1. introduction to Genetic Algorithms Yonatan Shichel

2. Genetic Algorithms  Bio-Inspired  Bio-Inspired artificial intelligence class of probabilistic optimization algorithms §Well-suited for nonlinear/hard problems with a large search space §Developed by John Holland §Influenced by Darwin’s Origin of species What are Genetic Algorithms?

3. Evolution  Variety  Variety of species individuals within the population  Competition  Competition for limited resources  Overproduction  Overproduction of offspring generation §Survival of the fittest Origin of Species, 1859 Darwin’s principles

4. Evolution §Initial population Variety of shapes, colors, behaviors Each individual fits differently to the environment How does it work?

5. Evolution §Initial population §Reproduction Offspring combines both parents properties Siblings may differ in properties Mutations may occur How does it work?

6. Evolution §Initial population §Reproduction §Limited environmental resources Only a portion of the individuals survive Survival chances – according to fitness measure...... usually. How does it work?

7. Evolution Observations §Changes in the population content “good” properties are kept, “bad” are distinct evolutionary pressure

8. Genetic Algorithms The computational model produce an initial population of individuals while (termination condition not met) do evaluate the fitness of all individuals select fitter individuals for reproduction recombine between individuals mutate individuals

9. Genetic Algorithms The computational model initial population produce an initial population of individuals termination condition while ( termination condition not met) do evaluate evaluate the fitness of all individuals select select fitter individuals for reproduction recombine recombine between individuals mutate mutate individuals

10. Genetic Algorithms The computational model GnGnGnGn 55 44 12 31 95 32 87 12 0 65 53 2 91 73 + G n+1 = crossover mutation fitness

11. GA in action The Knapsack problem (NP) §There are N items: Each item i has a weight w i Each item i has a value v i §The knapsack has a limited capacity of W units. §The problem description: Maximize While

12. GA in action The Knapsack problem (NP) §For example: §Knapsack capacity = 100 JIHGFEDCBA 1230183425545192614 21411750231470182420

13. GA in action Before we begin… genome encoding 1.Define the genome encoding fitness function 2.Define the fitness function

14. GA in action Genome Encoding Bit array: 0 = don’t take the item 1 = take the item (items taken: A, B, E) 0000010011 -----E--BA

15. GA in action Genome Encoding Bit array: 0 = don’t take the item 1 = take the item (items taken: A, B, C, D, E, F, G, I) 0101111111 -I-GFEDCBA

16. GA in action Fitness Function JIHGFEDCBA 1230183425545192614 21411750231470182420

17. GA in action Fitness Function JIHGFEDCBA 1230183425545192614 21411750231470182420

18. Genetic Algorithms Fitness Evaluation produce an initial population of individuals while (termination condition not met) do evaluate evaluate the fitness of all individuals select fitter individuals for reproduction recombine between individuals mutate individuals

19. Genetic Algorithms Fitness Evaluation For each individual, calculate the fitness value:

20. Genetic Algorithms Selection produce an initial population of individuals while (termination condition not met) do evaluate the fitness of all individuals select select fitter individuals for reproduction recombine between individuals mutate individuals

21. Genetic Algorithms Selection §Fitness-proportionate (roulette wheel) §Rank Selection (scaling) §Tournament Selection §…

22. Genetic Algorithms Crossover produce an initial population of individuals while (termination condition not met) do evaluate the fitness of all individuals select fitter individuals for reproduction recombine recombine between individuals mutate individuals

23. Genetic Algorithms Crossover Using a crossover probability P C per individual: §Single point crossover §Two/multi points crossover §Uniform / weighted crossover §…

24. Genetic Algorithms Mutation produce an initial population of individuals while (termination condition not met) do evaluate the fitness of all individuals select fitter individuals for reproduction recombine between individuals mutate mutate individuals

25. Genetic Algorithms Mutation Using a crossover probability P M per bit: §Bit flip mutation §Bit switch mutation §…

26. Genetic Algorithms Crossover & Mutation examples

27. Genetic Algorithms Initial Population initial population produce an initial population of individuals while (termination condition not met) do evaluate the fitness of all individuals select fitter individuals for reproduction recombine between individuals mutate individuals

28. Genetic Algorithms Initial Population Create a fixed size population using: §Random generated individuals §Individuals resulted from previous evolutionary runs

29. GA in action Initial Population Example of random population:

30. Genetic Algorithms Termination Condition produce an initial population of individuals termination condition while ( termination condition not met) do evaluate the fitness of all individuals select fitter individuals for reproduction recombine between individuals mutate individuals

31. Genetic Algorithms Termination Condition §When an optimal solution is found §When the results converge to constant value §After a predetermined number of generations

32. Genetic Algorithms Sample Evolutionary Run §Population size: 100 individuals §Crossover: Single pt., P C =0.9 §Mutation: Bit flip, P M =0.01 §Selection: tournament, groups of 2 §Termination condition: after 100 generations

33. Genetic Algorithms Sample Evolutionary Run

34. Genetic Algorithms Conclusions §GA is nondeterministic – two runs may end with different results §There’s no indication whether best individual is optimal §Fitness tends to converge during time

35. Genetic Algorithms GA variations §Coevolution Cooperative Competitive §Parallel GA §Hybrid GA