that must be dealt with in the JSP is that many proposed solutions have

infinite cost: i.e., there exists such that . In fact, it is quite simple to

concoct examples of such by ensuring that two machines willdeadlock,so that each waits

for the output of the other's next step.
http://en.wikipedia.org/wiki/Travelling_salesman_problemhttp://en.wikipedia.org/wiki/Disjunctive_graphhttp://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-4http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-4http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-4http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-5http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-5http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-5http://en.wikipedia.org/wiki/Finite_sethttp://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Deadlockhttp://en.wikipedia.org/wiki/Deadlockhttp://en.wikipedia.org/wiki/Set_(mathematics)http://en.wikipedia.org/wiki/Finite_sethttp://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-5http://en.wikipedia.org/wiki/Job_shop_scheduling#cite_note-4http://en.wikipedia.org/wiki/Disjunctive_graphhttp://en.wikipedia.org/wiki/Travelling_salesman_problem


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TRAVELING SALESMAN PROBLEM :

"The traveling salesman problem, or TSP for short, is this: given a finite number of 'cities' along with

the cost of travel between each pair of them, find the cheapest way of visiting all the cities and

returning to your starting point."

A solution: distance = 941

The traveling salesman must visit every city in his territory exactly once (possibly then return to

the starting point).

Given the cost of travel between all cities, how should he plan his itinerary for minimum total

cost of the entire tour?

TSP NP-Complete

Complexities :

Testing every possibility for an N city tour would be O(N!) math additions.

A 30 city tour would take additions.

Assuming 1 billion additions per second, this would take over 8,000,000,000,000,000

years, i.e., 8 million billion years. The age of the universe since the big bang is only about 14 billion years.

GA approach :

Can find a pretty good solution in less than a minute


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Representation: randompermutation, example of a tour for 9 cities,

(6 7 8 9 3 4 1 2 5)

Each represent an individual animal or organism

Population:a group of random tours

A community of individuals


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A solution, cost = 800


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A solution, distance = 652

Best Solution (Distance = 420)


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I have developed a solution to the Traveling Salesman Problem (TSP) using a Genetic

Algorithm (GA). In the Traveling Salesman Problem, the goal is to find the shortest distance

between N different cities. The path that the salesman takes is called a tour.

Testing every possibility for an N city tour would be N! math additions. A 30 city tour would have

to measure the total distance of be 2.65 X 1032different tours. Assuming a trillion additions per

second, this would take 252,333,390,232,297 years. Adding one more city would cause the time

to increase by a factor of 31. Obviously, this is an impossible solution.

A genetic algorithm can be used to find a solution is much less time. Although it might not find the

best solution, it can find a near perfect solution for a 100 city tour in less than a minute. There are

a couple of basic steps to solving the traveling salesman problem using a GA.

First, create a group of many random tours in what is called a population. This algorithm

uses a greedy initial population that gives preference to linking cities that are close to each

other.

Second, pick 2 of the better (shorter) tours parentsin the population and combine them

to make 2 new childtours. Hopefully, these children tour will be better than either parent.

A small percentage of the time, the child tours are mutated. This is done to prevent all

tours in the population from looking identical.

The new child tours are inserted into the population replacing two of the longer tours. The

size of the population remains the same.

New children tours are repeatedly created until the desired goal is reached.

As the name implies, Genetic Algorithms mimic nature and evolution using the principles

of Survival of the Fittest.

The two complex issues with using a Genetic Algorithm to solve the Traveling SalesmanProblem are the encoding of the tour and the crossoveralgorithm that is used to combine the

two parent tours to make the child tours.

In a standard Genetic Algorithm, the encoding is a simple sequence of numbers and Crossover

is performed by picking a random point in the parent's sequences and switching every number

in the sequence after that point. In this example, the crossover point is between the 3rdand

4thitem in the list. To create the children, every item in the parent's sequence after the

crossover point is swapped.

Parent 1 F A B |E C G D

Parent 2 D E A |C G B F

Child 1 F A B |C G B F

Child 1 D E A |E C G D


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The difficulty with the Traveling Salesman Problem is that every city can only be used once in a

tour. If the letters in the above example represented cities, this child tours created by this

crossover operation would be invalid. Child 1 goes to city F & B twice, and never goes to cities

D or E.

The encoding cannot simply be the list of cities in the order they are traveled. Other encoding

methods have been created that solve the crossover problem. Although these methods will not

create invalid tours, they do not take into account the fact that the tour "A B C D E F G" is the

same as "G F E D C B A". To solve the problem properly the crossover algorithm will have to

get much more complicated.

My solution stores the linksin both directions for each tour. In the above tour example, Parent 1

would be stored as:

City First Connection Second Connection

A F B

B A E

C E G

D G F

E B C

F D A

G C D

The crossover operation is more complicated than combining 2 strings. The crossover will take

every link that exists in both parents and place those links in both children. Then, for Child 1 it

alternates between taking links that appear in Parent 2 and then Parent 1. For Child 2, it

alternates between Parent 2 and Parent 1 taking a different set of links. For either child, there isa chance that a link could create an invalid tour where instead of a single path in the tour there

are several disconnected paths. These links must be rejected. To fill in the remaining missing

links, cities are chosen at random. Since the crossover is not completely random, this is

considered a greedy crossover.

