Fuzzy Genetic Algorithm

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Fuzzy Genetic Algorithm A Solution to The Problem 1

description

A brief idea about Fuzzy Genetic Algorithm and its application.

Transcript of Fuzzy Genetic Algorithm

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Fuzzy Genetic Algorithm

A Solution to The Problem

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….Contents…. Introduction

Fuzzy logic

Genetic Algorithm

Fuzzy Genetic Algorithm

Different FGA Approach

Application Sector

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INTRODUCTION

After scientists became disillusioned with classical and neo-

classical attempts at modeling intelligence, they looked in other

directions.

Two prominent fields arose, connectionism (neural networking,

parallel processing) and evolutionary computing.

It is the latter that this essay deals with - genetic algorithms and

genetic programming.

Fuzzy logic is a form of many-valued logic

A Fuzzy Genetic Algorithm (FGA) is considered as a GA that uses

fuzzy logic based techniques

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WHAT IS FUZZY LOGIC? Definition of fuzzy

Fuzzy – “not clear, distinct, or precise; blurred”

Definition of fuzzy logic A form of knowledge representation suitable

for notions that cannot be defined precisely, but which depend upon their contexts.

Compared to traditional binary sets fuzzy logic variables may have a truth value that ranges in degree between 0 and 1

Membership Function The membership function represents the

degree of truth as an extension of valuation.

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FUZZY LOGIC - HISTORY

The term "fuzzy logic" was introduced with

the 1965 proposal of fuzzy set theory by

Lotfi A. Zadeh.

Fuzzy logic has been applied to many fields,

from control theory to artificial intelligence.

Fuzzy logics however had been studied

since the 1920s as infinite-valued logics

notably by Łukasiewicz and Tarski.

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A point on that scale has three "truth values"—one for each of the

three functions.

red arrow points to zero, this temperature may be interpreted as

"not hot“

The orange arrow (pointing at 0.2) may describe it as "slightly

warm“

The blue arrow (pointing at 0.8) "fairly cold"

Fuzzy Truth Values

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What is Genetic Algorithm?

A genetic algorithm (or GA) is a search technique used in

computing to find true or approximate solutions to

optimization and search problems.

Genetic algorithms are categorized as global search heuristics.

Genetic algorithms are a particular class of evolutionary

algorithms that use techniques inspired by evolutionary

biology such as inheritance, mutation, selection, and

crossover (also called recombination).

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The new population is then used in the next iteration of the

algorithm.

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.

If the algorithm has terminated due to a maximum number of

generations, a satisfactory solution may or may not have been

reached.

What is Genetic Algorithm?

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Genetic Algorithm Flow ChartInitial Population

Selection

Mating

Crossover

Mutation

Terminate

• The evolution usually starts from a

population of randomly generated

individuals

• Individual solutions are selected through

a fitness-based process

• This generational process is repeated

until a termination condition has been

reached.

• improve the solution through repetitive

application of the mutation, crossover,

inversion and selection operators

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FUZZY GENETIC ALGORITHM The use of FL based techniques for either improving GA behaviour and

modeling GA components, the results obtained have been called fuzzy genetic algorithms (FGAs),

The application of GAs in various optimization and search problems involving fuzzy systems.

An FGA may be defined as an ordering sequence of instructions in which some of the instructions or algorithm components may be designed with fuzzy logic based tools

A fuzzy fitness finding mechanism guides the GA through the search space by combining the contributions of various criteria/features that have been identified as the governing factors for the formation of the clusters.

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A single objective optimization model cannot serve the purpose of a fitness

measuring index because we are looking at multiple criteria that could be

responsible for stringing together data items into clusters. This is true; not

only for the clustering problem but for any problem solving using GA that

involves multiple criteria. In multi-criteria optimization, the notion of

optimality is not clearly defined. A solution may be best w.r.t. one criterion

but not so w.r.t. the other criteria. Pareto optimality offers a set of non-

dominated solutions called the P-optimal set where the integrity of each of

the criteria is respected.

WHY FGA?

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The algorithm has two computational elements that work together.i) The Genetic Algorithm (GA) andii) The Fuzzy Fitness Finder (FFF).

FGA Model

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Cossover is a genetic operator used to vary the programming of a chromosome or chromosomes from one generation to the next. It is analogous to reproduction and biological crossover, upon which genetic algorithms are based. Cross over is a process of taking more than one parent solutions and producing a child solution from them.

Crossover

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Mutation is a genetic operator used to maintain genetic diversity from one generation of a population of genetic algorithm chromosomes to the next.

It is analogous to biological mutation. Mutation alters one or more gene values in a chromosome from its initial state.

In mutation, the solution may change entirely from the previous solution. Hence GA can come to better solution by using mutation.

Mutation occurs during evolution according to a user-definable mutation probability.

This probability should be set low. If it is set too high, the search will turn into a primitive random search.

Mutation

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Flowchart of FGA

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FGA

Fuzzy

While the population of the genetic algorithm undergoes evolution at every generation, the relatively ‘good’ solutions reproduce while the relatively ‘bad’ solutions die. To distinguish between solutions, an objective (evaluation) function is used. In the simple cases, there is only one criterion for optimization for example, maximization of profit or minimization of cost. But in many real-world decision making problems, there is a need for simultaneous optimization of multiple objectives.

GA

· A genetic representation for potential solutions to the problem.· Method to create an initial population of potential solutions· An evaluation function to rate solutions in terms of their “fitness”· Selection of individuals for the next generation· Genetic operators that alter the composition of the childrenIn order to make a successful run of a GA, the values for the parameters of the GA have to be defined like the population size, parameters for the genetic operators and the terminating condition.

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Steps of Fuzzy in FGA• The Fuzzy Fitness Finder• Input and Output Criteria

• Fuzzification of Inputs• Fuzzy Inference Engine

• Defuzzification of Output

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Different FGA Approach

Pittsburgh Approach

Iterative Rule Learning Approach

Michigan Approach

The Nagoya Approach

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Application Sector

Electrical Engg.

Mechanical Engg.

Economics

Artificial Intelligence

Approx. in all sectors of life.

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Thank You