Genetic Algorithms. Seth Bacon. 4/25/2005 Seth Bacon 1

Transcription

1 Genetic Algorithms Seth Bacon 4/25/2005 Seth Bacon 1

2 What are Genetic Algorithms Search algorithm based on selection and genetics Manipulate a population of candidate solutions to find a good solution 4/25/2005 Seth Bacon 2

3 What are GAs used for Approximate solutions for NP- Complete and NP-Hard problems Artificial Intelligence Business, engineering and science. 4/25/2005 Seth Bacon 3

4 The Population Each member of the population is represented by a chromosome Typically a binary string although they can be more complex Each chromosome is generated at random (usually) Each chromosome represents a solution (although not necessarily a good one) 4/25/2005 Seth Bacon 4

5 Steps of a GA Generate Initial Population Run Tournament Fitness evaluation Selection Crossover Mutation Reach conclusion 4/25/2005 Seth Bacon 5

6 Generation of Initial Pop Must supply a large enough population to create genetic diversity The longer the chromosome the greater the population The more noise (poor solutions not leading to the good solution) the greater the population A correctly-sized population is the first step toward competent and efficient genetic algorithms. Cantú-Paz 4/25/2005 Seth Bacon 6

7 Fitness Evaluation Ranks a chromosome based on it s performance Defined by the user Unique to each problem 4/25/2005 Seth Bacon 7

8 Selection Technique for selecting parents of the next generation Based on rank from fitness Different selection schemes Selection of top x-chromosomes Random selection of top x-chromosomes out of top y-chromosomes (y > x) Etc. Try to keep population diverse to protect from a premature poor solutions 4/25/2005 Seth Bacon 8

9 Crossover Mating of two different chromosomes Methods Randomly chosen crossover point. Everything to the left of the point stays put. Everything to the right switches with the other chromosome. n-point crossover Completely random crossover (n = length of chromosome) Used to explore the solution space. Controlled randomness? 4/25/2005 Seth Bacon 9

10 Mutation Randomly changes a value in the chromosome Used to keep diversity up However its probability should be kept low or else you are destroying too much information. 4/25/2005 Seth Bacon 10

11 Reaching a Conclusion After x number of generations you stop and take out the most robust chromosome. When improvement of the chromosomes per generation has reached a plateau When the fittest chromosome has bred all the others out of the population. (Only happens w/o mutation) 4/25/2005 Seth Bacon 11

12 Parallel GAs Single-population master-slave GAs Multiple-population GAs Fine-grained GAs Hierarchical hybrid (Not discussed) 4/25/2005 Seth Bacon 12

13 Master-Slave GAs Very similar to serial GAs Slaves calculate the fitness T p = Time to compute a generation T c = is the communication time between processors P = the number of processors T f = the time require for a fitness evaluation n = size of the population T p = PT c + nt f /P 4/25/2005 Seth Bacon 13

14 Master-Slave GAs P* = sqrt(nt f /T c ) 4/25/2005 Seth Bacon 14

15 Master Slave GAs 4/25/2005 Seth Bacon 15

16 Multiple-Population GAs Distributed panmictic population Panmictic - random mating within a breeding population Only occasional breeding between processors Each population converges on a solution Increases diversity 4/25/2005 Seth Bacon 16

17 Fine Grained GAs Each processor has its own subpopulation (preferably consisting of only one chromosome) Fitness and mutation per processor Selection and mating on a local neighborhood (which overlap) Diffuses population across all subpopulation well suited for massively parallel SIMD computers, but it is also possible to implement them very efficiently on coarse-grain MIMD computers. Cantú-Paz 4/25/2005 Seth Bacon 17

18 Examples ample_f.html Highly recommend this site let s you play with a lot of the concepts rams.html 4/25/2005 Seth Bacon 18

19 Sources Cantu-Paz, Erick. Efficient and Accurate Parallel Genetic Algorithms. Kluwer Academic Publishers 2000 Antonette M. Logar, Edward M. Corwin, ans Thomas M. English. Implementation of Massively Parallel Genetic Algorithms On the MasPar MP-1. Department of Computer Science 4/25/2005 Seth Bacon 19