Eventually, this GA would make every solution look identical. This is not ideal. Once every tour

in the population is identical, the GA will not be able to find a better solution. There are two ways


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around this. The first is to use a very large initial population so that it takes the GA longer to

make all of the solutions the same. The second method is mutation, where some child tours

are randomly altered to produce a new unique tour.

This Genetic Algorithm also uses a greedy initial population. The city links in the initial tours are

not completely random. The GA will prefer to make links between cities that are close to each

other. This is not done 100% of the time, becuase that would cause every tour in the initial

population to be very similar.

There are 6 parameters to control the operation of the Genetic Algorithm:

Population Size - The population size is the initial number of random tours that are

created when the algorithm starts. A large population takes longer to find a result. A

smaller population increases the chance that every tour in the population will eventually

look the same. This increases the chance that the best solution will not be found.

Neighborhood / Group Size- Each generation, this number of tours are randomly chosen

from the population. The best 2 tours are the parents. The worst 2 tours get replaced by

the children. For group size, a high number will increase the likelyhood that the really good

tours will be selected as parents, but it will also cause many tours to never be used as

parents. A large group size will cause the algorithm to run faster, but it might not find the

best solution.

Mutation %- The percentage that each child after crossover will undergo mutationWhen

a tour is mutated, one of the cities is randomly moved from one point in the tour to another.

# Nearby Cities- As part of a greedy initial population, the GA will prefer to link cities that

are close to each other to make the initial tours. When creating the initial population this

is the number of cities that are considered to be close.

Nearby City Odds %- This is the percent chance that any one link in a random tour inthe initial population will prefer to use a nearby city instead of a completely random city. If

the GA chooses to use a nearby city, then there is an equally random chance that it will

be any one of the cities from the previous parameter.

Maximum Generations - How many crossovers are run before the algorithm is

terminated.

The other options that can be configured are (note: these are only available in the downloadable

version):

Random Seed - This is the seed for the random number generator. By having a fixed

instead of a random seed, you can duplicate previous results as long as all otherparameters are the same. This is very helpful when looking for errors in the algorithm.

City List- The downloadable version allows you to import city lists from XML files. Again,

when debugging problems it is useful to be able to run the algorithm with the same exact

parameters.

The starting parameter values are:


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Parameter Initial Value

Population Size 10,000

Group Size 5

Mutation 3 %

# Nearby Cities 5

Nearby City Odds 90 %

Note: I originally wrote this program in 1995 in straight C. The tours in the population were stored

as an array of 32 bit int's, where each bit indicated a connection. Ex: If tour[0] =

00000000000001000000010000000000 in binary, then city 0 connected to city 11 and 19. Thatimplementation was much faster than the current C# version. The greedy part of crossover could

be performed by doing a binary AND on the two tours. While that code was very fast, it had a lot

of binary operations, was limited in the number of cities it could support, and the code wasn't

readable. Hopefully, this new version will allow for more re-use.


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APPLICATIONS OF GENETIC ALGORITHMS :

The keys of the success in GA applications are effective GA representation and meaningful

fitness evaluation. The demand of Genetic Algorithm comes from their grace and simplicity as

robust search algorithms. Also from their power to discover good solution quickly for complex

high- dimensional problems. The benefits of using the GA approach is the ease to handle

arbitrary kinds of constraints and objectives. For problem solving and modeling Gas have beenused. GA are applied to number of engineering and scientific problems, in business and

entertainment including the followings-

1. Automatic Programming - These algorithms are used to evolve computer programs for

unique tasks and to design other computational structures. For instance, storage

network and cellular automata.

2. OptimizationThese algorithm used in a various optimization tasks which include

numerical optimization and combinatorial optimization problems like circuit design. Job

shop scheduling (JSP) and travelling salesman problem.

3. Models of Social Systems-These algorithms are used to study evolutionary aspects of

social systems like the evolution of communication and trail following behavior in ants

and the evolution of cooperation.

4. Ecological Models- To model ecological phenomenon like host-parasite co-evolutions,

biological arm races, and symbiosis and resources flow in ecological GAs are used.

5. Economical Models- To model processes of innovation, the development of bidding

strategies and the emergence of economic markets GAs are used.

6. Population Genetics Models- Genetic algorithms are employed to study questions in

population genetics like under what situations will a gene for recombination be

evolutionary viable?

7. Immune System Models- To model various aspects of the natural immune system

which include somatic mutation during an individuals lifetime and discovery of multi-

gene families during evolutionary time GAs are used.

8. Machine And Robot Learning- Genetic algorithms are used to control and design

robots, symbolic production systems, to evolve rules for learning classifier and to design

neural networks. These algorithms are also used machine learning applications that

includes prediction and classification.

9. Interaction between Evolution and Learning- To study how individual learning and

species evolution affect one another GAs are used.


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SOME OTHER APPLICATIONS OF GENETIC ALGORITHM

Airlines Revenue Management.

