HEURISTIC OPTIMIZATIONiridia.ulb.ac.be/~stuetzle/Teaching/HO13/Slides/Lecture11a.pdf · Heuristic Optimization 2011 11 O ine conﬁguration Remark: Conﬁguration scenario requires

HEURISTIC OPTIMIZATION

Automatic Algorithm Configuration

Design choices and parameters everywhere

Todays high-performance optimizers involve a largenumber of design choices and parameter settings

I exact solvers

I design choices include alternative models, pre-processing,variable selection, value selection, branching rules . . .

I many design choices have associated numerical parametersI example: CPLEX 10.1.1 has 159 user-specifiable parameters,

about 80 influence the solver’s search mechanism

I approximate algorithms

I design choices include solution representation, operators,neighborhood, pre-processing, strategies, . . .

I many design choices have associated numerical parametersI example: ACO algorithms: see later

Heuristic Optimization 2011 2

Example: Ant Colony Optimization


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Probabilistic solution construction

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ACO design choices and numerical parameters

I solution constructionI choice of pheromone modelI choice of heuristic informationI choice of constructive procedureI numerical parameters

I ↵,� influence the weight of pheromone and heuristicinformation, respectively

I q0 determines greediness of construction procedureI m, the number of ants

I pheromone update

I which ants deposit pheromone and how much?I numerical parameters

I ⇢: evaporation rateI ⌧0: initial pheromone level

I local searchI . . . many more . . .


Designing optimization algorithms

Challenges

I many alternative design choices

I nonlinear interactions among algorithm componentsand/or parameters

I performance assessment is di�cult

Traditional design approach

I trial–and–error design guided by expertise/intuition prone to over-generalizations, implicit independenceassumptions, limited exploration of design alternatives

Can we make this approach more principled and automatic?


Towards automatic algorithm configuration

Automated algorithm configuration

I apply powerful search techniques to design algorithms

I use computation power to explore algorithm design spaces

I free human creativity for higher level tasks


Why automatic algorithm configuration?

I improvement over manual, ad-hoc methods for tuning

I reduction of development time and human intervention

I increase number of considerable degrees of freedom

I empirical studies, comparisons of algorithms

I support for end users of algorithms


Configuration is a stochastic optimization/learning problem

Random influences

I stochasticity of the parameterized algorithm

I stochasticity due to the “sampling” of the instance to betackled

Learning aspects

I algorithm configuration should solve unseen instances

Configuration problem is a stochastic mixed discrete–continuousoptimization problem with machine learning aspects


Main configuration approaches

O✏ine configuration

I configure algorithm before deploying it

I configuration done on training instances

Online configuration

I adapt parameter setting while solving an instance

I typically limited to a set of known crucial algorithmparameters


O✏ine configuration

Remark: Configuration scenario requires the definition ofperformance measure to be optimized

I maximize solution quality (within given computation time)

I minimize computation time (to reach optimal solution)


Towards a shift of paradigm in algorithmdesign

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Approaches to configuration and tuning

I numerical optimization techniquesI e.g. CMA-ES [Hansen & Ostermeier, 2001], MADS [Audet &

Orban, 2006]

I heuristic search methodsI e.g. ParamILS [Hutter, Hoos, Leyton-Brown, Stutzle, 2009], genetic

programming [Fukunaga, 2002], gender-based GA [Sellman et al,2010], . . .

I experimental design, ANOVAI e.g. CALIBRA [Adenso-Diaz & Laguna, 2006], [Ridge, Kudenko,

2007, Ruiz Maroto, 2006, Coy et al., 2000]

I response surface methods (model-based optimization)I e.g. SPO [Bartz-Beielstein, 2006], SMAC [Hutter, Hoos,

Leyton-Brown, 2011]

I sequential statistical testing, F-race, iterated F-raceI e.g. [Birratari, Stutzle, Paquete, Varrentrap, 2002;Balaprakash,

Birattari, Stutzle, 2007]


Example of application scenario

I Mario collects phone orders for 30 minutes

I scheduling deliveries is an optimization problem

I a di↵erent instance arises every 30 minutes

I limited amount of time for scheduling, say one minute

I good news: Mario has an SLS algorithm!

