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Genetic Algorithms, Search Algorithms

Genetic Algorithms, Search Algorithms. Jae C. Oh. Overview . Search Algorithms Learning Algorithms GA Example. Brief History. Evolutionary Programming Fogel in 1960s Individuals are encoded to be finite state machines Intellgent Behavior Evolutionary Strategies

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Genetic Algorithms, Search Algorithms

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  1. Genetic Algorithms, Search Algorithms Jae C. Oh

  2. Overview • Search Algorithms • Learning Algorithms • GA • Example

  3. Brief History • Evolutionary Programming • Fogel in 1960s • Individuals are encoded to be finite state machines • Intellgent Behavior • Evolutionary Strategies • Rechenberg, Schwefel in 1960s • Real-valued parameter optmization • Genetic Algorithms • Holland in 1960s • Adaptive Systems • Crossover Operators

  4. Current Status • Wide variety of evolutionary algorithms • No one seriously tries to distinguish them except for some cases and purposes. • We will call all Evolutionary Algorithms • And I will call them Genetic Algorithms or Evolutionary Algorithms for generic terms

  5. Search

  6. Search

  7. Search

  8. Notion of Search Space • Real world problem • Search space • Abstraction -> State Space • Exploring the state space for given problem  Search Algorithms The Peak Search Space

  9. Learning Algorithms • Finding (through search) a suitable program, algorithm, function for a given problem Learning Algorithm Training Data (Experience) Program

  10. Learning Algorithms (function Optimizations) Problem instance Set of Hypothesis The One?? Hypothesis Space Program Space Function Space

  11. Learning Algorithms (Digression) • How do we know the found hypothesis, program, function, etc. are the one we are looking for? • We don’t know for sure • Is there any mathematical way of telling how good hypothesis is? • I.e., |h(x) – f(x)| = ? • Computational Learning Theory can tell us this • Valiant (1984)

  12. What are Genetic Algorithms? • Find solutions for a problem with the idea of evolution. Search and optimization techniques based on Darwin’s Principle of Natural Selection. • Randomized search and optimization algorithms guided by the principle of Darwin’s natural selection: Survival of fittest. • Evolve potential solutions • Step-wise refinement? • Mutations? Randomized, parallel search • Models natural selection • Population based • Uses fitness to guide search

  13. Evolution is a search process From the Tree of the Life Website,University of Arizona Orangutan Human Gorilla Chimpanzee

  14. AGTGACCA TGGACTA AAGACTT AGGACTA AGGGCAA CAGCACCA AGCACTA AAGGCCT TGGACTT TAGCCCT AGCACTT AGGGCAT TCGCCCA AGTACAA AAGGCAA TAGGCCTA AGTGCTA AGGGCAT TAGCCCA TAGACTT AGCACAA AGCGCTT Evolution is parallel search

  15. Genetic Algorithm Overview • Starting with a subset of n randomly chosen solutions ( )from the search space (i.e. chromosomes). This is the population • This population is used to produce a next generation of individuals by reproduction • Individuals with a higher fitness (| - |)have more chance to reproduce (i.e. natural selection)

  16. GA in Pseudo code 0 START : Create random population of n chromosomes 1 FITNESS : Evaluate fitness f(x) of each chromosome in the population 2 NEW POPULATION 0 SELECTION : Based on f(x) 1 RECOMBINATION: Cross-over chromosomes 2 MUTATION : Mutatechromosomes 3 ACCEPTATION : Reject or accept new one 3 REPLACE : Replace old with new population: the new generation 4 TEST : Test problem criterium 5 LOOP : Continue step 1 – 4 until criterium is satisfied

  17. GA vs. Specialized Alg. Genetic Algorithms (GAs) GA Efficiency Specialized Algo. Problems P Specialized algorithms – best performance for special problems Genetic algorithms – good performance over a wide range of problems

  18. Randomized Algorithms • Guided random search technique • Uses the payoff function to guide search Hill Climbing local optima Global optima

  19. Evolutionary Algorithms? • Search Algorithms? • Learning Algorithms? • Function Optimization Algorithms? They are fundamentally the same!!

  20. Things needed for GAs • How do we represent individuals? Domain Dependent • How do we interpret individuals?Domain Dependent • What is the fitness function?Domain Dependent • How are individual chosen for reproduction?Choose better individuals (probabilistic) • How do individuals reproduce?Crossover, Mutation, etc. • How is the next generation generated?Replace badly performing individuals

  21. Chromosome A 10110010110011100101 Chromosome B 11111110000000011111 Chromosome 1.235  5.323  0.454  2.321  2.454 Chromosome A 1  5  3  2  6  4  7  9  8 Chromosome (left), (back), (left), (right), (forward) Chromosome B 8  5  6  7  2  3  1  4  9 Encoding Methods Binary Encoding/Ternary Encoding Permutation Encoding (TSP) Real numbers, etc. Specialized

  22. Fitness Function • A fitness function quantifies the optimality of a solution (chromosome) so that that particular solution may be ranked against all the other solutions. • A fitness value is assigned to each solution depending on how close it actually is to solving the problem. • Ideal fitness function correlates closely to goal + quickly computable. • Example. In TSP, f(x) is sum of distances between the cities in solution. The lesser the value, the fitter the solution is

  23. Producing Offspring The process that determines which solutions are to be preserved and allowed to reproduce and which ones deserve to die out. • The primary objective of the recombination operator is to emphasize the good solutions and eliminate the bad solutions in a population, while keeping the population size constant. • “Selects The Best, Discards The Rest”.

  24. Roulette Wheel Selection Chromosome # Fitness 1 15.3089 2 15.4091 3 4.8363 4 12.3975 4 3 2 1 Spin Strings that are fitter are assigned a larger slot and hence have a better chance of appearing in the new population.

  25. GA in Action for 8-Queen

  26. Fitness for 8-Queen? Minimum conflict fitness function.

  27. Theory (Schema Theorem) • Schema • Substring where some positions left undecided • 246***** • Instance of this schema: 24613587 • Theorem: if the average of the instances the schema is above the mean fitness of the population, the number of instances of the schema will increase over time.

  28. Applications • Many many… • VLSI, TSP, Function Optimization, Data mining, security, etc.

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