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Chapter 6: Transform and Conquer

The Design and Analysis of Algorithms. Chapter 6: Transform and Conquer. Genetic Algorithms. Genetic Algorithms. What is a GA Terms and Definitions Basic Genetic Algorithm Example Selection Methods Crossover Methods Mutation. What is a GA.

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Chapter 6: Transform and Conquer

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  1. The Design and Analysis of Algorithms Chapter 6:Transform and Conquer Genetic Algorithms

  2. Genetic Algorithms • What is a GA • Terms and Definitions • Basic Genetic Algorithm • Example • Selection Methods • Crossover Methods • Mutation

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

  4. Terms and Definitions (1) • A solutionis coded by astring, also calledchromosome. The words string and chromosome are used interchangeably • A strings fitnessis a measure of how good a solution it codes. Fitness is calculated by a fitness function.

  5. Terms and Definitions (2) • 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). • 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.

  6. Terms and Definitions (3) • Crossoveris 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 1 0 0 | 1 1 0 Parent 2 0 1 1 | 1 0 0 Offspring1 1 0 01 0 0 Offspring2 0 1 11 1 0

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

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

  9. New Population • 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. • Mutation: With a mutation probability mutate new offspring at each locus (position in chromosome).

  10. Termination Criteria • After a pre-specified number of generations • 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

  11. Example: The Knapsack Problem • A knapsack with capacity C, • A set of items each with volume and value. • Find a subset of the items that can fit in the knapsack and has maximum value. • This is an optimization NP problem. Given n items, the number of all subsets to be examined is 2n.

  12. Example (cont.) Sample candidate solutions O1 O2 O3 O4 Volume Value 1 0 1 0 1 8 7 2 1 0 0 1 9 8 3 1 0 1 0 5 6 4 0 1 1 1 9 10 <<<<< 5 0 1 1 0 4 5

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

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

  15. Tournament Selection Saves time used for sorting • Fix a constant k < 1, e.g. k =0.75 • Randomly choose two individuals and a random number r < 1 • if r < k, select the individual with the higher fitness to be a parent, otherwise select the other individual to be a parent • Repeat steps 2 and 3 until the new generation is created

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

  17. Applications • Optimization problems • Search in a pool of candidate solutions Tutorial: http://www.obitko.com/tutorials/genetic-algorithms/

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