Artificial creativity

Audio watermark insertion/detection

Automated design =computer-automated design Biology and computational chemistry

Control engineering

Financial Mathematics

File allocation for adistributed system

Filtering and signal processing

Finding hardware bugs
http://en.wikipedia.org/wiki/Computational_creativityhttp://en.wikipedia.org/w/index.php?title=Audio_watermark_insertion/detection&action=edit&redlink=1http://en.wikipedia.org/wiki/Computer-automated_designhttp://en.wikipedia.org/wiki/Control_engineeringhttp://en.wikipedia.org/wiki/Distributed_systemhttp://en.wikipedia.org/wiki/Distributed_systemhttp://en.wikipedia.org/wiki/Control_engineeringhttp://en.wikipedia.org/wiki/Computer-automated_designhttp://en.wikipedia.org/w/index.php?title=Audio_watermark_insertion/detection&action=edit&redlink=1http://en.wikipedia.org/wiki/Computational_creativity


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Game theory equilibrium resolution

Economics

Mechanical engineering

Mobile communications infrastructureoptimization

Power electronics design

DIFFERENCE BETWEEN GENETIC ALGORITHM AND TRADITIONAL METHOD:

GAs are radically different from most traditional optimization methods. Genetic algorithms work

with a string coding of variables instead of the variables. The advantages of working with a codingof variable is that coding discretizes the search space even though the function may be

continuous. On the other hand, since GA requires only function values at discrete points, a

discrete or discontinuous function can be handled with no extra cost. This allows GA to be applied

to a wide variety of problems. Genetic algorithm operators exploits the similarities in string

structure to make an effective search. Genetic algorithm works with a population of points instead

of a single points instead of a single point. In GA, previously found good information is emphasized

using reproduction operator and propagated adaptively through crossover and mutation

operators. Genetic algorithm is a population based search algorithm and multiple optimal

solutions can be captured. Hence reducing the effort to use the algorithm many times.
http://en.wikipedia.org/wiki/Game_theoryhttp://en.wikipedia.org/wiki/Genetic_algorithm_in_economicshttp://en.wikipedia.org/wiki/Mechanical_engineeringhttp://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Power_electronicshttp://en.wikipedia.org/wiki/Power_electronicshttp://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Mechanical_engineeringhttp://en.wikipedia.org/wiki/Genetic_algorithm_in_economicshttp://en.wikipedia.org/wiki/Game_theory


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Multi modal function

Even though Gas, are different than most traditional search algorithms, there are some

similarities. In traditional search methods, where a search direction is used to find a new point, at

least two points are either implicitly or explicitly used to define the search direction. In the cross

over operator, two points are used to create new points. Thus, cross over operator is similar to a

directional search method with an exception that the search direction is not fixed for all points in

the population and that no effort is made to find the optimal point in any particular direction. Since

two points used in crossover operator are chosen at random, many search directions are possible.

Among them, some may lead to global basin and some may not. The reproduction operator has

an indirect effect of filtering the good search direction and helps to guide the search. The purposeof mutation operator is to create a point in the vicinity of the current point. The search in the

mutation operator is similar to a local search method such as exploratory search used in Hooke-

Jeeves method.

ISSUES OF GENETIC ALGORITHM:-

The following issues are important while applying GA to practical problems, namely

1. Choosing basic implementation issues such as

a. Representation

b. Population size and mutation rate

c. Selection, deletion policies

d. Crossover and mutation operators.2. Termination criterion

3. Performance and scalability

4. Solution is only as good as the evaluation functions.

BENEFITS OF GENETIC ALGORITHM:-

The benefits of genetic algorithm are-


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1. Easy to understand.

2. Modular, separate from application

3. Supports multi-objective optimization

4. Good for noisy environment

5. We always get an answer and the answer gets better with the time.

6. Inherently parallel and easily distributed.

7. There are many ways to speed up and improve a GAs basic applications as knowledge

about the problem domain is general.

8. Easy to exploit for previous or alternate solutions.

9. Flexible in forming building blocks for hybrid applications.

EVOLUTIONARY COMPUTATION :

In computer science, evolutionary computation is a subfield of artificial intelligence (more

particularly computational intelligence) that involves continuous optimization and combinatorial

optimization problems. Its algorithms can be considered global optimization methods with

ametaheuristic orstochastic optimization character and are mostly applied for black box problems

(no derivatives known), often in the context of expensive optimization.

Evolutionary computation uses iterative progress, such as growth or development in a population.

This population is thenselected in a guidedrandom search usingparallel processing to achieve

the desired end. Such processes are often inspired by biological mechanisms ofevolution.

As evolution can produce highly optimised processes and networks, it has many applications

incomputer science.

Techniques-

Evolutionary computing techniques mostly involvemetaheuristicoptimizationalgorithms.

Broadly speaking, the field includes:

