HEURISTIC OPTIMIZATION Automatic Algorithm Configuration Design choices and parameters everywhere Todays high-performance optimizers involve a large number 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 parameters I 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 parameters I example: multi-objective ACO algorithms with 22 parameters (plus several still hidden ones): see later Heuristic Optimization 2011 2
Example: Ant Colony Optimization Heuristic Optimization 2011 3 ��������� ����������� �������������� ��������� ������������� ������������� ����������� ����������������� ���������������� Heuristic Optimization 2011 4
Probabilistic solution construction g j ? ! ij " ij , i k Heuristic Optimization 2011 5 ACO design choices and numerical parameters I solution construction I choice of pheromone model I choice of heuristic information I choice of constructive procedure I numerical parameters I α , β influence the weight of pheromone and heuristic information, respectively I q 0 determines greediness of construction procedure I m , the number of ants I pheromone update I which ants deposit pheromone and how much? I numerical parameters I ρ : evaporation rate I τ 0 : initial pheromone level I local search I . . . many more . . . Heuristic Optimization 2011 6
Designing optimization algorithms Challenges I many alternative design choices I nonlinear interactions among algorithm components and/or parameters I performance assessment is di ffi cult Traditional design approach I trial–and–error design guided by expertise/intuition prone to over-generalizations, implicit independence assumptions, limited exploration of design alternatives Can we make this approach more principled and automatic? Heuristic Optimization 2011 7 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 Heuristic Optimization 2011 8
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 Heuristic Optimization 2011 9 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 be tackled Learning aspects I algorithm configuration should solve unseen instances Configuration problem is a stochastic mixed discrete–continuous optimization problem with machine learning aspects Heuristic Optimization 2011 10
Main configuration approaches O ffl 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 algorithm parameters Heuristic Optimization 2011 11 O ffl ine configuration Remark: Configuration scenario requires the definition of performance measure to be optimized I maximize solution quality (within given computation time) I minimize computation time (to reach optimal solution) Heuristic Optimization 2011 12
Towards a shift of paradigm in algorithm design ��������� ������������� ������������� ��������������� ����������������� Heuristic Optimization 2011 13 Towards a shift of paradigm in algorithm design ��������� ������������� ������������� ��������������� ����������������� Heuristic Optimization 2011 14
Towards a shift of paradigm in algorithm design ��������� ������������� ������������� ��������������� ����������������� ��������� ������� ���������� Heuristic Optimization 2011 15 Approaches to configuration and tuning I numerical optimization techniques I e.g. CMA-ES [Hansen & Ostermeier, 2001], MADS [Audet & Orban, 2006] I heuristic search methods I e.g. ParamILS [Hutter, Hoos, Leyton-Brown, St¨ utzle, 2009], genetic programming [Fukunaga, 2002], gender-based GA [Sellman et al, 2010], . . . I experimental design, ANOVA I 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-race I e.g. [Birratari, St¨ utzle, Paquete, Varrentrap, 2002;Balaprakash, Birattari, St¨ utzle, 2007] Heuristic Optimization 2011 16
Example of application scenario I Mario collects phone orders for 30 minutes I scheduling deliveries is an optimization problem I a di ff 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 one week Criterion: Good configurations find good solutions for future instances! Heuristic Optimization 2011 17 Brute-force approach to configuration 1. sample a set of configurations Θ 0 ⊆ Θ 2. estimate C ( θ ) for each θ ∈ Θ 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 each candidate configuration 2. poor performing candidate configurations are evaluated with same computational e ff ort as good ones Heuristic Optimization 2011 18
Remark : Estimation of expected cost Given I n runs for estimating expected cost of configuration θ I a large number of instances Question I how many runs on how many instances to minimize variance of estimate Answer I one run on each of n instances (Birattari, 2004) Heuristic Optimization 2011 19 The racing approach Θ I start with a set of initial candidates I consider a stream of instances I sequentially evaluate candidates I discard inferior candidates as su ffi cient evidence is gathered against them I . . . repeat until a winner is selected or until computation time expires i Heuristic Optimization 2011 20
The F-Race algorithm Statistical testing 1. family-wise tests for di ff erences among configurations I Friedman two-way analysis of variance by ranks 2. if Friedman rejects H 0 , perform pairwise comparisons to best configuration I apply Friedman post-hoc test Predecessors I racing algorithms in model-selection Maron & Moore (1994) Heuristic Optimization 2011 21 Sampling configurations F-race is a method for the selection of the best configuration and independent 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) Heuristic Optimization 2011 22
Full factorial design I full factorial design (FFD) was used in the first applications of F-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: l d Heuristic Optimization 2011 23 Random sampling design I Define a probability measure P X on the space X of parameter values I Sample the configurations I Apply F-Race to select the best I Performance attributed to the number of samples I advantages I arbitrary number of candidate configurations is sampled I no a priori definition of levels necessary I covers uniformly the parameter space Heuristic Optimization 2011 24
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 Heuristic Optimization 2011 25 I sample configurations from initial distribution While not terminate() 1. apply F-Race 2. modify the distribution 3. sample configurations with selection probability Heuristic Optimization 2011 26
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