Chapter 12

FUSION OF FUZZY SYSTEM AND GENETIC ALGORITHMS

Chi-Yuan Yeh

Genetic Algorithms

• Proposed by John Holland (1975)

• A Genetic Algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimization and search problems.

• GA uses techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover.

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Genetic Algorithm Flowchart

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Operations in Genetic Algorithms

1) Initialize a population of chromosomes (population size = n).

2) Evaluate the fitness of each chromosome in the population.

3) If the stop condition is satisfied, stop and return the best chromosome in the population.

4) Select n/2 pairs of chromosomes from the population. Chromosomes can be selected several times.

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Operations in Genetic Algorithms

5) Create new n chromosomes by mating the selected pairs by applying the crossover operator.

6) Apply the mutation operator to the new chromosomes.

7) Replace the old population with the new chromosomes.

8) Goto (2).

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Requirements in Genetic Algorithms

• Genetic Representation– A way of representing solutions/individuals in evolutionary

computation methods.

• Fitness Function:– A particular type of objective function that quantifies the

optimality of a solution

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Encoding Scheme

• Binary encoding– In binary encoding every chromosome is a string of bits, 0

or 1.

• Chromosome A: 101100101100101011100101

• Chromosome B: 111111100000110000011111

– Binary encoding is the most common, mainly because first works about GA used this type of encoding.

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Encoding Scheme

• Permutation Encoding– In permutation encoding, every chromosome is a string of

numbers, which represents number in a sequence.

• Chromosome A: 1 5 3 2 6 4 7 9 8

• Chromosome B: 8 5 6 7 2 3 1 4 9

– Permutation encoding can be used in ordering problems, such as travelling salesman problem or task ordering problem.

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Encoding Scheme

• Real-Valued Encoding – In real-value encoding, every chromosome is a string of

some values.

• Chromosome A: 1.2324 5.3243 0.4556 2.3293 2.4545

• Chromosome B: 2.3245 2.3253 4.4656 5.2193 0.8721

– Direct value encoding can be used in problems, where some complicated value, such as real numbers, are used.

– Use of binary encoding for this type of problems would be very difficult.

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Selection

• Selection is an operation which prepares reproductions.

• The selected chromosomes are called parents.

• Selection method– Roulette wheel selection

– Rank based selection• (0.3,0.25,0.2,0.15,0.1)

– …

10From: http://www.edc.ncl.ac.uk/highlight/rhjanuary2007g02.php/

Crossover

• Crossover operators produce two new chromosomes by exchanging information of the selected chromosomes.

• Crossover method– One-point

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Crossover

– Two-point

– …

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Crossover

• The crossover operations are not performed on every selected chromosome.

• Genetic algorithm decides, based on a given probability, whether it performs the crossover operation on the certain pair of chromosomes or not.

• It is called the crossover probability and given by users.

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Mutation

• Mutation operators change some randomly selected bits of chromosomes.

• If the chromosomes are binary strings, then ‘0’ are changed to ‘1’, and ‘1’ to ‘0’. It plays a secondary role after the crossover operator in genetic algorithms.

• The changing bits means making an offspring genetically different from its parents.

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Replacement

• A typical genetic algorithm totally replaces the old population with the newly created chromosomes, but it is not mandatory.

• There could be many variations.

• For example, after reproduction, the old and new populations are taken together, and among them the best n chromosomes are selected as the next population.

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Elitist strategy

• In order to escape from a local optimum, a kind of jump operation is needed. So, by using the mutation operator, we can get some offsprings different from their parents. That is, the genetic algorithms try to jump to other place.

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Fusion with Genetic Algorithms

• Identifying fuzzy systems with genetic algorithms

• Controlling parameters of genetic algorithms with fuzzy systems

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Identifying fuzzy systems with genetic algorithms

• Schematic diagram of identifying FSs with GAs

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Identifying fuzzy systems with genetic algorithms

• Tuning an existing fuzzy system

• Building a fuzzy system with genetic algorithm

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Tuning an existing fuzzy system

• Four fuzzy rules:

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Building a fuzzy system with genetic algorithm

• This method do not need an existing fuzzy system. This approach determines all the parameters of a fuzzy system by genetic algorithms without any priori knowledge.

• Thus, the chromosomes used in this method usually include most of the parameters such as the number and membership functions of linguistic terms.

• So, it is very important how to effectively represent those parameters because a long chromosome means a wide search space.

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Building a fuzzy system with genetic algorithm

• If a search space is wide, we cannot expect a good optimization result.

• So, most researches make restrictions; for example, some fix the number of linguistic terms or restrict the shape and position of membership functions.

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Building a fuzzy system with genetic algorithm

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Building a fuzzy system with genetic algorithm

• Determination of consequent parts

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Building a fuzzy system with genetic algorithm

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Controlling parameters of genetic algorithms with fuzzy systems

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Thanks for your attention!