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Empirical Algorithmics Reading Group Oct 11, 2007 Tuning Search Algorithms for Real-World Applications: A Regression Tree Based Approach by Thomas Bartz-Beielstein & Sandor Markon Presenter: Frank Hutter

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Motivation How to find a set of working parameters for direct search algorithms when the number of allowed epxeriments is low –i.e. find good parameters with few evaluations Taking a users perspective: –Adopt standard params from the literature –But NFL theorem: cant do good everywhere –Tune for instance class / for optimization instances even on a single instance

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Considered approaches Regression analysis ANOVA DACE CART

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Elevator Group Control Multi-objective problem –Overall service quality –Traffic throughput –Energy consumption –Transport capacity –Many more … Here: only one objective –Minimize time customers have to wait until they can enter the elevator car

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Optimization via Simulation Goal: Optimize expected performance E[y(x 1,…, x n )] (x 1,…, x n controllable) Black box function y

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Direct search algorithms Do not construct a model of the fitness function Interesting aside: same nomenclature as I use, but independent Here –Evolution strategy (special class of evolutionary algorithm) –Simulated annealing

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Evolution strategies (ES) Start out with parental population at t=0 For each new generation: –Create offsprings Select parent family of size \rho at random Apply recombination to object variables (?) and strategy parameters (?) –Mutation of each offspring –Selection

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Many parameters in ES Number of parent individuals Number of offspring individuals Initial mean step sizes ( i ) –Can choose problem-specific, different i for each dimension (not done here) Number of standard deviations (??) Mutation strength (global/individual, extended log-normal rule ??) Mixing number (size of each parent family) Recombination operator –For object variables –For strategy variables Selection mechanims, maximum life span Plus-strategies ( + ) and comma-strategies (, ) Can be generalized by (maximum age of individual)

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Simulated Annealing Proposal: Gaussian Markov kernel with scale proportional to the temperature Decrease temperature on a logarithmic cooling schedule Two parameters –Starting temperature –Number of function evaluations at each temperature

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Experimental Analysis of Search Heuristics Which parameters have the greatest effect? –Screening Which parameter setting might lead to an improved performance –Modelling –Optimization

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Design of experiments (DOE) Choose two factors for each parameter –Both qualitative and quantitative 2 k-p fractional factorial design –2: number of levels for each factor –K parameters –Only 2 k-p experiments –Can be generated from a full factorial design on k-p params –Resolution = (k-p) +1 (is this always the case?) Resolution 2: not useful – main effects are confounded with each other Resolution 3: often used, main effects are unconfounded with each other Resolution 4: all main effects are unconfounded with all 2-factor interactions Resolution 5: all 2-factor interactions are unconfounded with each other Here: 2 III 9-5 fractional factorial design

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Regression analysis Using stepAIC function built into R –Akaikes information criterion to penalize many parameters in the model –Line search to improve algorithms performance (?)

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Tree based regression Used for screening Based on the fractional factorial design Forward growing –Splitting criterion: minimal variance within the two children –Backward pruning: snipping away branches to maximize penalized cost Using rpart implementation from R –10-fold cross validation –1-SE rule: mean + 1stddev as pessimistic estimate –Threshold complexity parameter: visually chosen based on 1-SE rule

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Experimental results 5000 fitness evaluations as termination criterion Initialization already finds good parameters ! only small improvements possible Actual results not too important, but methods! Questions –Is strategy useful? –Improve parameters –Which analysis strategy works?

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Two splits (, ): Regression analysis:only first split significant Tuned algorithm found solution with quality y= –Which parameter settings? –What does mean? –How about multiple runs? strategy useful? regression tree analysis

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New Gupta vs. classical + selection Tune old and new variants Report new results and runtime for tuning –Just that they do not report the runtime for tuning

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Comparison of approaches on Simulated Annealing Only two (continuous) parameters Classical regression fails –No significant effects Regression tree –Best around 10,10 –Based on a full-factorial design with 2 levels each this is pretty shaky

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Comparison of approaches E.g. regression trees for screening, then DACE if only a few continuous parameters remain (why the restriction to few?)

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