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Fitness Uniform Selection Scheme (FUSS) Shane Legg & Marcus Hutter IDSIA, Switzerland Akshat Kumar Indian Institute of Technology

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Initial Population

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Collapse in Diversity

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FUSS

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Selection Schemes

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FUSS Selection

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Properties of FUSS Uses fitness to control population diversity Should be good on problems with many local optima and deep valleys in fitness landscape Doesn't require a similarly metric for the problem to be constructed Problem and representation independent Parameter free (unlike tournament selection etc.) Easy to implement Computationally efficient

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Test System Implemented FUSS in Java Steady State GA rather than a Generational GA Used the usual method of random deletion Generations = number of cycles / population size Tested FUSS against Tournament selection Tournament sizes of 2, 5 and 15

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Artificial Deceptive Problem Mutation Operator = new random value for the x or y from [0,1] Crossover Operator = x from one parent, y from the other Default mutation and crossover probabilities of 0.5

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Random Distance TSP Distance between each pair of cities is random from [0,1] Triangle inequality does not hold in general Deceptive version of TSP but still has some structure Mutation operator = swap position of two cities in the tour Crossover operator = "Partial Match Crossover" 50 runs with 20 cities in each test Population size 5,000

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Set Covering Problem NP-complete optimisation problem with real applications Low cost = high fitness Tested against standard benchmark set covering problems Population size = 5,000 Crossover probability = 1.0, Mutation probability = 0.5 Standard mutation and crossover operators 1001 1111 0011 4238 = 7 total cost

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CNF 3SAT An individual is a set of boolean values for the variables Fitness is the total number of clauses satisfied We used standard benchmark problems for the tests 150 variables, 645 clauses in test problems Mutation = flip state of one boolean variable Crossover = uniform crossover Population size = 10,000 Mutation probability & crossover probability = 0.5

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Diversity Under FUSS Total population diversity was high Diversity among fit individuals was poor Can we use the idea of preserving diversity by using fitness values in a more effective way?

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Fitness Uniform Deletion Scheme (FUDS) The idea: If we delete an individual which has a unique fitness value we must be losing population diversity If we delete an individual which has a common fitness value we are probably not losing much diversity Thus, dont do random deletion, rather always delete individuals with commonly occurring fitness values. Rather than controlling diversity through selection, control it through deletion, hence FUDS Use a normal selection scheme like tournament selection

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Summary Both FUSS and FUDS are: Problem and representation independent Easily implemented and computationally cheap Help maintain total population diversity FUSS has significant problems FUDS has very encouraging results Go to www.idsia.ch for a technical report on FUDSwww.idsia.ch Maybe other variants on these ideas will work also?

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