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	0.943	2287.571	0.000
baseline	singleBest	0.870	5189.358	525.787
baseline	singleBestByPar	0.870	5189.358	525.787
baseline	singleBestBySuccesses	0.870	5189.358	525.787
classif	rpart	0.880	4706.229	366.658
classif	randomForest	0.887	4455.380	331.809
classif	ksvm	0.883	4567.651	336.080
cluster	XMeans	0.860	5483.982	496.412
regr	lm	0.873	4930.556	374.985
regr	rpart	0.870	5119.231	455.661
regr	randomForest	0.910	3649.287	281.717

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: NA

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 28 to 10, resulting in a PAR10 score of 3398.882 for the reduced model. Analogously, the model that was generated based on 3 of the originally 51 features resulted in a PAR10 score of 3642.952. Below, you can find the list of the selected features and solvers:

Selected Features:
TRINARY., POSNEG.RATIO.VAR.entropy, HORNY.VAR.entropy

Selected Solvers:
ADS.cryptominisat.autotune, Glucose_nbSat, GlueMiniSat_2.2.10, GlueMiniSat_2.2.10.5, Lingeling_sr15bal,
Lingeling_sr15baq, abcdSAT, minisat_BCD, or.tools, riss_505_1