Evolutionary computing - soft computing

EVOLUTIONARY
COMPUTING
Submitted By: Sakshi Mahto M.Sc IV sem

Introduction
Evolutionary Computing is a research area within computer science. As the name
suggest, it is a special flavour of computing, which draws inspiration from the
process of natural evolution. The fundamental metaphor of evolutionary computing
relates this powerful natural evolution to a particular style of problem solving – that
of trial and error.
Evolutionary Computing: Why?
Evolutionary processes are subjects of scientific studies where the main objective is
to understand how evolution work. From the perspective of evolutionary computing
Represents the possibility of performing experiments differently from traditional
biology.
Evolutionary computation techniques can produce highly optimized solutions in a
wide range of problem settings, making them popular in computer science. Many
variants and extensions exist, suited to more specific families of problems and data
structures. Evolutionary computation is also sometimes used in evolutionary
biology as an in silico experimental procedure to study common aspects of general
evolutionary processes.

Flow chart of Evolutionary Computing

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. Candidate solutions 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). Evolution of 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 selection acts as a force increasing quality.
Many aspects of such an evolutionary process are stochastic. 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 higher fitness have a higher chance to be selected than
individuals with a lower fitness, but typically even the weak individuals have a
chance to become a parent or to survive.

Genetic algorithms and optimization
Genetic algorithms, as powerful and broadly applicable search and
optimization techniques, are perhaps the most widely known types of
evolutionary computation method today.
In general, a genetic algorithm has five basic components, as
summarized by Michalewicz.
1. A genetic representation of solutions to the problem.
2. A way to create an initial population of solutions.
3. An evaluation function rating solutions in terms of their fitness.
4. Genetic operators that alter the genetic composition of children
during reproduction.
5. Values for the parameters of genetic algorithms.

Flow Chart of Genetic Algorithm

The genetic algorithm maintains a population of individuals, say P(t), take t for
generations. Each Individual represents a potential solution to the problem.
Some individual undergo stochastic (having a random probability distribution)
transformation means of genetic operations to form new individuals
There are two type of transformation:
1.Mutation – Which creates new individuals by making changes in a single
individual.
2.Crossover – Which creates new individuals by combining parts of two
individuals.
New individuals called offspring C(t). A new populations is formed by
selecting the more fit individuals from parent population and offspring
population. The algorithim converges to the best individual, which hopefully
represent an optimal or suboptimal solution to the problem.

Procedure: Genetic Algorithm
begin
t 0;
initialize P(t);
evaluate P(t);
while (not termination condition) do
begin
recombine P(t) to yield C(t);
evaluate C(t);
select P(t + 1) from P(t) and C(t);
t t + 1;
end
end
One general principle for developing an implementation of genetic algorithms for
a real-world problem is to make a good balance between exploration and
exploitation of the search space.

The Schema Theorem
The two most important theoretical foundations of Genetic Algorithm are
Holland’s schema theorem and Goldberg’s building-block hypothesis.
The convergence analysis of simple genetic algorithm is based on concept of
schema. A schema is a bit pattern that functions as a set of binary strings.
The schema theorem asserts that the proportions of the better
schemata(similarly template) to the overall population increases as the
generation progresses and the search converges to the best solution with
respect to the optimization function.
The schema theory of genetic algorithm aims to predict the expected numbers
of solution in a given schema(a subset of the search space). According to
schema theorem, schemata with high fitness and small defining lengths
grow exponentially with time.
The exact schema theorem for genetic algorithm have been derived for
exactly predicting expected characteristics of the population of next
generation. The schema theorem based on concept of effective fitness.

Here m(H,t) is the number of strings belonging to schema H at
generation t, f(H) is the observed average fitness of schema H and at is
the observed average fitness at generation t. The probability of disruption p is
the probability that crossover or mutation will destroy the schema H.
where o(H) is the order of the schema, l is the length of the code, pm is the
probability of mutation and pc is the probability of crossover. So a schema with
a shorter defining length δ(H) is less likely to be disrupted.

Genetic Operators
A genetic operator is an operator used in genetic algorithms to guide the
algorithm towards a solution to a given problem. There are three main types of
operators (mutation, crossover and selection), which must work in
conjunction with one another in order for the algorithm to be successful.
Genetic operators are used to create and maintain genetic diversity (mutation
operator), combine existing solutions (also known as chromosomes) into new
solutions (crossover) and select between solutions (selection).
Mutation (or mutation-like) operators are said to be unary operators, as they
only operate on one chromosome at a time. In contrast, crossover operators are
said to be binary operators, as they operate on two chromosomes at a time,
combining two existing chromosomes into one new chromosome.