Evolutionary algorithms

Gene expression programming

Genetic algorithm

Genetic programming

Evolutionary programming Evolution strategy

Differential evolution

Swarm intelligence

Ant colony optimization

Particle swarm optimization

Artificial Bee Colony Algorithm
http://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Artificial_intelligencehttp://en.wikipedia.org/wiki/Computational_intelligencehttp://en.wikipedia.org/wiki/Continuous_optimizationhttp://en.wikipedia.org/wiki/Combinatorial_optimizationhttp://en.wikipedia.org/wiki/Combinatorial_optimizationhttp://en.wikipedia.org/wiki/Global_optimizationhttp://en.wikipedia.org/wiki/Metaheuristichttp://en.wikipedia.org/wiki/Stochastic_optimizationhttp://en.wikipedia.org/wiki/Artificial_selectionhttp://en.wikipedia.org/wiki/Randomhttp://en.wikipedia.org/wiki/Parallel_processinghttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Metaheuristichttp://en.wikipedia.org/wiki/Mathematical_optimizationhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Evolutionary_algorithmhttp://en.wikipedia.org/wiki/Gene_expression_programminghttp://en.wikipedia.org/wiki/Genetic_algorithmhttp://en.wikipedia.org/wiki/Genetic_programminghttp://en.wikipedia.org/wiki/Evolutionary_programminghttp://en.wikipedia.org/wiki/Evolution_strategyhttp://en.wikipedia.org/wiki/Differential_evolutionhttp://en.wikipedia.org/wiki/Swarm_intelligencehttp://en.wikipedia.org/wiki/Ant_colony_optimizationhttp://en.wikipedia.org/wiki/Particle_swarm_optimizationhttp://en.wikipedia.org/wiki/Artificial_Bee_Colony_Algorithmhttp://en.wikipedia.org/wiki/Artificial_Bee_Colony_Algorithmhttp://en.wikipedia.org/wiki/Particle_swarm_optimizationhttp://en.wikipedia.org/wiki/Ant_colony_optimizationhttp://en.wikipedia.org/wiki/Swarm_intelligencehttp://en.wikipedia.org/wiki/Differential_evolutionhttp://en.wikipedia.org/wiki/Evolution_strategyhttp://en.wikipedia.org/wiki/Evolutionary_programminghttp://en.wikipedia.org/wiki/Genetic_programminghttp://en.wikipedia.org/wiki/Genetic_algorithmhttp://en.wikipedia.org/wiki/Gene_expression_programminghttp://en.wikipedia.org/wiki/Evolutionary_algorithmhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Mathematical_optimizationhttp://en.wikipedia.org/wiki/Metaheuristichttp://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Parallel_processinghttp://en.wikipedia.org/wiki/Randomhttp://en.wikipedia.org/wiki/Artificial_selectionhttp://en.wikipedia.org/wiki/Stochastic_optimizationhttp://en.wikipedia.org/wiki/Metaheuristichttp://en.wikipedia.org/wiki/Global_optimizationhttp://en.wikipedia.org/wiki/Combinatorial_optimizationhttp://en.wikipedia.org/wiki/Combinatorial_optimizationhttp://en.wikipedia.org/wiki/Continuous_optimizationhttp://en.wikipedia.org/wiki/Computational_intelligencehttp://en.wikipedia.org/wiki/Artificial_intelligencehttp://en.wikipedia.org/wiki/Computer_science


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Bees algorithm

Artificial life (also seedigital organism)

Artificial immune systems

Cultural algorithms

Harmony search

Learning classifier systems

Learnable Evolution Model

Self-organization such asself-organizing maps,competitive learning

Evolutionary algorithms

Evolutionary algorithms form a subset of evolutionary computation in that they generally only

involve techniques implementing mechanisms inspired by biological evolution such as

reproduction, mutation, recombination, natural selection and survival of the fittest. Candidatesolutions to the optimization problem play the role of individuals in a population, and the cost

function determines the environment within which the solutions "live" (see also fitness

function).Evolutionof the population then takes place after the repeated application of the above

operators.

In this process, there are two main forces that form the basis of evolutionary

systems: Recombination and mutation create the necessary diversity and thereby facilitate

novelty, while selectionacts as a force increasing quality.

Many aspects of such an evolutionary process arestochastic.Changed pieces of information due

to recombination and mutation are randomly chosen. On the other hand, selection operators can

be either deterministic, or stochastic. In the latter case, individuals with a higherfitnesshave a

higher chance to be selected than individuals with a lowerfitness,but typically even the weak

individuals have a chance to become a parent or to survive.

Evolutionary algorithm :

Inartificial intelligence,an evolutionary algorithm(EA) is asubset ofevolutionary computation,

a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms

inspired by biological evolution, such as reproduction, mutation, recombination,and selection.Candidate solutions to the optimization problem play the role of individuals in a

population, and the fitness function determines the quality of the solutions (see also loss

function).Evolution of the population then takes place after the repeated application of the above

operators. Artificial evolution (AE) describes a process involving individual evolutionary

