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Unformatted text preview: 3/10/05 M.A. Breuer 1 Genetic Algorithms 3/10/05 M.A. Breuer 2 Genetic Algorithms (GA) ! A class of probabilistic search algorithms ! Inspired by natural genetics and biological evolution ! Uses concept of “survival of fittest” ! GA originally developed by John Holland (1975) 3/10/05 M.A. Breuer 3 GA –general concepts " Iterative procedure (iterative improvement) " Produces a series of “generations of populations”, one per iteration " Each member of a population (a bag) represents a feasible solution, called a chromosome " The elements of a chromosome are genes . In our examples, genes might be gates or wires, chromosomes might be placements or partitions. 3/10/05 M.A. Breuer 4 " p 1 p 3 A bag A chromosome Combine and die(mating) 1 2 3 k m evolution Chromosomea feasible solution Selection Crossover Mutation p k . . . . . . 3 operators are: x 3 4 x 3 1 x 3 1 2 p m p 2 Evolution: A pictorial view 3/10/05 M.A. Breuer 5 Notation and concepts " The population during iteration i of GA is denoted by the “ bag ” p i = { x 1 i , x 2 i , … , x n i }. " x m i denotes the m th member (a chromosome) of the population in the i th iteration, and n is the size of the population. " p i is a bag, not a set, hence can contain repeated solutions (elements), i.e., all entries need not be unique. " _____________ p 1 may be created randomly or by a deterministic (constructive) heuristic. " cost ( x ) is the cost of solution x . This function is user supplied. fillin 3/10/05 M.A. Breuer 6 More on notation and concepts " Assume cost ( x ) ! 0 " x . " Let fitness ( x ) =1/[1+ cost ( x )]. Thus " x , 0 # fitness ( x ) # 1. " average_fitness ( p i ) = fitness ( x j i ) for j =1,2, … , n " best_fitness ( p i ) = max{ fitness ( x j i )} over all j " Going from p 1 to p 2 to p 3 … is called “evolution” " Goal: ensure that it is highly likely that average_fitness ( p k ) > average_fitness ( p i ) for k > i " We go from p i to p i +1 via an evolution function that usually consists of three components, called operators . They are known as selection , crossover (mating), and mutation . 1 n j " 3/10/05 M.A. Breuer 7 Operators " Selection : select some members (chromosomes) from the current population to populate the next generation. Try to select “highly fit” chromosomes. " Use an _________ roulette wheel technique to select objects. " Note: a ________ of 0.37 is the same as 37%. 2 1 n 3 4 Area is proportional to fitness value . . . fillin 3/10/05 M.A. Breuer 8 Example Chromosome fitness A 0.21 B 0.14 C 0.10 D 0.02 E 0.33 F 0.20 1.00 A 21% D 2% 10% F 20% E 33% B 14% C 3/10/05 M.A. Breuer 9 More concepts " When wheel is turned and eventually stops, probability of stopping at A is 0.21....
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This note was uploaded on 12/04/2009 for the course EE 581 at USC.
 '09
 BREUER

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