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	1.000	219.867	0.000
baseline	singleBest	0.879	9017.077	937.668
baseline	singleBestByPar	0.879	9017.077	937.668
baseline	singleBestBySuccesses	0.879	9017.077	937.668
classif	rpart	0.955	3441.043	293.571
classif	randomForest	0.973	2209.651	216.007
classif	ksvm	0.971	2320.161	216.629
cluster	XMeans	0.925	5759.005	633.543
regr	lm	0.985	1395.820	171.390
regr	rpart	0.977	1959.323	240.377
regr	randomForest	0.984	1430.131	150.767

The following default feature steps were used for model building:

basic, basic_extended, lower_bounding, greedy_probing, A._probing, ILP_probing, CP_probing

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 86 / 86 instance features:

Variable.Count, VPOPS.Mean, POPS.Count, PSS.Maximum, PSS.Mean,
PSS.Standard.Deviation, VPOPS.Maximum, VPOPS.Standard.Deviation, Pattern.database.lower.bound.In.degree.Maximum, Pattern.database.lower.bound.In.degree.Mean,
Pattern.database.lower.bound.In.degree.Standard.Deviation, Pattern.database.lower.bound.Leaf.Count, Pattern.database.lower.bound.NTC.Count, Pattern.database.lower.bound.NTC.Max, Pattern.database.lower.bound.NTC.Mean,
Pattern.database.lower.bound.NTC.Standard.Deviation, Pattern.database.lower.bound.Out.degree.Maximum, Pattern.database.lower.bound.Out.degree.Mean, Pattern.database.lower.bound.Out.degree.Standard.Deviation, Pattern.database.lower.bound.Root.Count,
Pattern.database.lower.bound.Total.Degree.Maximum, Pattern.database.lower.bound.Total.Degree.Mean, Pattern.database.lower.bound.Total.Degree.Standard.Deviation, Simple.lower.bound.In.degree.Maximum, Simple.lower.bound.In.degree.Mean,
Simple.lower.bound.In.degree.Standard.Deviation, Simple.lower.bound.Leaf.Count, Simple.lower.bound.NTC.Count, Simple.lower.bound.NTC.Max, Simple.lower.bound.NTC.Mean,
Simple.lower.bound.NTC.Standard.Deviation, Simple.lower.bound.Out.degree.Maximum, Simple.lower.bound.Out.degree.Mean, Simple.lower.bound.Out.degree.Standard.Deviation, Simple.lower.bound.Root.Count,
Simple.lower.bound.Total.Degree.Maximum, Simple.lower.bound.Total.Degree.Mean, Simple.lower.bound.Total.Degree.Standard.Deviation, Greedy.hill.climbing.Error.bound, Greedy.hill.climbing.In.degree.Maximum,
Greedy.hill.climbing.In.degree.Mean, Greedy.hill.climbing.In.degree.Standard.Deviation, Greedy.hill.climbing.Leaf.Count, Greedy.hill.climbing.Out.degree.Maximum, Greedy.hill.climbing.Out.degree.Mean,
Greedy.hill.climbing.Out.degree.Standard.Deviation, Greedy.hill.climbing.Root.Count, Greedy.hill.climbing.Total.Degree.Maximum, Greedy.hill.climbing.Total.Degree.Mean, Greedy.hill.climbing.Total.Degree.Standard.Deviation,
Anytime.window.A..Error.bound, Anytime.window.A..In.degree.Maximum, Anytime.window.A..In.degree.Mean, Anytime.window.A..In.degree.Standard.Deviation, Anytime.window.A..Leaf.Count,
Anytime.window.A..Out.degree.Maximum, Anytime.window.A..Out.degree.Mean, Anytime.window.A..Out.degree.Standard.Deviation, Anytime.window.A..Root.Count, Anytime.window.A..Total.Degree.Maximum,
Anytime.window.A..Total.Degree.Mean, Anytime.window.A..Total.Degree.Standard.Deviation, GOBNILP.Error.bound, GOBNILP.In.degree.Maximum, GOBNILP.In.degree.Mean,
GOBNILP.In.degree.Standard.Deviation, GOBNILP.Leaf.Count, GOBNILP.Out.degree.Maximum, GOBNILP.Out.degree.Mean, GOBNILP.Out.degree.Standard.Deviation,
GOBNILP.Root.Count, GOBNILP.Total.Degree.Maximum, GOBNILP.Total.Degree.Mean, GOBNILP.Total.Degree.Standard.Deviation, CPBayes.Error.bound,
CPBayes.In.degree.Maximum, CPBayes.In.degree.Mean, CPBayes.In.degree.Standard.Deviation, CPBayes.Leaf.Count, CPBayes.Out.degree.Maximum,
CPBayes.Out.degree.Mean, CPBayes.Out.degree.Standard.Deviation, CPBayes.Root.Count, CPBayes.Total.Degree.Maximum, CPBayes.Total.Degree.Mean,
CPBayes.Total.Degree.Standard.Deviation

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 8 to 5, resulting in a PAR10 score of 1180.894 for the reduced model. Analogously, the model that was generated based on 5 of the originally 86 features resulted in a PAR10 score of 1085.356. Below, you can find the list of the selected features and solvers:

Selected Features:
Variable.Count, Pattern.database.lower.bound.Total.Degree.Maximum, Greedy.hill.climbing.In.degree.Standard.Deviation, GOBNILP.Out.degree.Mean, GOBNILP.Root.Count

Selected Solvers:
astar.ec, astar.comp, cpbayes, ilp.141, ilp.162