Automatic Solver Configuration and Solver Portfolios Meinolf Sellmann IBM Research Watson AI for Optimization
Why Tune Algorithms? Develops Pretunes Expert Documents Parameters Algorithm Tune Instances Users AI for Optimization CP 2011 Meinolf Sellmann
Why Tune Algorithms? AI for Optimization CP 2011 Meinolf Sellmann
Tuning vs Configuration AI for Optimization CP 2011 Meinolf Sellmann
Why Tune Algorithms? • Algorithms have parameters – Implicit in the implementation – Open to user – Big influence on practical performance (speed, accuracy, robustness, etc) • The practice: manual tuning – Takes a lot of time, often not very good – Requires user to learn meaning of parameters • Objectives – Automate tuning – Automatic algorithm customization – Aid developers in algorithm configuration – Enable fair comparison of algorithms AI for Optimization CP 2011 Meinolf Sellmann
Why Bundle Algorithms? AI for Optimization CP 2011 Meinolf Sellmann
Why Bundle Algorithms? AI for Optimization CP 2011 Meinolf Sellmann
Content • Instance-Oblivious Tuning • Algorithm Portfolios – Overview of Approaches – Overview of Approaches – Parameters: Variable Tree – SATzilla Representation – CP-Hydra – GGA: Gender-Based – 3S Genetic Algorithm – GGA: Numerical Results • Instance-Specific Tuning – Overview of Approaches – ISAC: Feature-based Parameter Selection – ISAC: Numerical Results AI for Optimization CP 2011 Meinolf Sellmann
Instance-oblivious Tuning • One parameter set fits all • Most common way of tuning • Customization only by parameterization + manual tuning AI for Optimization CP 2011 Meinolf Sellmann
Overview of Methods • Popular Tuning Methods – Enumerate all configurations – Test specific configurations (based on some understanding of the parameters) – Hand tuning (usually by limited local search) – Automated tuning AI for Optimization CP 2011 Meinolf Sellmann
Overview of Methods • Continuous parameters – Mesh-adaptive Direct Search, MADS [Audet et al, '06] – Population-based, e.g. CMA-ES [Hansen et al, '95] • Categorical parameters – Hill-climbing, Composer [Gratch et al, '92] – Beam search, MULTI-TAC [Minton, '93] – Racing algorithms, F-Race [Birattari et al, '02] – CALIBRA [Adenso-Diaz & Laguna, '06] – Iterated Local Search, ParamILS [Hutter et al, '07] • Model-Based Parameter Optimization – Sequential Parameter Optimization (SPO) [Bartz-Beielstein et al., '05] – Extensions of SPO [Hutter et al, ‘09] • Non-model-based configuration for general parameters – Gender-based genetic algorithm (GGA) [Ansotegui et al. ‘09] AI for Optimization CP 2011 Meinolf Sellmann
C ovariance M atrix A daptation E volution S trategy • General optimizer for highly non-linear continuous optimization problems • Black box optimization (derivatives not available) • The typical difference quotients are not useful • Discontinuities • Noise and outlier • Many local optima • In summary: Black box optimization in a rough or rugged landscape. AI for Optimization CP 2011 Meinolf Sellmann
C ovariance M atrix A daptation E volution S trategy • Repeat – Sample m times around “point of interest” according to N( , ). – Determine best sampling point and set to it. – Adapt . AI for Optimization CP 2011 Meinolf Sellmann
C ovariance M atrix A daptation E volution S trategy AI for Optimization CP 2011 Meinolf Sellmann
C ovariance M atrix A daptation E volution S trategy AI for Optimization CP 2011 Meinolf Sellmann
C ovariance M atrix A daptation E volution S trategy AI for Optimization CP 2011 Meinolf Sellmann
C ovariance M atrix A daptation E volution S trategy AI for Optimization CP 2011 Meinolf Sellmann
Multi-TAC • Selector for heuristics in backtrack search • Beam Search Approach • Repeat – Add a single heuristic to each current search method – Evaluate all resulting search methods – Keep the best m methods AI for Optimization CP 2011 Meinolf Sellmann
Multi-TAC ( o , o , o ) ( 1 , o , o ) ( o , 1 , o ) ( o , o , 1 ) ( o , o , 2 ) ( o , 2 , o ) ( 2 , o , o ) ( o , o , 3 ) ( 3 , o , o ) ( 4 , o , o ) AI for Optimization CP 2011 Meinolf Sellmann
Multi-TAC ( 1 , o , o ) ( 12 , o , o ) ( 1 , 1 , o ) ( 1 , o , 1 ) ( 1 , 2 , o ) ( 1 , o , 2 ) ( 13 , o , o ) ( 1 , o , 3 ) ( 14 , o , o ) ( 3 , o , o ) ( 31 , o , o ) ( 3 , 1 , o ) ( 3 , o , 1 ) ( 3 , o , 2 ) ( 3 , 2 , o ) ( 32 , o , o ) ( 3 , o , 3 ) ( 34 , o , o ) AI for Optimization CP 2011 Meinolf Sellmann
