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	0.980	20768926.162	0.000
baseline	singleBest	0.971	28978538.201	820965.751
baseline	singleBestByPar	0.971	28978538.201	820965.751
baseline	singleBestBySuccesses	0.971	28978538.201	820965.751
classif	rpart	0.969	31798065.226	1124141.120
classif	randomForest	0.971	29688043.470	900576.134
classif	ksvm	0.976	24277795.373	363677.250
cluster	XMeans	0.974	26137656.548	494292.295
regr	lm	0.975	25495667.902	481113.659
regr	rpart	0.973	27564806.069	663797.158
regr	randomForest	0.975	25293640.127	436294.922

The following default feature steps were used for model building:

cheap_pattern, cheap_target, distance_pattern, distance_target, lad_features

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 35 / 35 instance features:

cheap.pattern.time, cheap.pattern.vertices, cheap.pattern.edges, cheap.pattern.loops, cheap.pattern.meandeg,
cheap.pattern.maxdeg, cheap.pattern.degisfixed, cheap.pattern.density, cheap.target.time, cheap.target.vertices,
cheap.target.edges, cheap.target.loops, cheap.target.meandeg, cheap.target.maxdeg, cheap.target.degisfixed,
cheap.target.density, distance.pattern.time, distance.pattern.isconnected, distance.pattern.meandistance, distance.pattern.maxdistance,
distance.pattern.proportiondistancege2, distance.pattern.proportiondistancege3, distance.pattern.proportiondistancege4, distance.target.time, distance.target.isconnected,
distance.target.meandistance, distance.target.maxdistance, distance.target.proportiondistancege2, distance.target.proportiondistancege3, distance.target.proportiondistancege4,
lad.values.removed, lad.values.removed.percent, lad.values.removed.min, lad.values.removed.max, lad.time

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 2, resulting in a PAR10 score of 24235562.563 for the reduced model. Analogously, the model that was generated based on 5 of the originally 35 features resulted in a PAR10 score of 23231401.992. Below, you can find the list of the selected features and solvers:

Selected Features:
cheap.pattern.vertices, distance.pattern.maxdistance, distance.pattern.proportiondistancege2, distance.pattern.proportiondistancege3, lad.time

Selected Solvers:
supplementallad, glasgow2