algorithms; EAs are individual components that participate in an AE.
http://en.wikipedia.org/wiki/Bees_algorithmhttp://en.wikipedia.org/wiki/Artificial_lifehttp://en.wikipedia.org/wiki/Digital_organismhttp://en.wikipedia.org/wiki/Artificial_immune_systemhttp://en.wikipedia.org/wiki/Cultural_algorithmhttp://en.wikipedia.org/wiki/Harmony_searchhttp://en.wikipedia.org/wiki/Learning_classifier_systemhttp://en.wikipedia.org/wiki/Learnable_Evolution_Modelhttp://en.wikipedia.org/wiki/Self-organizationhttp://en.wikipedia.org/wiki/Self-organizing_maphttp://en.wikipedia.org/wiki/Competitive_learninghttp://en.wikipedia.org/wiki/Evolutionary_algorithmshttp://en.wikipedia.org/wiki/Evolutionary_algorithmshttp://en.wikipedia.org/wiki/Biological_evolutionhttp://en.wikipedia.org/wiki/Biological_evolutionhttp://en.wikipedia.org/wiki/Reproductionhttp://en.wikipedia.org/wiki/Reproductionhttp://en.wikipedia.org/wiki/Mutationhttp://en.wikipedia.org/wiki/Mutationhttp://en.wikipedia.org/wiki/Genetic_recombinationhttp://en.wikipedia.org/wiki/Genetic_recombinationhttp://en.wikipedia.org/wiki/Natural_selectionhttp://en.wikipedia.org/wiki/Natural_selectionhttp://en.wikipedia.org/wiki/Survival_of_the_fittesthttp://en.wikipedia.org/wiki/Survival_of_the_fittesthttp://en.wikipedia.org/wiki/Candidate_solutionshttp://en.wikipedia.org/wiki/Candidate_solutionshttp://en.wikipedia.org/wiki/Candidate_solutionshttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Stochastichttp://en.wikipedia.org/wiki/Stochastichttp://en.wikipedia.org/wiki/Stochastichttp://en.wikipedia.org/wiki/Physical_fitnesshttp://en.wikipedia.org/wiki/Physical_fitnesshttp://en.wikipedia.org/wiki/Physical_fitnesshttp://en.wikipedia.org/wiki/Physical_fitnesshttp://en.wikipedia.org/wiki/Physical_fitnesshttp://en.wikipedia.org/wiki/Physical_fitnesshttp://en.wikipedia.org/wiki/Artificial_intelligencehttp://en.wikipedia.org/wiki/Subsethttp://en.wikipedia.org/wiki/Evolutionary_computationhttp://en.wikipedia.org/wiki/Metaheuristichttp://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Biological_evolutionhttp://en.wikipedia.org/wiki/Reproductionhttp://en.wikipedia.org/wiki/Mutationhttp://en.wikipedia.org/wiki/Genetic_recombinationhttp://en.wikipedia.org/wiki/Natural_selectionhttp://en.wikipedia.org/wiki/Candidate_solutionhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Candidate_solutionhttp://en.wikipedia.org/wiki/Natural_selectionhttp://en.wikipedia.org/wiki/Genetic_recombinationhttp://en.wikipedia.org/wiki/Mutationhttp://en.wikipedia.org/wiki/Reproductionhttp://en.wikipedia.org/wiki/Biological_evolutionhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Metaheuristichttp://en.wikipedia.org/wiki/Evolutionary_computationhttp://en.wikipedia.org/wiki/Subsethttp://en.wikipedia.org/wiki/Artificial_intelligencehttp://en.wikipedia.org/wiki/Physical_fitnesshttp://en.wikipedia.org/wiki/Physical_fitnesshttp://en.wikipedia.org/wiki/Stochastichttp://en.wikipedia.org/wiki/Evolutionhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Fitness_functionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Loss_functionhttp://en.wikipedia.org/wiki/Candidate_solutionshttp://en.wikipedia.org/wiki/Candidate_solutionshttp://en.wikipedia.org/wiki/Survival_of_the_fittesthttp://en.wikipedia.org/wiki/Natural_selectionhttp://en.wikipedia.org/wiki/Genetic_recombinationhttp://en.wikipedia.org/wiki/Mutationhttp://en.wikipedia.org/wiki/Reproductionhttp://en.wikipedia.org/wiki/Biological_evolutionhttp://en.wikipedia.org/wiki/Evolutionary_algorithmshttp://en.wikipedia.org/wiki/Competitive_learninghttp://en.wikipedia.org/wiki/Self-organizing_maphttp://en.wikipedia.org/wiki/Self-organizationhttp://en.wikipedia.org/wiki/Learnable_Evolution_Modelhttp://en.wikipedia.org/wiki/Learning_classifier_systemhttp://en.wikipedia.org/wiki/Harmony_searchhttp://en.wikipedia.org/wiki/Cultural_algorithmhttp://en.wikipedia.org/wiki/Artificial_immune_systemhttp://en.wikipedia.org/wiki/Digital_organismhttp://en.wikipedia.org/wiki/Artificial_lifehttp://en.wikipedia.org/wiki/Bees_algorithm


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Evolutionary algorithms often perform well approximating solutions to all types of problems

because they ideally do not make any assumption about the underlying fitness landscape;this

generality is shown by successes in fields as diverse

asengineering,art,biology,economics,marketing,genetics,operations research,robotics,social

sciences,physics,politics andchemistry.

Techniques from evolutionary algorithms applied to the modeling of biological evolution are

generally limited to explorations of micro evolutionary processes. The computer

simulationsTierra andAvida attempt to modelmacro evolutionary dynamics.

In most real applications of EAs, computational complexity is a prohibiting factor. In fact, this

computational complexity is due to fitness function evaluation.Fitness approximation is one of

the solutions to overcome this difficulty. However, seemingly simple EA can solve often complex

problems; therefore, there may be no direct link between algorithm complexity and problem

complexity.

Implementation of biological processes :

1. Generate the initialpopulation ofindividuals randomly - first Generation

2. Evaluate thefitness of each individual in that population

3. Repeat on thisgeneration until termination (time limit, sufficient fitness achieved, etc.):

1. Select the best-fit individuals forreproduction - parents

2.Breed new individuals throughcrossover and mutation operations to give birthtooffspring

3. Evaluate the individual fitness of new individuals

4. Replace least-fit population with new individuals

Evolutionary algorithm types :

Similar techniques differ in the implementation details and the nature of the particular applied

problem.

Genetic algorithm - This is the most popular type of EA. One seeks the solution of a problem

in the form of strings of numbers (traditionally binary, although the best representations are

usually those that reflect something about the problem being solved), by applying operators

such as recombination and mutation (sometimes one, sometimes both). This type of EA is

often used inoptimization problems.

