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Genetic Algorithms: Solving the Traveling Salesman Problem Thomas Abtey SUNY Oswego

Genetic Algorithms: Solving the Traveling Salesman Problem Thomas Abtey SUNY Oswego. Genetic Algorithm. - Invented by John Holland, 1960's - Analogies to Biological Evolution - Fitness - Selection - Crossover (Reproduction) - Mutation

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Genetic Algorithms: Solving the Traveling Salesman Problem Thomas Abtey SUNY Oswego

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  1. Genetic Algorithms: Solving the Traveling Salesman ProblemThomas AbteySUNY Oswego

  2. Genetic Algorithm • - Invented by John Holland, 1960's • - Analogies to Biological Evolution • - Fitness • - Selection • - Crossover (Reproduction) • - Mutation • - Uses in Optimization, Approximation

  3. - Evolution is a process of selection and reproduction - Inheritance from Parents to Children - Simplified cycle: - For a population, assign fitness values to each individual - Create a new population by breeding (and mutating) the fittest individuals Genetic Algorithm (cont.)

  4. - “Given a set of cities and their distances, what is the shortest tour possible visiting each city only once?” - For 9 cities, 9! = 362,880 possible solutions - Application in scheduling/order problems - Brute-force method time becomes enormous Traveling Salesman Problem

  5. - Population is a list of individuals - Individual is a list of cities - City is a name (and a set of distances) > Houston Hollywood Las-Vegas SLC Chicago NYC Oswego Miami Philadelphia Genetic Approach to TSP

  6. - A mutation alters city ordering in an Individual - Two cities are chosen randomly to be switched (A B* C D E F G* H) (A G* C D E F B* H) Mutation

  7. Crossover - Based on Greedy Subtour Crossover (GSX) by Sengoku and Yoshihara: - Choose two parents, i1 and i2 - Choose a city as a mid-point for new tour - From midpoint, do until tour will be invalid: - Place i1's cities to front of new tour - Place i2's cities to back of new tour - Remaining cities (if any) will be appended to back of new tour

  8. Example: Mom = (ABCDEFGHI) Dad = (DFEGAHBCI) Mid-Point = G --------------------------- (G) (FG) (FGA) (EFGA) (EFGAH) (DEFGAH) (DEFGAHB-) (-CDEFGAHB-) =>(CDEFGAHBI) Crossover (cont.)

  9. Brute-Force Solution: - (Hollywood Las-Vegas SLC Houston Chicago Philadelphia NYC Oswego Miami) - A length of 40* - Multiple tours of length 40 * Multiplying this value by 1,000 will give actual geographic distance in miles. Results

  10. - GA Solution: - Quickly reduces average tour length in a pop - Comes close to actual solution - GA with 25 individuals over 55 generations: Generation 1 average fitness .. 112.2 Generation 2 average fitness .. 91.53846 Generation 3 average fitness .. 83.34615 Generation 4 average fitness .. 78.23077 … Generation 54 average fitness .. 52.115383 Generation 55 average fitness .. 58.615383 Results (cont.)

  11. Senguko, H., Yoshihara, I. “A Fast TSP Solver Using GA on JAVA”. 1993. Mitchell, M. “Introduction to Genetic Algorithms”. 1997. Holland, H. “Adaptation in Natural and Artificial System: an introductory analysis with applications to biology, control, and artificial intelligence”. 1975. Common LISP. http://clisp.cons.org References & Resources

  12. o ------ o / \ o o \ / o ------ o Questions?

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