1. Genetic Algorithms What is a GA Terms and definitions Basic algorithm

2. 2 What is a GA Searches for good solutions among possible solutions. Searches for good solutions among possible solutions. Uses evolutionary mechanisms including natural selection, reproduction, mutation Uses evolutionary mechanisms including natural selection, reproduction, mutation The best possible solution may be missed The best possible solution may be missed Useful in problems that are too big or too difficult to solve with conventional techniques. Useful in problems that are too big or too difficult to solve with conventional techniques.

3. 3 Terms and definitions (1) A solution is coded by a string, also called chromosome. The words string and chromosome are used interchangeably A solution is coded by a string, also called chromosome. The words string and chromosome are used interchangeably A strings fitness is a measure of how good a solution it codes. Fitness is calculated by a fitness function. A strings fitness is a measure of how good a solution it codes. Fitness is calculated by a fitness function.

4. 4 Terms and definitions (2) Selection: The procedure to choose parents Selection: The procedure to choose parents Roulette wheel selection is a way of picking out a string from among a group of strings (a population). Roulette wheel selection is a way of picking out a string from among a group of strings (a population). A wedge on a roulette wheel proportional to the string's fitness. A wedge on a roulette wheel proportional to the string's fitness. A 'fit' string is more likely to be chosen than an 'unfit' string. A 'fit' string is more likely to be chosen than an 'unfit' string.

5. 5 Terms and definitions (3) Crossover is the procedure by which two chromosomes mate to create a new offspring chromosome Crossover is the procedure by which two chromosomes mate to create a new offspring chromosome parent 1 is copied of up to a randomly chosen point, and parent 2 is copied from that point onwards. parent 1 is copied of up to a randomly chosen point, and parent 2 is copied from that point onwards. Parent 1 1 0 0 | 1 1 0 Parent 2 0 1 1 | 1 0 0 Offspring1 1 0 0 1 0 0 Offspring2 0 1 1 1 1 0

6. 6 Terms and definitions (4) Mutation : with a certain probability flip a bit in the offspring Mutation : with a certain probability flip a bit in the offspring Various ways to implement mutation, optional. Various ways to implement mutation, optional.

7. 7 Basic Genetic Algorithm Basic Genetic Algorithm 1. Start: Generate random population of n chromosomes (suitable solutions for the problem) 2. Fitness: Evaluate the fitness f(x) of each chromosome x in the population 3. New population: Create a new population by repeating following steps until the new population is complete 4. Test: If the end condition is satisfied, stop, and return the best solution in current population

8. 8 New population Selection: Select two parent chromosomes from a population according to their fitness (the better fitness, the bigger chance to be selected) Selection: Select two parent chromosomes from a population according to their fitness (the better fitness, the bigger chance to be selected) Crossover: With a crossover probability cross over the parents to form a new offspring (children). If no crossover was performed, offspring is an exact copy of parents. Crossover: With a crossover probability cross over the parents to form a new offspring (children). If no crossover was performed, offspring is an exact copy of parents. Mutation: With a mutation probability mutate new offspring at each locus (position in chromosome). Mutation: With a mutation probability mutate new offspring at each locus (position in chromosome).

9. 9 Termination Criteria after a pre-specified number of generations after a pre-specified number of generations when an individual solution reaches a pre-specified level of fitness when an individual solution reaches a pre-specified level of fitness when the variation of individuals from one generation to the next reaches a pre-specified level of stability, e.g. all become equal when the variation of individuals from one generation to the next reaches a pre-specified level of stability, e.g. all become equal

10. 10 Issues to Address How to represent an individual How to represent an individual How to choose How to choose the fitness function the fitness function the selection method the selection method the crossover method the crossover method the frequency of mutations the frequency of mutations

11. 11 More on Selection Roulette Wheel Selection: proportional to the fitness Roulette Wheel Selection: proportional to the fitness Rank Selection: rank is assigned based on fitness, then choose proportional to the rank Rank Selection: rank is assigned based on fitness, then choose proportional to the rank Steady-State Selection: sort and always choose the best Steady-State Selection: sort and always choose the best Elitism: copy the best individuals in the next generation Elitism: copy the best individuals in the next generation Tournament selection Tournament selection

12. 12 More on Crossover Random point of split Random point of split Fixed point of split Fixed point of split Single point: split in two Single point: split in two Two points: split in three Two points: split in three Uniform: bits are chosen randomly Uniform: bits are chosen randomly Arithmetic crossover: the offspring is a result of some arithmetic operation Arithmetic crossover: the offspring is a result of some arithmetic operation Two parents Two parents Three parents Three parents

13. 13 Applications Optimization problems Optimization problems Search in a pool of candidate solutions Search in a pool of candidate solutionsTutorial: http://cs.felk.cvut.cz/~xobitko/ga/