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	0.740	13360.664	0.000
baseline	singleBest	0.497	25649.093	1342.483
baseline	singleBestByPar	0.500	25589.269	1434.686
baseline	singleBestBySuccesses	0.500	25589.269	1434.686
classif	rpart	0.642	18329.712	535.658
classif	randomForest	0.649	17946.066	455.816
classif	ksvm	0.679	16446.063	322.946
cluster	XMeans	0.524	24067.250	958.472
regr	lm	0.611	19715.731	554.417
regr	rpart	0.611	19835.519	674.197
regr	randomForest	0.666	17097.651	366.765

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 15 to 6, resulting in a PAR10 score of 16117.924 for the reduced model. Analogously, the model that was generated based on 7 of the originally 113 features resulted in a PAR10 score of 15280.096. Below, you can find the list of the selected features and solvers:

Selected Features:
vars_clauses_ratio, POSNEG_RATIO_CLAUSE_entropy, cl_num_min, cl_size_mean, SP_bias_mean,
SP_bias_coeff_variation, SP_unconstraint_mean

Selected Solvers:
MPhaseSAT_2011.02.15, QuteRSat_2011.05.12_fixed_, SAT09referencesolverclasp_1.2.0.SAT09.32, Sol_2011.04.04, clasp_2.0.R4092.crafted,
sattime_2011.03.02