Genetic programming - Here the solutions are in the form of computer programs, and their

fitness is determined by their ability to solve a computational problem.

Evolutionary programming - Similar to genetic programming, but the structure of the program

is fixed and its numerical parameters are allowed to evolve.
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Gene expression programming - Like genetic programming, GEP also evolves computer

programs but it explores a genotype-phenotype system, where computer programs of

different sizes are encoded in linear chromosomes of fixed length.

Evolution strategy - Works with vectors of real numbers as representations of solutions, and

typically uses self-adaptive mutation rates. Differential evolution - Based on vector differences and is therefore primarily suited

fornumerical optimization problems.

Neuro evolution - Similar to genetic programming but the genomes represent artificial neural

networks by describing structure and connection weights. The genome encoding can be direct

or indirect.

Learning classifier system - Here the solutions are classifiers (rules or conditions). A

Michigan-LCS works with individual classifiers whereas a Pittsburgh-LCS uses populations of

classifier-sets. Initially, classifiers were only binary, but now include real, neural net, orS-

expression types. Fitness is determined with either a strength or accuracy basedreinforcement approach.

SWARM INTELLIGENCE :

Swarm intelligence (SI) is artificial intelligence based on the collective behavior of

decentralized, self-organized systems

Swarm intelligence (SI) is the collective behavior of decentralized, self-organized systems,

natural or artificial. The concept is employed in work onartificial intelligence.The expression wasintroduced byGerardo Beni and Jing Wang in 1989, in the context of cellular robotic systems.[1]

SI systems consist typically of a population of simpleagents orboids interacting locally with one

another and with their environment. The inspiration often comes from nature, especially biological

systems. The agents follow very simple rules, and although there is no centralized control

structure dictating how individual agents should behave, local, and to a certain degree random,

interactions between such agents lead to theemergence of "intelligent" global behavior, unknown

to the individual agents. Examples in natural systems of SI includeant colonies,birdflocking,

animalherding,bacterial growth,and fishschooling.The definition of swarm intelligence is still

not quite clear. In principle, it should be a multi-agent system that has self-organized behaviourthat shows some intelligent behaviour.

The application of swarm principles torobots is calledswarm robotics,while 'swarm intelligence'

refers to the more general set of algorithms. 'Swarm prediction' has been used in the context of

forecasting problems.
http://en.wikipedia.org/wiki/Gene_expression_programminghttp://en.wikipedia.org/wiki/Evolution_strategyhttp://en.wikipedia.org/wiki/Differential_evolutionhttp://en.wikipedia.org/wiki/Numerical_optimizationhttp://en.wikipedia.org/wiki/Neuroevolutionhttp://en.wikipedia.org/wiki/Learning_classifier_systemhttp://en.wikipedia.org/wiki/S-expressionhttp://en.wikipedia.org/wiki/S-expressionhttp://en.wikipedia.org/wiki/Collective_behaviorhttp://en.wikipedia.org/wiki/Decentralizationhttp://en.wikipedia.org/wiki/Self-organizationhttp://en.wikipedia.org/wiki/Artificial_intelligencehttp://en.wikipedia.org/wiki/Gerardo_Benihttp://en.wikipedia.org/wiki/Swarm_intelligence#cite_note-1http://en.wikipedia.org/wiki/Swarm_intelligence#cite_note-1http://en.wikipedia.org/wiki/Swarm_intelligence#cite_note-1http://en.wikipedia.org/wiki/Intelligent_agenthttp://en.wikipedia.org/wiki/Boidshttp://en.wikipedia.org/wiki/Emergencehttp://en.wikipedia.org/wiki/Ant_colonyhttp://en.wikipedia.org/wiki/Flocking_(behavior)http://en.wikipedia.org/wiki/Herdinghttp://en.wikipedia.org/wiki/Bacteria#Growth_and_reproductionhttp://en.wikipedia.org/wiki/Shoaling_and_schoolinghttp://en.wikipedia.org/wiki/Robothttp://en.wikipedia.org/wiki/Swarm_roboticshttp://en.wikipedia.org/wiki/Swarm_roboticshttp://en.wikipedia.org/wiki/Robothttp://en.wikipedia.org/wiki/Shoaling_and_schoolinghttp://en.wikipedia.org/wiki/Bacteria#Growth_and_reproductionhttp://en.wikipedia.org/wiki/Herdinghttp://en.wikipedia.org/wiki/Flocking_(behavior)http://en.wikipedia.org/wiki/Ant_colonyhttp://en.wikipedia.org/wiki/Emergencehttp://en.wikipedia.org/wiki/Boidshttp://en.wikipedia.org/wiki/Intelligent_agenthttp://en.wikipedia.org/wiki/Swarm_intelligence#cite_note-1http://en.wikipedia.org/wiki/Gerardo_Benihttp://en.wikipedia.org/wiki/Artificial_intelligencehttp://en.wikipedia.org/wiki/Self-organizationhttp://en.wikipedia.org/wiki/Decentralizationhttp://en.wikipedia.org/wiki/Collective_behaviorhttp://en.wikipedia.org/wiki/S-expressionhttp://en.wikipedia.org/wiki/S-expressionhttp://en.wikipedia.org/wiki/Learning_classifier_systemhttp://en.wikipedia.org/wiki/Neuroevolutionhttp://en.wikipedia.org/wiki/Numerical_optimizationhttp://en.wikipedia.org/wiki/Differential_evolutionhttp://en.wikipedia.org/wiki/Evolution_strategyhttp://en.wikipedia.org/wiki/Gene_expression_programming


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Example algorithms :

Particle swarm optimization

Particle swarm optimization (PSO) is aglobal optimization algorithm for dealing with problems in

which a best solution can be represented as a point or surface in an n-dimensional space.