Operators
Selection: Selection operators give preference to better solutions (chromosomes),
allowing them to pass on their 'genes' to the next generation of the algorithm. The
best solutions are determined using some form of objective function (also known as
a 'fitness function' in genetic algorithms), before being passed to the crossover
operator. Different methods for choosing the best solutions exist, for example, fitness
proportionate selection and tournament selection.
Crossover : Crossover is the process of taking more than one parent solutions
(chromosomes) and producing a child solution from them. By recombining portions
of good solutions, the genetic algorithm is more likely to create a better
solution. The 'cut and splice crossover' and 'uniform crossover' methods. The
crossover method is often chosen to closely match the chromosome's representation
of the solution, this may become particularly important when variables are grouped
together as building blocks, which might be disrupted by a non-respectful crossover
operator.

Mutation: The mutation operator encourages genetic diversity amongst
solutions and attempts to prevent the genetic algorithm converging to a local
minimum by stopping the solutions becoming too close to one another. In
mutating the current pool of solutions, a given solution may change entirely
from the previous solution. By mutating the solutions, a genetic algorithm can
reach an improved solution solely through the mutation operator. Again,
different methods of mutation may be used; these range from a simple bit
mutation (flipping random bits in a binary string chromosome with some low
probability) to more complex mutation methods, which may replace genes in
the solution with random values chosen from the uniform distribution or
the Gaussian distribution. As with the crossover operator, the mutation
method is usually chosen to match the representation of the solution within
the chromosome.
While each operator acts to improve the solutions produced by the genetic
algorithm working individually, the operators must work in conjunction with
each other for the algorithm to be successful in finding a good solution. Using the
selection operator on its own will tend to fill the solution population with copies
of the best solution from the population. If the selection and crossover operators
are used without the mutation operator, the algorithm will tend to converge to
a local minimum, that is, a good but sub-optimal solution to the problem.

Genetic Algorithms with neural networks
An neural network, in general is a highly interconnected network of a large
number of processing elements called neurons in an architecture inspired by
the brain. An NN can be massively parallel and therefore is said exhibit
parallel distributing processing.
Neuro-Genetic Hybrids: Genetic algorithms offered themselves as
potential candidate to neural network in 1989,1990). The integration of
GA(genetic algorithms) with NN(neural network) has turned out
useful(Schaffer et al., 1992).
Genetic algorithms encode the parameters of NN as a string of the
properties of the network, this is, chromosomes. A large population of
chromosomes representing the many possible parameter sets for the given
NN is generated. Combined GA-NN technology also known as ‘GANN’
have ability to locate the neighbourhood of the optimal solution .
Drawbacks of GANN algorithim are:
The large amount of memory required to handle and manipulate
chromosomes for a given network.

Fuzzy-Genetic Hybrids
Fuzzy systems have been integrated with GA. Kosko (1992) has shown that
fuzzy systems line NN are universal approximates in the fact that they exhibit
the capability to approximate general nonlinear functions to any desired
degree of accuracy.
When it comes to automatically identifying and building a fuzzy system, given
the high degree of nonlinearity of the output, traditional linear optimization
tools have several limitations. Therefore, in the framework of soft computing,
genetic algorithms (GAs) and genetic programming (GP) methods have been
used successfully to identify structure and parameters of fuzzy systems.
Genetic algorithms for fuzzy system identification:
Given the high degree of nonlinearity of the output of a fuzzy system,
traditional linear optimization tools do have their limitations. Genetic
algorithms have demonstrated to be a robust and very powerful tool to
perform tasks such as the generation of fuzzy rule base, optimization of fuzzy
rule bases, generation of membership functions, and tuning of membership
functions (Cordón et al., 2001a). All these tasks can be considered as
optimization or search processes within large solution spaces (Bastian and
Hayashi, 1995) (Yuan and Zhuang, 1996) (Cordón et al., 2001)

Fuzzy genetic algorithm approach

Issues In GA
There are two important issues with respect to search strategies: exploiting the
best solution and exploring the search space. The genetic algorithm provide a
directed random search in complex landscapes. Genetic operators perform
essentially a blind search.
Encoding Issue:
How to encode a solution of the problem into a chromosome is a key issue
when using genetic algorithms. The issue has been investigated from many
aspects, such as mapping characters from genotype space to phenotype
space

Bibliography
Google Books:
https://books.google.co.in/books?id=U7MuV1q6P1oC&printsec=frontcover&dq
=genetic+algorithm+and+optimization&hl=en&sa=X&ved=0ahUKEwjtpKvL14Lp
AhWqyDgGHRiKAw4Q6AEIMDAB#v=onepage&q=genetic%20algorithm%20a
nd%20optimization&f=false
https://books.google.co.in/books?id=0eznlz0TF-
IC&pg=PA30&dq=the+schema+theorem&hl=en&sa=X&ved=0ahUKEwiy2rfB54
LpAhXfxDgGHTMrB88Q6AEIKzAA#v=onepage&q=the%20schema%20theore
m&f=false
https://books.google.co.in/books?id=bVbj9nhvHd4C&printsec=frontcover&dq=
Genetic+algorithm+with+neural+network&hl=en&sa=X&ved=0ahUKEwja9oGvi
oPpAhWizjgGHaVGDwAQ6AEIPTAC#v=onepage&q=Genetic%20algorithm%2
0with%20neural%20network&f=false
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