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A First Course in Genetic Algorithms Tim Watson G6.71

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1 A First Course in Genetic Algorithms Tim Watson G6.71

2 What is a GA? Evolutionary Algorithm –Create random population of possible solutions in the form of bitstrings –See how good each one is (test fitness) –Produce next generation (fitter are more likely to get into next generation) –Crossover, mutate and make next generation the current one

3 What can they do? Schedule Barcelona Olympics Aircraft Design Dynamic Routing in Networks Robot Arm Trajectory Planning Lab Task Scheduling for US Navy Aircraft Missile Evasion Evolving aNN Architecture Parameter Tuning for Sonar Systems Conformational Analysis of DNA

4 Example: Onemax 1.Initial population: Calculate fitness: Reproduce: Crossover & Mutate:

5 Biological Terminology Genes etc. –Gene –Locus (plural loci) –Allele (also called gene value) –(Pleiotropic gene) Genotype (Chromosome) Phenotype Fitness Landscape

6 GA Theory Schema Theorem –GA searches schemata in parallel –10 represents 10, 1#, #0 and ## –The theorem is rubbish! Building Block Hypothesis –Good, small sequences are found and recombined to form good solutions No Free Lunch Theorem

7 GA Parameters Population Size –Static or Dynamic? Chromosome Size –Fixed or Variable? Crossover Rate –One-point, two-point or uniform? Mutation Rate –Fixed or Variable? Fitness Function Termination Criteria

8 Prediction Test! What happens to the population statistics in a standard GA with random fitness, no crossover, no mutation and chromsize equals 16? –Best, Worst, Mean, Std. Dev., column counts Best=17, Worst=1, Mean=9ish, Std. Dev. constant-ish, pop converges randomly.

9 Reproduction in GAs Need selective pressure for reproduction to improve the population fitness –None leads to random walk (slow) –Some leads to geometric growth of best (fast) Infinite populations select individuals on relative fitness: fit/mean(fit) Finite populations also affected by how many copies are already present

10 Types of Selection Fitness-Proportionate –Fitness scaling based on raw fitness where if fit a < fit b then scaled(fit a )  scaled(fit b ) –Scaling can be altered dynamically Rank-Order Tournament Elitism

11 Initialising the Population Uniformly at random Best Guesses Converged to Best Known From Real World Hybrid

12 Mutation Goal of selection: survival of the fittest Goal of mutation: explore lost or never seen alleles Random reset versus bit flip –Reset rate = ½ bit flip rate Mutation as a spring In infinite time every possible population visited an infinite number of times Alternative to mutation: complement

13 Crossover Goal: to try out different combinations of good bits of individuals Crossover point –One-point –Two-point –N-point –Uniform

14 Crossover (2) Closer genes are less likely to be split by crossover –AB###### probability of split with one-point crossover = 1/7 –A######B probability of split = 1 Local maxima can occur (e.g. for onemax) fit= fit= All children have lower fitness than parents

15 Design Decisions If genes are linked then the representaion of an individual ought to keep them close together Get the balance right: –Popsize too small  premature convergence –Popsize too large  too slow to compute –Mutation rate too low  not enough exploring –Mutation rate too high  too much noise

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