Genetic Algorithms. Moreno Marzolla Dip. di Informatica Scienza e Ingegneria (DISI) Università di Bologna.

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1 Genetic Algorithms Moreno Marzolla Dip. di Informatica Scienza e Ingegneria (DISI) Università di Bologna Slides credit: Ozalp Babaoglu

2 History Pioneered by John Henry Holland in the 1970 s Got popular in the late 1980 s Based on ideas from Darwinian Evolution Can be used to solve a variety of problems that are not easy to solve using traditional techniques Complex Systems 2

3 Evolution in the real world Each cell of a living thing contains chromosomes strings of DNA Each chromosome contains a set of genes blocks of DNA Each gene largely determines some physical aspect of the organism (like eye color) A collection of genes is called the genotype A collection of aspects is called the phenotype Complex Systems 3

4 Evolution in the real world Reproduction involves recombination of genes from parents and small amounts of mutation (errors) in copying Evolutionary biology: organism's genotype largely determines its phenotype and hence its fitness ability to produce new offsprings and propagate its genotype Basis for Darwinian Evolution Evolutionary game theory: the fitness of an organism determined by its interactions with other organisms in a population Complex Systems 4

5 Evolution in the real world adaptation = variation + heredity + selection Complex Systems 5

6 Genetic Algorithms Suppose you have a problem You don t know how to solve it algorithmically Can we use a computer to somehow find a solution? Repeat Generate a random feasible solution Test the solution to evaluate its goodness Until solution is good enough Complex Systems 6

7 Can we use this dumb idea? Sometimes yes: if there are only a few possible solutions and you have enough time then such a method could be used For most problems no: many possible solutions with no time to try them all so this method can not be used Complex Systems 7

8 A less-dumb idea (GA) Generate a set of random solutions Repeat Test each solution in the set and rank them Remove some bad solutions from set Duplicate (reproduce) some good solutions Make small changes to some of them Until best solution is good enough Complex Systems 8

9 How do you encode a solution? Obviously this depends on the problem! GA s often encode solutions as fixed length bit strings (e.g , , ) Each bit represents some aspect of the proposed solution to the problem For GA s to work, we need to be able to test any string and get a score indicating how good that solution is Complex Systems 9

10 Adding Sex Crossover Although it may work for simple search spaces, our algorithm is still very naive It relies on random mutation to find a good solution It has been found that by introducing sex into the algorithm better results are obtained This is done by selecting two parents during reproduction and combining their genes to produce offspring Complex Systems 10

11 Adding Sex - Crossover Two high scoring parent bit strings (chromosomes) are selected and are combined with some probability (crossover rate) Producing two new offsprings (bit strings) Each offspring may then be changed randomly (mutation) Complex Systems 11

12 Crossover - Recombination Parent1 Offspring Parent2 Offspring Crossover single point - random With some high probability (crossover rate) apply crossover to the parents (typical values are 0.8 to 0.95) Complex Systems 12

13 Mutation mutate Offspring Offspring Offspring Offspring Original offspring Mutated offspring With some small probability (the mutation rate) flip each bit in the offspring (typical values between 0.1 and 0.001) Complex Systems 13

14 Many Variants of GA Different kinds of selection Tournament Elitism, etc. Different recombination Multi-point crossover 3 way crossover etc. Different kinds of encoding other than bit strings Integer values Ordered set of symbols Different kinds of mutation Complex Systems 14

15 Many parameters to set Any GA implementation needs to decide on a number of parameters: Population size (N), mutation rate (m), crossover rate (c) Often these have to be tuned based on results obtained - no general theory to deduce good values Typical values might be: N = 50, m = 0.05, c = 0.9 Complex Systems 15

16 Example: vertex k-coloring problem Master Thesis of Pasquale Cautela Un algoritmo parallelo genetico per la k-colorabilità Given an undirected graph G = (V, E), assign each node a color chosen from a set {1, k} such that: adjacent nodes have different colors; the value of k is minimum (k is called the chromatic number X(G) of G) This graph is 3- colorable, but not 2- colorable Complex Systems 16

17 Example: vertex k-coloring problem A simple upper bound on the chromatic number X(G) of graph G is Χ (G) Δ(G)+1 where (G) is the maximum degree of nodes in G Computing the chromatic number X(G) for an arbitrary graph G is NP-hard Checking whether a graph is 2-colorable can be done in polynomial time Complex Systems 17

18 Genetic algorithm Let k = (G) while ( G is k-colorable ) do k k - 1; endwhile return X(G) = k + 1; GAs are used to test whether G is k-colorable Chromosomes Vectors of n integers in {1, k} (n is the number of nodes) Fitness function Number of conflicts (negated, best fitness is zero) Complex Systems 18

19 Simple NetLogo model Sample Models Computer Science Simple Genetic Algorithm Complex Systems 19