Some LLAMA benchmark results

LLAMA results

All results were produced by using the cross-validation splits in the repository with 10 folds and 1 repetitions.
The best values within a type (i.e., baseline (except for vbs), classif, regr and cluster) and performance measure (i.e., Percentage solved, PAR10, MCP) are colored green. Furthermore, the three best values over all groups within a performance measure are colored pink, the absolute best one is red.

The performance is measured in three different ways.

Percentage solved records the percentage of problem instances in the data set for which the selector selected an algorithm that was able to solve it with runstatus "ok" and the algorithm time plus the feature computation time was at most the timeout.
The penalized average runtime score (PAR10) measures the time required to run on all problem instances. If an instance was solved within the timeout by the algorithm the selector chose, the actual runtime is taken. If a timeout occurred, the timeout value was multiplied by 10.
The misclassification penalty (mcp) measures the additional time required to run on all problems if sub-optimal algorithms were used. That is, if an algorithm is run on a problem instance that is not the best, a performance loss is incurred. There are no additional penalties or factors for timeouts. The virtual best solver always has a misclassification penalty of zero.

algo	model	succ	par10	mcp
baseline	vbs	0.843	8187.518	0.000
baseline	singleBest	0.717	14605.904	718.386
baseline	singleBestByPar	0.717	14605.904	718.386
baseline	singleBestBySuccesses	0.717	14605.904	718.386
classif	rpart	0.730	13915.184	525.249
classif	randomForest	0.743	13328.756	535.679
classif	ksvm	0.727	14124.445	580.634
cluster	XMeans	0.720	14537.503	692.635
regr	lm	0.733	13756.662	526.941
regr	rpart	0.680	16443.019	817.668
regr	randomForest	0.747	13115.011	476.887

The following default feature steps were used for model building:

Pre, Basic, KLB, CG

Number of presolved instances: 0

The cost for using the feature steps (adapted for presolving) is: 0 or on average: 0

The feature steps correspond to the following 50 / 115 instance features:

nvarsOrig, nclausesOrig, nvars, nclauses, reducedVars,
reducedClauses, vars_clauses_ratio, POSNEG_RATIO_CLAUSE_mean, POSNEG_RATIO_CLAUSE_coeff_variation, POSNEG_RATIO_CLAUSE_min,
POSNEG_RATIO_CLAUSE_max, POSNEG_RATIO_CLAUSE_entropy, VCG_CLAUSE_mean, VCG_CLAUSE_coeff_variation, VCG_CLAUSE_min,
VCG_CLAUSE_max, VCG_CLAUSE_entropy, UNARY, BINARYp, TRINARYp,
VCG_VAR_mean, VCG_VAR_coeff_variation, VCG_VAR_min, VCG_VAR_max, VCG_VAR_entropy,
POSNEG_RATIO_VAR_mean, POSNEG_RATIO_VAR_stdev, POSNEG_RATIO_VAR_min, POSNEG_RATIO_VAR_max, POSNEG_RATIO_VAR_entropy,
HORNY_VAR_mean, HORNY_VAR_coeff_variation, HORNY_VAR_min, HORNY_VAR_max, HORNY_VAR_entropy,
horn_clauses_fraction, VG_mean, VG_coeff_variation, VG_min, VG_max,
CG_mean, CG_coeff_variation, CG_min, CG_max, CG_entropy,
cluster_coeff_mean, cluster_coeff_coeff_variation, cluster_coeff_min, cluster_coeff_max, cluster_coeff_entropy

Algorithm and Feature Subset Selection

In order to get a better insight of the scenarios, forward selections have been applied to the solvers and features to determine whether small subsets achieve comparable performances. Following this approach, we reduced the number of solvers from 18 to 3, resulting in a PAR10 score of 12177.555 for the reduced model. Analogously, the model that was generated based on 5 of the originally 112 features resulted in a PAR10 score of 10667.869. Below, you can find the list of the selected features and solvers:

Selected Features:
cl_size_max, SP_bias_coeff_variation, SP_unconstraint_max, SP_unconstraint_q75, saps_FirstLocalMinStep_Median

Selected Solvers:
QuteRSat_2011.05.12_fixed_, SAT09referencesolverprecosat_236, glucose_2