I . . . but the SLS algorithm must be tuned

I You have a limited amount of time for configuring it, say oneweek

Criterion:Good configurations find good solutions for future instances!


Brute-force approach to configuration

1. sample a set of configurations ⇥0 ✓ ⇥

2. estimate C(✓) for each ✓ 2 ⇥0

3. return the configuration with the lowest estimate

Disadvantages of brute-force configuration

1. one needs to determine a priori how many runs on eachcandidate configuration

2. poor performing candidate configurations are evaluated withsame computational e↵ort as good ones


Remark: Estimation of expected cost

Given

I n runs for estimating expected cost of configuration ✓

I a large number of instances

Question

I how many runs on how many instances to minimize varianceof estimate

Answer

I one run on each of n instances (Birattari, 2004)


The racing approach

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I start with a set of initial candidates

I consider a stream of instances

I sequentially evaluate candidates

I discard inferior candidatesas su�cient evidence is gathered against them

I . . . repeat until a winner is selectedor until computation time expires


The F-Race algorithm

Statistical testing

1. family-wise tests for di↵erences among configurations

I Friedman two-way analysis of variance by ranks

2. if Friedman rejects H0, perform pairwise comparisons to bestconfiguration

I apply Friedman post-hoc test

Predecessors

I racing algorithms in model-selection Maron & Moore (1994)


Sampling configurations

F-race is a method for the selection of the best configuration andindependent of the way the set of configurations is sampled

Sampling configurations and F-race

I full factorial design

I random sampling design

I iterative refinement of a sampling model (iterative F-race)


Full factorial design

I full factorial design (FFD) was used in the first applications ofF-race to make comparisons to other ways of doing races

I levels for FFD can be determined manually, randomly, etc.

I FFD has significant disadvantages

I expertise for selecting the levels of each parameter

I exponential growth with number d of parameters: ld


Random sampling design

I Define a probability measure PX onthe space X of parameter values

I Sample the configurations

I Apply F-Race to select the best

I Performance attributed to the numberof samples

I advantagesI arbitrary number of candidate

configurations is sampledI no a priori definition of levels

necessaryI covers uniformly the parameter space


Iterative re-finement

I modify the probability measure:I using previously seen promising configurations to favor the

search towards promising regions

I sample from the newly defined distribution

I apply F-race

I iterate through this process


I sample configurationsfrom initial distribution

While not terminate()

1. apply F-Race

2. modify the distribution

3. sample configurationswith selection probability


Tuning MMAS for TSP

I 3 continuous parameters; only continuous partI FFD: {apriori knowledge, random}

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Successful applications

From IRIDIA

I winning algorithm in a time-tabling competition

I improving vehicle routing and scheduling software of SAP

I new state-of-the-art metaheuristics for the probabilistic TSPand stochastic VRPs

I various state-of-the-art algorithms in continuous optimizationI PSO for large-scale continuous functionsI continuous ACO algorithms

Other groups

I Satenstein: configurable software framework for SAT solving

I Configuration of MIP solvers (Cplex etc.) with speed-ups ofup to two orders of magnitude

I . . .Heuristic Optimization 2011 28

Conclusions

Status

I using automatic configuration tools is rewarding in terms ofdevelopment time and algorithm performance

I interactive usage of configurators allows humans to focus oncreative part of algorithm design

I many application opportunities also in other areas thanoptimization

Future work

I more powerful configurators

I more and more complex applications

I best practice


Documents

HEURISTIC OPTIMIZATIONiridia.ulb.ac.be/~stuetzle/Teaching/HO13/Slides/Lecture11a.pdf · Heuristic Optimization 2011 11 O ine conﬁguration Remark: Conﬁguration scenario requires