genetic optimization of electric machines, a state of the art study

15/06/2003 NORPIE 2004, Trondheim 1

Genetic Optimization of Electric Machines, a State

of the Art Study

S. E. Skaar, R. Nilssen


Outline of Presentation

•Introduction•Useful Terms in GA•Selection of encoding•Strategies to improve GA•GA used in design optimization of electrical machines•Summary


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


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


Flowchart of GA


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


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


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


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


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


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


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


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


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


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


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


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


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


– 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


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


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


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


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


Thank you for your attention

genetic optimization of electric machines, a state of the art study

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