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	0.863	7137.571	10.836
baseline	singleBest	0.804	10126.835	390.100
baseline	singleBestByPar	0.804	10126.835	390.100
baseline	singleBestBySuccesses	0.805	10213.286	521.551
classif	rpart	0.814	9693.348	314.755
classif	randomForest	0.814	9661.883	279.970
classif	ksvm	0.812	9728.371	300.952
cluster	XMeans	0.804	10185.511	381.364
regr	lm	0.822	9278.063	278.841
regr	rpart	0.806	10107.674	391.658
regr	randomForest	0.825	9092.107	226.589

The following default feature steps were used for model building:

base, tud_base

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 142 / 483 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, BINARYp, TRINARYp,
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,
tud_clauses, tud_vars, tud_clauses_size_1, tud_clauses_size_2, tud_clauses_size_3,
tud_clauses_size_4, tud_clauses_size_5, tud_clauses_size_6, tud_clauses_size_7, tud_clauses_size_8,
tud_clauses_size_.._9, tud_horn_clauses, tud_clause.variable_degree_min, tud_clause.variable_degree_max, tud_clause.variable_degree_mode,
tud_clause.variable_degree_mean, tud_clause.variable_degree_stdev, tud_clause.variable_degree_entropy, tud_clause.variable_degree_valuesRate, tud_clause.variable_degree_Q1,
tud_clause.variable_degree_Q2, tud_clause.variable_degree_Q3, tud_variable.clause_degree_zcount, tud_variable.clause_degree_min, tud_variable.clause_degree_max,
tud_variable.clause_degree_mode, tud_variable.clause_degree_mean, tud_variable.clause_degree_stdev, tud_variable.clause_degree_entropy, tud_variable.clause_degree_valuesRate,
tud_variable.clause_degree_Q1, tud_variable.clause_degree_Q2, tud_variable.clause_degree_Q3, tud_clause.variable_polarity_min, tud_clause.variable_polarity_max,
tud_clause.variable_polarity_mode, tud_clause.variable_polarity_mean, tud_clause.variable_polarity_stdev, tud_clause.variable_polarity_entropy, tud_clause.variable_polarity_valuesRate,
tud_clause.variable_polarity_Q1, tud_clause.variable_polarity_Q2, tud_clause.variable_polarity_Q3, tud_variable.clause_polarity_zcount, tud_variable.clause_polarity_min,
tud_variable.clause_polarity_max, tud_variable.clause_polarity_mode, tud_variable.clause_polarity_mean, tud_variable.clause_polarity_stdev, tud_variable.clause_polarity_entropy,
tud_variable.clause_polarity_valuesRate, tud_variable.clause_polarity_Q1, tud_variable.clause_polarity_Q2, tud_variable.clause_polarity_Q3, tud_Clause.Var_steps,
tud_SymmTime0_zcount, tud_SymmTime0_min, tud_SymmTime0_max, tud_SymmTime0_mode, tud_SymmTime0_mean,
tud_SymmTime0_stdev, tud_SymmTime0_entropy, tud_SymmTime0_valuesRate, tud_SymmTime0_Q1, tud_SymmTime0_Q2,
tud_SymmTime0_Q3, tud_Symmetry0_steps, tud_SymmTime1_zcount, tud_SymmTime1_min, tud_SymmTime1_max,
tud_SymmTime1_mode, tud_SymmTime1_mean, tud_SymmTime1_stdev, tud_SymmTime1_entropy, tud_SymmTime1_valuesRate,
tud_SymmTime1_Q1, tud_SymmTime1_Q2, tud_SymmTime1_Q3, tud_Symmetry1_steps, tud_SymmTime2_zcount,
tud_SymmTime2_min, tud_SymmTime2_max, tud_SymmTime2_mode, tud_SymmTime2_mean, tud_SymmTime2_stdev,
tud_SymmTime2_entropy, tud_SymmTime2_valuesRate, tud_SymmTime2_Q1, tud_SymmTime2_Q2, tud_SymmTime2_Q3,
tud_Symmetry2_steps, tud_Symmetry_computation_steps

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 10 to 6, resulting in a PAR10 score of 8800.582 for the reduced model. Analogously, the model that was generated based on 3 of the originally 477 features resulted in a PAR10 score of 8549.498. Below, you can find the list of the selected features and solvers:

Selected Features:
tud_resolution_graph_weights_Q1, tud_variable.clause_polarity_derivative_min, tud_RWH.1_mode

Selected Solvers:
maplecms, maplecomsps, maplecomsps_lrb, maple_glucose, riss5,
splatz