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	0.701	3662.241	0.000
baseline	singleBest	0.477	6338.901	254.757
baseline	singleBestByPar	0.477	6338.901	254.757
baseline	singleBestBySuccesses	0.477	6338.901	254.757
classif	rpart	0.557	5379.761	145.837
classif	randomForest	0.623	4597.806	81.395
classif	ksvm	0.622	4616.676	86.260
cluster	XMeans	0.495	6118.221	223.522
regr	lm	0.592	4961.727	107.506
regr	rpart	0.578	5140.133	131.323
regr	randomForest	0.649	4293.168	57.886

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 8, resulting in a PAR10 score of 4281.406 for the reduced model. Analogously, the model that was generated based on 6 of the originally 113 features resulted in a PAR10 score of 4035.973. Below, you can find the list of the selected features and solvers:

Selected Features:
POSNEG_RATIO_CLAUSE_mean, VCG_CLAUSE_coeff_variation, HORNY_VAR_max, VG_min, cl_size_q75,
SP_unconstraint_coeff_variation

Selected Solvers:
clasp2, cryptominisat2011, glueminisat, marchrw, mphaseSAT,
mxc09, sol, sparrow