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Using GA’s to Solve Problems

Using GA’s to Solve Problems. Amy Hoover. What is a Genetic Algorithm?. Genetic Algorithm – “a search technique … to find exact or approximate solutions to optimization and search problems.” -Wikipedia. Components of a GA. Chromosome How we represent the individual Fitness function

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Using GA’s to Solve Problems

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  1. Using GA’s to Solve Problems Amy Hoover

  2. What is a Genetic Algorithm? • Genetic Algorithm – “a search technique … to find exact or approximate solutions to optimization and search problems.” -Wikipedia

  3. Components of a GA • Chromosome • How we represent the individual • Fitness function • How we rate the individual • Mutation • Crossover

  4. How do GAs work? • Randomize initial population (of 5) • Note: These were arbitraily picked • A = 10111 • B = 11100 • C = 00110 • D = 00001 • E = 11011

  5. Evaluate the fitness of each individual (A, B, C, D, E) in the population • A = 10111 (fitness = 1+ 0 + 1 + 1+ 1 = 4) • B = 11100 (fitness = 1 + 1 + 1+ 0 + 0 = 3) • C = 00110 (fitness = 0 + 0 + 1+ 1 + 0 = 2) • D = 00001 (fitness = 0 + 0 + 0+ 0 + 1 = 1) • E = 11011 (fitness = 1 + 1 + 0+ 1 + 1 = 4)

  6. Repeat • Select parents • Who would we choose from the previous generation? (A and E) • Mate the parents, they plus their offspring form next generation • How do we mate them? • What will the next generation look like?

  7. Next Generation • A = 10111 (parent 1 clone) • E = 11011 (parent 2 clone) • F = ? • G = ? • H = ? • Which generation are F, G, and H from?

  8. Next Generation • A = 10111 (parent 1) • E = 11011 (parent 2) • F = ? • G = ? • H = ? • Which generation are F, G, and H from? • How can we make F, G, H?

  9. Crossover and Mutation • Let’s make F, G, H (Gen 1 from initial generation 0) • A = 10111 (parent 1) • E = 11011 (parent 2) • F = 11111 (Mutate A) • G = 11011(Crossover AE 2nd 3rd bits of E on A, also clone E ) • H = 10011 (Crossover AE 3rd and 4th of E) • Which generation are F, G, and H from? • How can we make F, G, H?

  10. Calculate the fitness of each individual • A = 10111 (parent 1) • E = 11011 (parent 2) • F = 11111 (Mutate A) • G = 11011 (Crossover AE) • H = 10011 (Crossover AE)

  11. Calculate the fitness of each individual • A = 10111 = 4 • E = 11011 = 4 • F = 11111 = 5 • G = 11011 = 4 • H = 10011 = 3 • Select parents (F,G)

  12. Repeat • Select parents (A, E, F, G, H) • How do we pick the parents? • Pick the top 2 from A, E, F, G, H • Mate parents (crossover, mutation) • Calculate fitness • (Repeat Select parents…)

  13. Example • Problem: I want to maximize the number of 0’s in a bit string • (I want A = 00000) • Let’s work through the psuedo code

  14. Example • Problem: I want to maximize the number of 0s in a bit string • (I want A = 00000) • Step 1: Randomize the initial population • A = 01101 • B = 11011 • C = 01010 • D = 01111 • E = 11111

  15. Example • Initial Population (gen 0) • A = 01101 • B = 11011 • C = 01010 • D = 01111 • E = 11111 • Calculate fitness (recall 0’s are good, 1’s are bad, we want to reward good genes!)

  16. Example • Initial Population • A = 01101 = 1 + 0 + 0 + 1 + 0 = 2 • B = 11011 = 0 + 0 + 1 + 0 + 0 = 1 • C = 01010 = 1 + 0 + 1 + 0 + 1 = 3 • D = 01111 = 1 + 0 + 0 + 0 +0 = 1 • E = 11111 = 0 + 0 + 0 + 0 +0 = 0 • Reward 0’s, not 1’s

  17. Example • Initial Population • A = 01101 = 1 + 0 + 0 + 1 + 0 = 2 • B = 11011 = 0 + 0 + 1 + 0 + 0 = 1 • C = 01010 = 1 + 0 + 1 + 0 + 1 = 3 • D = 01111 = 1 + 0 + 0+ 0+ 0 = 1 • E = 11111 = 0 + 0 + 0 + 0 + 0 = 0

  18. Example • Who should our parents be? (A and C) • A = 01101 = 1 + 0 + 0 + 1 + 0 = 2 • B = 11011 = 0 + 0 + 1 + 0 + 0 = 1 • C = 01010 = 1 + 0 + 1 + 0 + 1 = 3 • D = 01111 = 1 + 0 + 0+ 0+ 0 = 1 • E = 11111 = 0 + 0 + 0 + 0 + 0 = 0

  19. Example • Who should our parents be? • A = 01101 = 1 + 0 + 0 + 1 + 0 = 2 • C = 01010 = 1 + 0 + 1 + 0 + 1 = 3 • What next?

  20. Mating! • A = 01101 = 1 + 0 + 0 + 1 + 0 = 2 • C = 01010 = 1 + 0 + 1 + 0 + 1 = 3 • F = 01100 = 3 • G = 01110 = 2 • H = 01011 = 2

  21. Calculate Fitness! • A = 01101 = 1 + 0 + 0 + 1 + 0 = 2 • C = 01010 = 1 + 0 + 1 + 0 + 1 = 3 • F = 01100 = 3 • G = 01110 = 2 • H = 01011 = 2

  22. Pick the top two! • A = 01101 = 1 + 0 + 0 + 1 + 0 = 2 • C = 01010 = 1 + 0 + 1 + 0 + 1 = 3 • F = 01100 = 3 • G = 01110 = 2 • H = 01011 = 2 • Parents, C and F

  23. Start Over! • C = 01010 = 1 + 0 + 1 + 0 + 1 = 3 • F = 01100 = 3 • G = ? • H = ? • I = ?

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