Multi-TAC ( 34 , o , 2 ) ( 341 , o , 2 ) ( 34 , 1 , 2 ) ( 34, o , 21 ) ( 34 , 2 , 2 ) ( 34 , o , 23 ) ( 342, o , 2 ) ( 3 , o , 2 ) ( 31 , o , 2 ) ( 3 , 1 , 2 ) ( 3 , o , 21 ) ( 3 , o , 23 ) ( 3 , 2 , 2 ) ( 32 , o , 2 ) ( 34 , o , 2 ) AI for Optimization CP 2011 Meinolf Sellmann
F-Race • How to determine whether one meta- heuristic works better than another? • Repeat – Pick a new instance – Run and rank all algorithms still in the race – Remove inferior algorithms AI for Optimization CP 2011 Meinolf Sellmann
F-Race 1 2 3 4 5 5 1 6 4 3 5 3 2 2 1 2 2 7 6 6 4 5 4 7 4 3 1 3 2 1 1 AI for Optimization CP 2011 Meinolf Sellmann
F-Race Friedmann Test AI for Optimization CP 2011 Meinolf Sellmann
GGA • General purpose tuner • Handles various types of parameters • Provides high-quality configurations – Robustly – With reasonable computational effort • Exploits – Optimization technology – Parallelism AI for Optimization CP 2011 Meinolf Sellmann
Content • Instance-Oblivious Tuning • Algorithm Portfolios – Overview of Approaches – Overview of Approaches – Parameters: Variable Tree – SATzilla Representation – CP-Hydra – GGA: Gender-Based – 3S Genetic Algorithm – GGA: Numerical Results • Instance-Specific Tuning – Overview of Approaches – ISAC: Feature-based Parameter Selection – ISAC: Numerical Results AI for Optimization CP 2011 Meinolf Sellmann
Variable Trees Categorical Parameter r r g Independence & 1 Numerical Parameter & .5 2 Ordinal Parameter 1 .7 3 AI for Optimization
Variable Trees • Parameter structure represented by an And-Or structure • Represents parameter (in)dependence • Example: 2 f ( x ) ( x x x q ) 3 i 3 i 1 3 i 2 i i [ 0 , n ] & x 3i x 3n x 0 . . . . . . x 1 x 3i+1 X 3n+1 x 2 x 3i+2 X 3n+2 AI for Optimization
Generic Crossover Operator r r N C g r r g & 1 & .7 & .5 2 .9 1 & 1 .7 3 .6 1 2 O r r g O N & 1 N C C & .9 2 C C C 1 2 .6 AI for Optimization CP 2011 Meinolf Sellmann
Genetic Algorithm • Computational Limitations – Low number of individuals – Low number of generations • What did nature do when going from to ? AI for Optimization CP 2011 Meinolf Sellmann
Gender-based Genetic Algorithm • Optimization Problems – Low number of generations aggressive optimization – Low number of individuals emphasis on diversity • How can genders help? – Split the population into two genders: competitive (C) and non-competitive (N) – Save 50% of evaluations – Racing: Winners determine evaluation time! – Can afford aggressive selection pressure on C – Individuals in N provide the needed diversity AI for Optimization CP 2011 Meinolf Sellmann
Gender-based Genetic Algorithm C N N N C Race in N Tournament N N Crossover Mutation N N N C Aging and Death N N AI for Optimization CP 2011 Meinolf Sellmann
Population Control • All members have an age • Only 2/ A of the N population mates • 1/A of each population dies at age A C N C N Children 1 X% 2 A A 1 Mating A 1/A die of old age AI for Optimization CP 2011 Meinolf Sellmann
Content • Instance-Oblivious Tuning • Algorithm Portfolios – Overview of Approaches – Overview of Approaches – Parameters: Variable Tree – SATzilla Representation – CP-Hydra – GGA: Gender-Based – 3S Genetic Algorithm – GGA: Numerical Results • Instance-Specific Tuning – Overview of Approaches – ISAC: Feature-based Parameter Selection – ISAC: Numerical Results AI for Optimization CP 2011 Meinolf Sellmann
Results • Test against a standard GA – 3 functions with various dependencies – Tested with various population sizes and numbers of generations AI for Optimization CP 2011 Meinolf Sellmann
Results AI for Optimization CP 2011 Meinolf Sellmann
Results Competitive best fitness Non-competitive best fitness Competitive average fitness Non-competitive average fitness AI for Optimization CP 2011 Meinolf Sellmann
Results • Standard GA vs. GGA tuning SAT-solver SAPS • 40 generations with 30 members • Cutoff of 10 seconds • GA wastes lots of time on bad solutions AI for Optimization CP 2011 Meinolf Sellmann
Results SAPS (ms) SAT4J (s) AI for Optimization CP 2011 Meinolf Sellmann
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