Hypotheses are plotted in this space and seeded with an initial velocity, as well as a

communication channel between the particles. Particles then move through the solution space,

and are evaluated according to somefitness criterion after each timestep. Over time, particles are

accelerated towards those particles within their communication grouping which have better fitness

values. The main advantage of such an approach over other global minimization strategies such

as simulated annealing is that the large number of members that make up the particle swarm

make the technique impressively resilient to the problem oflocal minima.

Ant colony optimization

Ant colony optimization (ACO), introduced by Dorigo in his doctoral dissertation, is a class

of optimization algorithms modeled on the actions of an ant colony. ACO is a probabilistic

technique useful in problems that deal with finding better paths through graphs. Artificial 'ants'

simulation agentslocate optimal solutions by moving through aparameter spacerepresenting

all possible solutions. Natural ants lay downpheromones directing each other to resources while

exploring their environment. The simulated 'ants' similarly record their positions and the quality of

their solutions, so that in later simulation iterations more ants locate better solutions.

Artificial bee colony algorithm

Artificial bee colony algorithm (ABC) is a meta-heuristic algorithm introduced by Karaboga in

2005, and simulates the foraging behaviour of honey bees. The ABC algorithm has three phases:employed bee, onlooker bee and scout bee. In the employed bee and the onlooker bee phases,

bees exploit the sources by local searches in the neighbourhood of the solutions selected based

on deterministic selection in the employed bee phase and the probabilistic selection in the

onlooker bee phase. In the scout bee phase which is an analogy of abandoning exhausted food

sources in the foraging process, solutions that are not beneficial anymore for search progress are

abandoned, and new solutions are inserted instead of them to explore new regions in the search

space. The algorithm has a well-balanced exploration and exploitation ability.

Differential evolution

Differential evolution is similar to genetic algorithm and pattern search. It uses multiagents or

search vectors to carry out search. It has mutation and crossover, but do not have the global best

solution in its search equations, in contrast with the particle swarm optimization.
http://en.wikipedia.org/wiki/Particle_swarm_optimizationhttp://en.wikipedia.org/wiki/Global_optimizationhttp://en.wikipedia.org/wiki/Velocityhttp://en.wikipedia.org/wiki/Fitness_(biology)http://en.wikipedia.org/wiki/Simulated_annealinghttp://en.wikipedia.org/wiki/Local_minimahttp://en.wikipedia.org/wiki/Ant_colony_optimizationhttp://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Ant_colonyhttp://en.wikipedia.org/wiki/Probabilistic_algorithmhttp://en.wikipedia.org/wiki/Probabilistic_algorithmhttp://en.wikipedia.org/wiki/Parameter_spacehttp://en.wikipedia.org/wiki/Pheromonehttp://en.wikipedia.org/wiki/Artificial_bee_colony_algorithmhttp://en.wikipedia.org/wiki/Random_selectionhttp://en.wikipedia.org/wiki/Differential_evolutionhttp://en.wikipedia.org/wiki/Differential_evolutionhttp://en.wikipedia.org/wiki/Random_selectionhttp://en.wikipedia.org/wiki/Artificial_bee_colony_algorithmhttp://en.wikipedia.org/wiki/Pheromonehttp://en.wikipedia.org/wiki/Parameter_spacehttp://en.wikipedia.org/wiki/Probabilistic_algorithmhttp://en.wikipedia.org/wiki/Probabilistic_algorithmhttp://en.wikipedia.org/wiki/Ant_colonyhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Ant_colony_optimizationhttp://en.wikipedia.org/wiki/Local_minimahttp://en.wikipedia.org/wiki/Simulated_annealinghttp://en.wikipedia.org/wiki/Fitness_(biology)http://en.wikipedia.org/wiki/Velocityhttp://en.wikipedia.org/wiki/Global_optimizationhttp://en.wikipedia.org/wiki/Particle_swarm_optimization


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The bees algorithm

Thebees algorithm in its basic formulation was created by Pham and his co-workers in 2005 and

further refined in the following years.[7]Modelled on the foraging behaviour ofhoney bees, the

algorithm combines global explorative search with local exploitative search. A small number of

artificial bees (scouts) explores randomly the solution space (environment) for solutions of highfitness (highly profitable food sources), whilst the bulk of the population search (harvest) the

neighbourhood of the fittest solutions looking for the fitness optimum. A deterministics recruitment

procedure which simulates the waggle dance of biological bees is used to communicate the

scouts' findings to the foragers, and distribute the foragers depending on the fitness of the

neighbourhoods selected for local search. Once the search in the neighbourhood of a solution

stagnates, the local fitness optimum is considered to be found, and the site is abandoned. In

summary, the Bees Algorithm searches concurrently the most promising regions of the solution

space, whilst continuously sampling it in search of new favourable regions.

