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	0.769	8377.272	0.000
baseline	singleBest	0.677	11703.780	324.411
baseline	singleBestByPar	0.677	11703.780	324.411
baseline	singleBestBySuccesses	0.677	11703.780	324.411
classif	rpart	0.703	10979.251	251.551
classif	randomForest	0.706	10846.879	213.988
classif	ksvm	0.713	10600.157	195.542
cluster	XMeans	0.673	12048.544	342.396
regr	lm	0.694	11295.926	266.618
regr	rpart	0.689	11507.334	312.707
regr	randomForest	0.712	10671.904	209.066

The following default feature steps were used for model building:

ALL

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 54 / 54 instance features:

nvarsOrig, nclausesOrig, nvars, nclauses, reducedVars,
reducedClauses, Pre.featuretime, 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, BINARY.,
TRINARY., Basic.featuretime, 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, KLB.featuretime, 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, CG.featuretime

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 7 to 4, resulting in a PAR10 score of 10107.083 for the reduced model. Analogously, the model that was generated based on 3 of the originally 54 features resulted in a PAR10 score of 10231.654. Below, you can find the list of the selected features and solvers:

Selected Features:
nvarsOrig, nclausesOrig, VG.max

Selected Solvers:
MaxHS, Open.WBO.ms.pre, UWrMaxSAT, maxino2018