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	0.937	400.179	0.000
baseline	singleBest	0.859	880.547	58.884
baseline	singleBestByPar	0.859	880.547	58.884
baseline	singleBestBySuccesses	0.859	880.547	58.884
classif	rpart	0.895	654.968	28.429
classif	randomForest	0.892	672.120	28.876
classif	ksvm	0.883	724.782	35.594
cluster	XMeans	0.890	688.782	37.140
regr	lm	0.902	615.052	26.043
regr	rpart	0.901	625.056	31.855
regr	randomForest	0.919	512.830	15.588

The following default feature steps were used for model building:

Static, Dynamic.1, Dynamic.2, Dynamic.3, Dynamic.4

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 138 / 138 instance features:

Frac_Neg_Body, Frac_Pos_Body, Frac_Unary_Rules, Frac_Binary_Rules, Frac_Ternary_Rules,
Frac_Integrity_Rules, Tight, Problem_Variables, Free_Problem_Variables, Assigned_Problem_Variables,
Constraints, Constraints.Vars, Created_Bodies, Program_Atoms, SCCS,
Nodes_in_Positive_BADG, Rules, Normal_Rules, Cardinality_Rules, Choice_Rules,
Weight_Rules, Frac_Normal_Rules, Frac_Cardinality_Rules, Frac_Choice_Rules, Frac_Weight_Rules,
Equivalences, Atom.Atom_Equivalences, Body.Body_Equivalences, Other_Equivalences, Frac_Atom.Atom_Equivalences,
Frac_Body.Body_Equivalences, Frac_Other_Equivalences, Binary_Constraints, Ternary_Constraints, Other_Constraints,
Frac_Binary_Constraints, Frac_Ternary_Constraints, Frac_Other_Constraints, Choices.1, Conflicts.Choices.1,
Avg_Conflict_Levels.1, Avg_LBD_Levels.1, Learnt_from_Conflict.1, Learnt_from_Loop.1, Frac_Learnt_from_Conflict.1,
Frac_Learnt_from_Loop.1, Literals_in_Conflict_Nogoods.1, Literals_in_Loop_Nogoods.1, Frac_Literals_in_Conflict_Nogoods.1, Frac_Literals_in_Loop_Nogoods.1,
Removed_Nogoods.1, Learnt_Binary.1, Learnt_Ternary.1, Learnt_Others.1, Frac_Removed_Nogood.1,
Frac_Learnt_Binary.1, Frac_Learnt_Ternary.1, Frac_Learnt_Others.1, Skipped_Levels_while_Backjumping.1, Avg_Skipped_Levels_while_Backjumping.1,
Longest_Backjumping.1, Running_Avg_Conflictlevel.1, Running_Avg_LBD.1, Choices.2, Conflicts.Choices.2,
Avg_Conflict_Levels.2, Avg_LBD_Levels.2, Learnt_from_Conflict.2, Learnt_from_Loop.2, Frac_Learnt_from_Conflict.2,
Frac_Learnt_from_Loop.2, Literals_in_Conflict_Nogoods.2, Literals_in_Loop_Nogoods.2, Frac_Literals_in_Conflict_Nogoods.2, Frac_Literals_in_Loop_Nogoods.2,
Removed_Nogoods.2, Learnt_Binary.2, Learnt_Ternary.2, Learnt_Others.2, Frac_Removed_Nogood.2,
Frac_Learnt_Binary.2, Frac_Learnt_Ternary.2, Frac_Learnt_Others.2, Skipped_Levels_while_Backjumping.2, Avg_Skipped_Levels_while_Backjumping.2,
Longest_Backjumping.2, Running_Avg_Conflictlevel.2, Running_Avg_LBD.2, Choices.3, Conflicts.Choices.3,
Avg_Conflict_Levels.3, Avg_LBD_Levels.3, Learnt_from_Conflict.3, Learnt_from_Loop.3, Frac_Learnt_from_Conflict.3,
Frac_Learnt_from_Loop.3, Literals_in_Conflict_Nogoods.3, Literals_in_Loop_Nogoods.3, Frac_Literals_in_Conflict_Nogoods.3, Frac_Literals_in_Loop_Nogoods.3,
Removed_Nogoods.3, Learnt_Binary.3, Learnt_Ternary.3, Learnt_Others.3, Frac_Removed_Nogood.3,
Frac_Learnt_Binary.3, Frac_Learnt_Ternary.3, Frac_Learnt_Others.3, Skipped_Levels_while_Backjumping.3, Avg_Skipped_Levels_while_Backjumping.3,
Longest_Backjumping.3, Running_Avg_Conflictlevel.3, Running_Avg_LBD.3, Choices.4, Conflicts.Choices.4,
Avg_Conflict_Levels.4, Avg_LBD_Levels.4, Learnt_from_Conflict.4, Learnt_from_Loop.4, Frac_Learnt_from_Conflict.4,
Frac_Learnt_from_Loop.4, Literals_in_Conflict_Nogoods.4, Literals_in_Loop_Nogoods.4, Frac_Literals_in_Conflict_Nogoods.4, Frac_Literals_in_Loop_Nogoods.4,
Removed_Nogoods.4, Learnt_Binary.4, Learnt_Ternary.4, Learnt_Others.4, Frac_Removed_Nogood.4,
Frac_Learnt_Binary.4, Frac_Learnt_Ternary.4, Frac_Learnt_Others.4, Skipped_Levels_while_Backjumping.4, Avg_Skipped_Levels_while_Backjumping.4,
Longest_Backjumping.4, Running_Avg_Conflictlevel.4, Running_Avg_LBD.4

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 11 to 8, resulting in a PAR10 score of 493.017 for the reduced model. Analogously, the model that was generated based on 3 of the originally 134 features resulted in a PAR10 score of 478.545. Below, you can find the list of the selected features and solvers:

Selected Features:
Constraints.Vars, Frac_Choice_Rules, Learnt_from_Loop.1

Selected Solvers:
clasp.2.1.3.h1.n1, clasp.2.1.3.h11.n1, clasp.2.1.3.h2.n1, clasp.2.1.3.h3.n1, clasp.2.1.3.h4.n1,
clasp.2.1.3.h6.n1, clasp.2.1.3.h8.n1, clasp.2.1.3.h9.n1