Artificial immune systems

Artificial immune systems (AIS) concerns the usage of abstract structure and function of the

immune system to computational systems, and investigating the application of these systems

towards solving computational problems from mathematics, engineering, and information

technology. AIS is a sub-field of Biologically inspired computing, and natural computation, with

interests in Machine Learning and belonging to the broader field of Artificial Intelligence.

Grey wolf optimizer

The Grey wolf optimizer (GWO) algorithm mimics the leadership hierarchy and hunting

mechanism of gray wolves in nature proposed by Mirjalili et al. in 2014.[8]Four types of grey

wolves such as alpha, beta, delta, and omega are employed for simulating the leadership

hierarchy. In addition, three main steps of hunting, searching for prey, encircling prey, and

attacking prey, are implemented to perform optimization.

Bat algorithm

Bat algorithm (BA) is a swarm-intelligence-based algorithm, inspired by theecholocation behavior

ofmicrobats.BA uses a frequency-tuning and automatic balance of exploration and exploitation

by controlling loudness and pulse emission rates.

Gravitational search algorithm

Gravitational search algorithm (GSA) based on the law of gravity and the notion of mass

interactions. The GSA algorithm uses the theory of Newtonian physics and its searcher agents

are the collection of masses. In GSA, there is an isolated system of masses. Using the

gravitational force, every mass in the system can see the situation of other masses. The

gravitational force is therefore a way of transferring information between different masses

(Rashedi, Nezamabadi-pour and Saryazdi 2009).[10] In GSA, agents are considered as objects
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and their performance is measured by their masses. All these objects attract each other by a

gravity force, and this force causes a movement of all objects globally towards the objects with

heavier masses. The heavy masses correspond to good solutions of the problem. The position of

the agent corresponds to a solution of the problem, and its mass is determined using a fitness

function. By lapse of time, masses are attracted by the heaviest mass. We hope that this masswould present an optimum solution in the search space. The GSA could be considered as an

isolated system of masses. It is like a small artificial world of masses obeying the Newtonian laws

of gravitation and motion (Rashedi, Nezamabadi-pour and Saryazdi 2009). A multi-objective

variant of GSA, called Non-dominated Sorting Gravitational Search Algorithm (NSGSA), was

proposed by Nobahari and Nikusokhan in 2011.

Altruism algorithm

Researchers in Switzerland have developed an algorithm based on Hamilton's rule of kin

selection. This algorithm shows how altruism in a swarm of entities can, over time, evolve and

result in more effective swarm behaviour.

Glowworm swarm optimization

Glowworm swarm optimization (GSO), introduced by Krishnanand and Ghose in 2005 for

simultaneous computation of multiple optima of multimodal functions.[14][15][16][17] The algorithm

shares a few features with some better known algorithms, such as ant colony

optimization andparticle swarm optimization,but with several significant differences. The agents

in GSO are thought of asglowworms that carry aluminescence quantity calledluciferin along with

them. The glowworms encode the fitness of their current locations, evaluated using the objective

function, into a luciferin value that they broadcast to their neighbors. The glowworm identifies its

neighbors and computes its movements by exploiting an adaptive neighborhood, which is

bounded above by its sensor range. Each glowworm selects, using aprobabilistic mechanism,a

neighbor that has a luciferin value higher than its own and moves toward it. These movements

based only on local information and selective neighbor interactionsenable the swarm of

glowworms to partition into disjoint subgroups that converge on multiple optima of a given

multimodal function.

Self-propelled particles

Self-propelled particles (SPP), also referred to as the Vicsek model, was introduced in 1995 by

Vicsek et al.as a special case of theboids model introduced in 1986 byReynolds.A swarm is

modelled in SPP by a collection of particles that move with a constant speed but respond to a

random perturbation by adopting at each time increment the average direction of motion of the

other particles in their local neighbourhood. SPP models predict that swarming animals share

certain properties at the group level, regardless of the type of animals in the swarm.Swarming

systems give rise toemergent behaviours which occur at many different scales, some of which
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are turning out to be both universal and robust. It has become a challenge in theoretical physics

to find minimal statistical models that capture these behaviours.

Stochastic diffusion search

Stochastic diffusion search (SDS) is an agent-basedprobabilistic global search and optimization

technique best suited to problems where the objective function can be decomposed into multiple

independent partial-functions. Each agent maintains a hypothesis which is iteratively tested by

evaluating a randomly selected partial objective function parameterized by the agent's current

hypothesis. In the standard version of SDS such partial function evaluations are binary, resulting

in each agent becoming active or inactive. Information on hypotheses is diffused across the

population via inter-agent communication. Unlike thestigmergic communication used in ACO, in

SDS agents communicatehypotheses via a one-to-one communication strategy analogous to the

tandem running procedure observed in Leptothorax acervorum.[27] A positive feedback

mechanism ensures that, over time, a population of agents stabilize around the global-best

solution. SDS is both an efficient and robust global search and optimization algorithm, which hasbeen extensively mathematically described. Recent work has involved merging the global search

properties of SDS with other swarm intelligence algorithms.

Multi-swarm optimization

Multi-swarm optimization is a variant of particle swarm optimization (PSO) based on the use of

multiple sub-swarms instead of one (standard) swarm. The general approach in multi-swarm

optimization is that each sub-swarm focuses on a specific region while a specific diversification

method decides where and when to launch the sub-swarms. The multi-swarm framework is

especially fitted for the optimization on multi-modal problems, where multiple (local) optima exist.
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soft computing unit-5 by arun pratap singh

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