Genetic Algorithms, Search Algorithms Jae C. Oh

Overview Search Algorithms Learning Algorithms GA Example

Brief History Evolutionary Programming Evolutionary Strategies 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

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

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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

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

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

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)

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

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

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

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)

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 : Mutate chromosomes 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

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

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

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

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

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

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

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”.

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.

GA in Action for 8-Queen

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

Theory (Schema Theorem) 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.

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