influence of the migration process on the learning ...¾pop n. École polytechnique de montréal...

Influence of the Migration Process on Influence of the Migration Process on the Learning Performances of Fuzzy the Learning Performances of Fuzzy

Knowledge BasesKnowledge Bases

Khaled Akrout, Luc Baron, Marek Balazinski and Sofiane Achiche

École Polytechnique de Montréal, Québec, Canada

École Polytechnique de Montréal 2/24

OutlineOutlineIntroductionIntroductionProblem DefinitionProblem DefinitionReal Coded Genetic Algorithm Real Coded Genetic Algorithm (RCGA)(RCGA)Real/Binary Like Coded GeneticReal/Binary Like Coded GeneticAlgorithm (RBLGA)Algorithm (RBLGA)MigrationMigration

-- Learning Learning underunder Migration Migration ConclusionsConclusions


Problem DefinitionProblem Definition

The use of Fuzzy Decision Support The use of Fuzzy Decision Support System requires an expert to build the System requires an expert to build the Fuzzy Knowledge Base (FKB)Fuzzy Knowledge Base (FKB)Automatic generation of FKB using a Automatic generation of FKB using a binary coded Genetic Algorithm has been binary coded Genetic Algorithm has been already developed already developed A real/binary like coded Genetic A real/binary like coded Genetic Algorithm (RBLGA) is shown in this Algorithm (RBLGA) is shown in this presentationpresentation


Fuzzy Decision Support System•• Screen printout of the FDSS FuzzyScreen printout of the FDSS Fuzzy--FlouFlou


Real Coded Genetic Algorithm (RCGA)Real Coded Genetic Algorithm (RCGA)

A GA is generally characterized by:A GA is generally characterized by:a coding scheme for each possible solution, using a coding scheme for each possible solution, using a set of real values;a set of real values;a fitness value that provides the quality of each a fitness value that provides the quality of each solution;solution;an initial set of solutions to the problem, called the an initial set of solutions to the problem, called the initial population, randomly generated or chosen initial population, randomly generated or chosen on a priori knowledge;on a priori knowledge;a set of reproduction, mutation and natural a set of reproduction, mutation and natural selection operators, that allow the evolution of the selection operators, that allow the evolution of the population.population.


Automatic learning process

Final solution


Automatic learning process


Coding of a FKB using a RBLCGACoding of a FKB using a RBLCGAChromosome

The full representation of the genotype (chromosome)

The genotype is represent by several sets of real and integer values, depending on the nature of the represented parameter

Chromosome of the fuzzy sets

A = {x1, x2, …, xi, …, xn}; xi are real values.

each value represents a summit of a fuzzy set

Chromosome of the fuzzy rules

B = {r1, r2, …, ri, … rk}, ri are integer values, k being the number of rules.


CodingFuzzy sets

Membership function Fuzzy rule- if X is X1

- and Y is Y1

- Then U is U1


Coding

Fuzzy sets

Conclusion : B = {u1, u2, u3, u4, u5}

Premise set : A = {x1, x2, x3, x4, x5}


CodingCodingFuzzy rules

Set of rules (integers) :

R = {r1 , r2 , … , ri , … , rk}

1 2 ik… …


ReproductionReproduction

The process is governed by the initiating probability The process is governed by the initiating probability pp11

This process is applied to the fuzzy sets onlyThis process is applied to the fuzzy sets only

Blended Crossover Alpha (BLXBlended Crossover Alpha (BLX--α) α) A, B the selected parents

A = {x1, x2, …, xi, …, xn} B = {y1, y2, …, yi, …, yn}

C being the offspring: C = {z1, z2, …, zi, …, zn}

maxi = maximum {xi, yi} mini = minimum {xi, yi} I = {maxi – mini} (α = 0.5)


ReproductionReproductionSimple Crossover (rules only)Simple Crossover (rules only)

Rfather = {rf1, rf2, …, rfi, …, rfk } Rmother = {rm1, rm2, …, rmi, …, rmk }

Roffspring = {rf1, rf2, …, rmi, …rmk}

Crossover site


Reproduction

Fuzzy set ReducerFuzzy set Reducer

This process is governed by the initiating probability This process is governed by the initiating probability PP22

Selected summit Fuzzy sets at the initial configuration

Fuzzy sets in the new configuration


MutationMutation

Mutation is a creation of an individual from an Mutation is a creation of an individual from an existing one by altering one gene.existing one by altering one gene.

The mutation is controlled by the probability The mutation is controlled by the probability pp33

The mutation used in this paper is an equivalent The mutation used in this paper is an equivalent to a BLXto a BLX--0.0, applied to one randomly selected 0.0, applied to one randomly selected individual.individual.


Evaluation & Natural SelectionEvaluation & Natural Selection

The objective function evaluates the The objective function evaluates the capacity of a knowledge base to capacity of a knowledge base to approximate the sampled data approximate the sampled data Fitness value Fitness value φ (φ (rmsrms))

Natural selection is performed on a Natural selection is performed on a population by keeping the most promising population by keeping the most promising individuals based on their fitness. individuals based on their fitness.


MigrationMigrationThree types of migration mechanisms betweenpopulations have been implemented :

Single migrationSingle migration

CircularCircular MigrationMigration

RandomRandom MigrationMigration


Single Migration

Single migration: at each generation only the bested FBKs is extracted from each population and transferred to the next population in the list.

Pop 1 Pop 2 Pop 3

Pop iPop jPop n


Circular MigrationCircular MigrationThe populations are placed into a circular list. At each generation a pourcentage of randomlyselected FBKs are extracted from each population and transfered to the next population in the list.

Pop 1 Pop 2 Pop 3

Pop iPop jPop n


Random MigrationRandom Migration

The random migration consists in extracting in each generation a percentage of randomly selected FBKs from each population and then redistributing them among the other populations.

Ens

Pop 1 …………………………….. …………………………………Pop 2 Pop 3

Pop iPop jPop n ………………………………. …………………………………

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Learning under random migrationImpact of the migration rate on the fitness


Learning under random migrationImpact of the number of generations on the fitness for the 2,4,8 and 16 populations


ConclusionsConclusionsA single migration does not improve the learning process

The application of migration process improves the learning performance in the neighborhood of the 30th generation:

2% for circular migration4.5% for random migration

The random migration process is the most effective for the migration rate of around 5%

Increasing the number of populations in the migration process slightly improves the performance by 1% to 2%.

influence of the migration process on the learning ...¾pop n. École polytechnique de montréal...

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