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	0.808	1758.139	0.000
baseline	singleBest	0.626	3401.815	170.949
baseline	singleBestByPar	0.626	3401.815	170.949
baseline	singleBestBySuccesses	0.626	3401.815	170.949
classif	rpart	0.696	2762.263	99.818
classif	randomForest	0.717	2572.056	77.554
classif	ksvm	0.702	2710.964	93.734
cluster	XMeans	0.638	3290.490	156.514
regr	lm	0.690	2824.379	110.260
regr	rpart	0.721	2548.488	86.283
regr	randomForest	0.776	2046.680	30.168

The following default feature steps were used for model building:

default

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 46 / 46 instance features:

EXIST_VARS, FORALL_VARS, TOTAL_VARS, CLAUSES, LITERALS,
EXIST_SET, FORALL_SET, TOTAL_SET, UNARY_CLAUSES, BINARY_CLAUSES,
TERNARY_MORE_CLAUSES, POS_HORN, NEG_HORN, EXIST_LIT_PER_CLAUSE, FORALL_LIT_PER_CLAUSE,
EXIST_VARS_PER_SET, FORALL_POS_LITS_PER_CLAUSE, FORALL_NEG_LITS_PER_CLAUSE, OCCS_POS_NO_PER_VAR, OCCS_FORALL_NO_PER_VAR,
OCCS_FORALL_POS_NO_PER_VAR, W_OCCS_POS_NO_PER_VAR, W_OCCS_FORALL_NO_PER_VAR, W_OCCS_FORALL_POS_NO_PER_VAR, W_PRODUCTS,
LITN_LIT, LITEP_LIT, LITEN_LITE, LITEN_LITN, LITFN_LIT,
LITFP_LITFN, OCCP_OCCN, OCCE_OCC, OCCEN_OCC, OCCFP_OCCF,
OCCEN_OCCE, OCCEN_OCCN, OCCFP_OCCFN, TERMORE_CLAUSE, NEG_HORN_CLAUSE,
WOCCN_WOCC, WOCCEP_WOCC, WOCCFN_WOCC, WOCCEP_WOCCE, WOCCEP_WOCCP,
WOCCFN_WOCCN

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 14 to 10, resulting in a PAR10 score of 2051.841 for the reduced model. Analogously, the model that was generated based on 6 of the originally 46 features resulted in a PAR10 score of 2003.861. Below, you can find the list of the selected features and solvers:

Selected Features:
TOTAL_SET, UNARY_CLAUSES, W_OCCS_FORALL_POS_NO_PER_VAR, OCCEN_OCCE, TERMORE_CLAUSE,
WOCCEP_WOCCP

Selected Solvers:
bcghostq, brareqs, depqbf, dual_ooq13, ghostq,
hiqqer3, ooq13, pre_dual_ooq13, rareqs, sqube