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	0.770	8337.099	0.000
baseline	singleBest	0.577	15330.171	716.756
baseline	singleBestByPar	0.577	15330.171	716.756
baseline	singleBestBySuccesses	0.577	15330.171	716.756
classif	rpart	0.717	10293.055	227.008
classif	randomForest	0.730	9829.105	165.690
classif	ksvm	0.704	10742.787	250.424
cluster	XMeans	0.660	12343.237	429.822
regr	lm	0.714	10388.712	227.928
regr	rpart	0.714	10405.537	244.754
regr	randomForest	0.744	9300.812	111.082

The following default feature steps were used for model building:

all_feats

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 5 to 5, resulting in a PAR10 score of 9203.960 for the reduced model. Analogously, the model that was generated based on 4 of the originally 46 features resulted in a PAR10 score of 9051.064. Below, you can find the list of the selected features and solvers:

Selected Features:
W_OCCS_FORALL_NO_PER_VAR, OCCP_OCCN, NEG_HORN_CLAUSE, WOCCEP_WOCC

Selected Solvers:
X2clsQ, QuBE, quantor, sKizzo, sSolve