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	0.821	2221.497	0.000
baseline	singleBest	0.736	3266.048	128.355
baseline	singleBestByPar	0.736	3266.048	128.355
baseline	singleBestBySuccesses	0.736	3266.048	128.355
classif	rpart	0.722	3449.570	121.238
classif	randomForest	0.772	2848.671	46.430
classif	ksvm	0.766	2924.275	58.629
cluster	XMeans	0.724	3433.010	118.633
regr	lm	0.759	3015.787	75.810
regr	rpart	0.738	3272.584	105.620
regr	randomForest	0.774	2832.076	49.036

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 31 to 7, resulting in a PAR10 score of 2764.164 for the reduced model. Analogously, the model that was generated based on 5 of the originally 113 features resulted in a PAR10 score of 2509.364. Below, you can find the list of the selected features and solvers:

Selected Features:
POSNEG_RATIO_CLAUSE_coeff_variation, TRINARYp, cl_num_q10, SP_bias_mean, SP_bias_coeff_variation

Selected Solvers:
clasp2, cryptominisat2011, glucose2, lingeling, lrglshr,
mphaseSAT64, mphaseSATm