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Motivation

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. Motivation.

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Motivation

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  1. Empirical Algorithmics Reading Group Oct 11, 2007Tuning Search Algorithms for Real-World Applications:A Regression Tree Based Approachby Thomas Bartz-Beielstein & Sandor MarkonPresenter: Frank Hutter

  2. 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 user’s perspective: • Adopt standard params from the literature • But NFL theorem: can’t do good everywhere • Tune for instance class / for optimization instances even on a single instance

  3. Considered approaches • Regression analysis • ANOVA • DACE • CART

  4. 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

  5. Optimization via Simulation • Goal: Optimize expected performanceE[y(x1,…, xn)] (x1,…, xn controllable) • Black box function y

  6. 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

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

  8. Many parameters in ES • Number of parent individuals • Number of offspring individuals • Initial mean step sizes (si) • Can choose problem-specific, different si 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 (m + l) and comma-strategies (m, l)Can be generalized by k (maximum age of individual)

  9. 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

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

  11. Design of experiments (DOE) • Choose two factors for each parameter • Both qualitative and quantitative • 2k-p fractional factorial design • 2: number of levels for each factor • K parameters • Only 2k-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: 2III9-5 fractional factorial design

  12. Regression analysis • Using stepAIC function built into R • Akaike’s information criterion to penalize many parameters in the model • Line search to improve algorithm’s performance (?)

  13. 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

  14. 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 k strategy useful? • Improve parameters • Which analysis strategy works?

  15. k strategy useful?regression tree analysis • Two splits (m, k):Regression analysis:only first split significant • Tuned algorithm foundsolution with quality y=32.252 • Which parameter settings? • What does 32.252 mean? • How about multiple runs?

  16. 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 

  17. 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

  18. 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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