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Genetic Optimization of Electric Machines, a State of the Art Study

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. Introduction.

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Genetic Optimization of Electric Machines, a State of the Art Study

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  1. Genetic Optimization of Electric Machines, a State of the Art Study S. E. Skaar, R. Nilssen NORPIE 2004, Trondheim

  2. Outline of Presentation • Introduction • Useful Terms in GA • Selection of encoding • Strategies to improve GA • GA used in design optimization of electrical machines • Summary NORPIE 2004, Trondheim

  3. Introduction • 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 NORPIE 2004, Trondheim

  4. 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 NORPIE 2004, Trondheim

  5. Flowchart of GA NORPIE 2004, Trondheim

  6. 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: 232 Genotype representation is: 11101000 NORPIE 2004, Trondheim

  7. Allele:The allele is the status(/value) of an individual geneExample: • 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 NORPIE 2004, Trondheim

  8. 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 NORPIE 2004, Trondheim

  9. 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 NORPIE 2004, Trondheim

  10. 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 NORPIE 2004, Trondheim

  11. 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 NORPIE 2004, Trondheim

  12. 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 NORPIE 2004, Trondheim

  13. 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 NORPIE 2004, Trondheim

  14. 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 NORPIE 2004, Trondheim

  15. 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 NORPIE 2004, Trondheim

  16. 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 NORPIE 2004, Trondheim

  17. 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 NORPIE 2004, Trondheim

  18. 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 NORPIE 2004, Trondheim

  19. 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 NORPIE 2004, Trondheim

  20. 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 NORPIE 2004, Trondheim

  21. 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 NORPIE 2004, Trondheim

  22. 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 NORPIE 2004, Trondheim

  23. 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 NORPIE 2004, Trondheim

  24. Thank you for your attention NORPIE 2004, Trondheim

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