2. Genetic Algorithms Nehaya Tayseer

3. 1.Introduction What is a Genetic algorithm? A search technique used in computer science to find approximate solutions for optimization and search problems A class of evolutionary algorithms that use techniques inspired by evolutionary biology such as inheritance, mutation, natural selection, and recombination (or crossover).

4. Cont’d- What is a Genetic algorithm? Typically implemented as a computer simulation in which a population of abstract representations (called chromosomes) of candidate solutions (called individuals) to an optimization problem evolves toward better solutions.

5. Introduction Some History! Genetic algorithms originated from the studies of cellular automata, conducted by John Holland and his colleagues at the University of Michigan in the mid 70’s. The first commercial genetic algorithm, called the evolver, was produced in 1985. now used by a majority of 500 companies to solve difficult scheduling, data fitting, trend spotting and budgeting problems

6. 2. Optimization Problems In mathematics, the term optimization, or mathematical programming, refers to the study of problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set.

7. Cont’d- Optimization Problems - A Simple Case 8 22 6 5 3 12 5 City A City B City E City D City C Figure 1: an example of a small sized optimization problem, here we have exactly 5 paths between city A and B. the number above the path is the cost of exploring the path. The optimal path is A,E,D,B with a total cost of 6.

8. Cont’d- Optimization Problems: Why do we need non trivial Techniques? City A City B Figure 2: an Example of a huge solution space, assume we have n cities between A and B. the n cities are fully connected then the solution space is n! size. Computationally, this problem is defined as NP-Hard.

9. Cont’d- Optimization Problems: Why do we need non trivial Techniques? Possible Solutions: - Choose any path. - Local Search algorithms - Genetic Algorithms - Neural Networks

10. The Canonical Genetic Algorithm Typical Operations in any Genetic Algorithm include: Initialization Selection Crossover Mutation Termination

11. Cont’d- Canonical GA Initialization Many individual solutions are randomly generated to form an initial population The population size depends on the nature of the problem (typically several hundreds) Each member of this population will be a binary string of length L which corresponds to the problem encoding Strings (individuals) are usually called Chromosomes.

12. Cont’d- Canonical GA Selection each string is then evaluated and assigned a fitness function. A fitness function is a particular type of objective function that quantifies the optimality of a solution (that is, a chromosome) in a genetic algorithm so that that particular chromosome may be ranked against all the other chromosomes

13. Cont’d- Canonical GA Selection In the canonical genetic algorithm, fitness is defined by: Where fi is the evaluation associated with string i and f º is the average evaluation of all the strings in the population. Fitness can also be assigned based on a string's rank in the population or by sampling methods

14. Cont’d- Canonical GA Selection (Duplication) Recombination (Crossover) String 1 String 2 String 3 String 4 … … String 1 Sring 2 String 3 OffSpring A OffSpringB OffSpringC OffSpringD OffSpringE OffSpringF Current Generation Intermediate Generation Next Generation Figure 3: One generation is broken down into a selection phase and recombination phase.

15. Cont’d- Canonical GA Selection Methods - Stochastic sampling with replacement: We might view the population as mapping onto a roulette wheel, where each individual is represented by a space that proportionally corresponds to its fitness. By repeatedly spinning the roulette wheel, individuals are chosen.

16. Cont’d- Canonical GA Selection Methods - Remainder stochastic sampling : if fitness is greater than 1.0, the integer portion of this number indicates how many copies of that string are directly placed in the intermediate population. All strings (including those with less than 1.0) then place additional copies In the intermediate population with a probability corresponding to the fractional portion of the fitness.

17. Cont’d- Canonical GA Remainder stochastic sampling Example, a string with fitness 1.36 places 1 copy in the intermediate population, and then receives a 0.36 chance of placing a second copy. A string with a fitness of 0.54 has a 0.54 chance of placing one string in the intermediate population

18. Cont’d- Canonical GA Crossover Creating the next population from the intermediate population One point crossover

19. Cont’d- Canonical GA One point crossover Example - Father: 1101001100101101 - Mother: yxyyxyxxyyyxyxxy - Crossover: 11010 \ / 01100101101 yxyyx / \ yxxyyyxyxxy - Children: 11010yxxyyyxyxxy and yxyyx01100101101

20. Cont’d- Canonical GA Mutation Maintains genetic diversity from one generation of chromosomes to the next. It is analogous to biological mutation. Usually performed by either flipping one bit in the chosen chromosome or setting the bit to 0 or 1. Typically the mutation rate is applied with less than 1% probability.

21. Cont’d- Canonical GA Termination The process of evaluation, selection, recombination and mutation forms one generation in the execution of a genetic algorithm. Common terminating conditions are A solution is found that satisfies minimum criteria Fixed number of generations reached Allocated budget (computation time/money) reached Manual inspection Combinations of the above.

22. Some Applications Artificial Creativity Code Breaking Design of water distribution systems Traveling Salesman Problem Scheduling applications Electronic circuit design

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