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	0.810	9841.233	0.000
baseline	singleBest	0.586	21132.115	1220.060
baseline	singleBestByPar	0.586	21132.115	1220.060
baseline	singleBestBySuccesses	0.586	21132.115	1220.060
classif	rpart	0.671	16854.266	766.573
classif	randomForest	0.697	15524.588	584.204
classif	ksvm	0.683	16230.220	652.442
cluster	XMeans	0.612	19914.273	1149.527
regr	lm	0.694	15674.298	606.436
regr	rpart	0.657	17486.690	761.604
regr	randomForest	0.700	15356.449	543.544

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 50 / 50 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, BINARY., TRINARY.,
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 37 to 11, resulting in a PAR10 score of 13757.915 for the reduced model. Analogously, the model that was generated based on 4 of the originally 48 features resulted in a PAR10 score of 13711.867. Below, you can find the list of the selected features and solvers:

Selected Features:
POSNEG.RATIO.CLAUSE.coeff.variation, BINARY., horn.clauses.fraction, VG.max

Selected Solvers:
CaDiCaL, Candy, YalSAT, Maple_CM_ordUIP., Maple_CM_ordUIP,
Maple_CM, MapleLCMDistChronoBT, Lingeling, gluHack, Glucose_Hack_Kiel_fastBVE,
Sparrow2Riss.2018.fixfix