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Genetic Optimization of Electric Machines, a State
of the Art Study
S. E. Skaar, R. Nilssen
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Outline of Presentation
•Introduction•Useful Terms in GA•Selection of encoding•Strategies to improve GA•GA used in design optimization of electrical machines•Summary
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Since J. H. Holland introduced the first Genetic Algorithm (GA) in 1975, GA has been used widely in various numerical optimization problems like:– combinatorial optimization– circuit design– design optimization of electrical devices
GAs are adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection and genetic
Introduction
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Useful Terms in GA In the following presentation a brief introduction to
GA will be given Some of the terms connected to GA will be presented
and given a brief description
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Flowchart of GA
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Phenotype:– refers to the outward characteristics of an
individual
Genotype:– the biological term refers to the overall genetic
make up of an individual
Practical example,For the number 232
GA the phenotype representation is: 232Genotype representation is: 11101000
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Allele:The allele is the status(/value) of an individual gene
Example:– binary representation of 11101000 (genotype)– each bit position corresponds to a gene of the chromosome– and each bit value corresponds to an allele
Number of states, K, for the gene:– for a low cardinality alphabet like the binary, K=2– each gene then can have the allele or state 0 or 1– from genetics we know DNA is represented with a cardinality
alphabet with K=4– the alleles here are A, C, G or T
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Encoding:– How the parameters are converted into a chromosome
string– Some encodings are:
• binary encoding
• Gray encoding
• real-number encoding
• integer or literal permutation encoding
• general data structure encoding
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Selection:– used in the reproduction loop, to select the parent individuals– can be accomplished using different strategies like:
• roulette wheel
• local tournament
• invoking of various ranking schemes
Fitness factor:– a factor used to evaluate selection (the first population) and
offspring (made by subsequent recombination)– fit offspring is kept, unfit offspring rejected– fitness factor ensures the “Survival of the fittest”- principle
laid down by Charles Darwin
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Mutation:– creation of new individuals (based on exciting ones) by
making changes in a single gene
– mutation only - represents a “random walk” in the neighbourhood of an accepted solution
– several mutation strategies exist
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Crossover:– creation of new individuals by combining parts from two parent
individuals
– several crossover strategies exist
– a variant of an Arithmetical Crossover called average crossover is illustrated in the figure above
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Hamming cliffs:– occurs when pairs of encoding in phenotype space has a
minimal distance, like the numbers 127 and 128– with binary encoding the genotype of these pairs would be
– to cross this Hamming cliff all bits has to change simultaneously
– the probability that mutation and crossover will occur may be very small
– in worst case this results in a large search space being unexplored, giving a premature convergence
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Elitism:– conservation of the best individuals of a generation
Penalty:– methods of penalizing infeasible solutions
Niching:– recombination within a limited sub-population– allows GA to finish a search within a niche population (with
diverse individuals)– make the GA capable of locating multiple optimal solutions
within a single population
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Selection of Encoding Presence of Hamming cliffs might effect the result of
an optimization using GA
Binary encoding handles Hamming cliffs poorly
Alternatives to binary encoding exist
Both real number and Gray encoding has been proposed
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Collins and Eaton claims there exists no encoding strategy performing well on all optimization problems
Goldberg states the selection of encoding to be far from clear cut– he describe the scenario of agonizing over the coding, and
recommend users to simply decide upon a prefered coding– his experience is that GA does “something” to whatever
coding and operator given– …and that this “something” oftentimes turns out surprisingly
good No clear advice on a specific coding selection is
given by GA researchers Adopting Goldberg's advice and keeping an overview
over pitfalls and problems for the chosen encoding might be the better approach
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Strategies to Improve GA Adopting GA to design
optimization of electrical machines will result in a multi dimensional solution space
For visualization let us assume a 3D space, like a chain of mountains
The majority of the tops would be local optima
Hopefully there is only one global optima
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With this kind of solution space one can not be sure to have found the right or best optimum
Using a simple GA (SGA), users will experience optima being lost
It is also hard to predict which optima is being chosen at each optimization run
The losses are due to three effects:– selection pressure– selection noise– operator disruption
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Selection noise (SN)– SN describes the variance of the generated population (example:
roulette wheel has a high SN)– a too low SN may give lack of convergence on small populations
Selection pressure– probability of the best individual being selected– can be reduced using fitness scaling
Operator disruption– population average should usually go up– if it goes up for a while, then goes down, this is due to operator
disruption– good solutions are then being replaced by worse offspring– to reduce operator disruption probability of crossover and mutation
can be lowered– will always exist a trade-off between diversity and convergence
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– to the extreme a probability of 0 for crossover and mutation would result in no selection pressure but also no useful search
– crossover does not introduce new alleles to the population– when a solution starts to converge, effect of crossover starts
to diminish– mutation introduce new alleles– having a high mutation rate would slow down convergence– high mutation rate gives a random variation and increased
disruption– this does not usually result in a useful diversity– a too high mutation rate will move GA towards a random
search method
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To enhance GA in performing better in design optimization, niching has proven feasible
Niching does a local hill climbing when encountering any “mountain” top
The result is then stored in a pool Next time the same top is encountered the GA steps
away, searching for a top not already climbed After an optimization the designer can analyse the
pool and explore solutions in a close radius to the different optima in the pool
In this way information of parameter values for several feasible solutions can be obtained
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GA used in design optimization of electrical machines
Study of work done in this field show changes/improvements in the use of GA
In the mid 90’s authors tend to use SGA with binary encoding
Recent work show a movement in the direction of using more complex GAs
There is also an growing awareness of the many aspects of GA
Niching has recently been tested with promising results
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Most of the papers on design optimization conclude GA to be a promising optimization method
Non of the papers gave GA a negative testimony The main advantages of GA was reported to be
– reasonable short computation time– no need of a good initial guess or starting point
Implementation of recombination and selective pressure effects the convergence of GA
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Summary An introduction to basic terms in GA has been given Selection of encoding and improvement strategies
has been discussed Using GA in design optimization of electrical
machines has been reported to be promising An evolution in the use of GA in this field was found
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Thank you for your attention