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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

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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