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	0.887	4105.887	0.000
baseline	singleBest	0.628	13443.350	957.458
baseline	singleBestByPar	0.628	13443.350	957.458
baseline	singleBestBySuccesses	0.628	13443.350	957.458
classif	rpart	0.750	9019.042	509.892
classif	randomForest	0.815	6679.567	281.549
classif	ksvm	0.818	6588.683	271.173
cluster	XMeans	0.767	8425.416	472.668
regr	lm	0.827	6246.406	235.028
regr	rpart	0.810	6848.252	296.954
regr	randomForest	0.835	5962.999	209.441

The following default feature steps were used for model building:

csp

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 36 / 198 instance features:

csp_log_lists, csp_log_bits, csp_log_constraints, csp_percent_avg_continuity, csp_log_extra_booleans,
csp_percent_dec_predicate, csp_percent_wsum, csp_log_booleans, csp_percent_alldiff, csp_perten_largeext,
csp_num_alldiff, csp_sqrt_max_domsize, csp_log_ranges, csp_percent_min_continuity, csp_log_extra_bits,
csp_percent_cumulative, csp_percent_ext, csp_sqrt_avg_domsize, csp_percent_element, csp_perten_naryext,
csp_perten_avg_predarity, csp_dyn_log_stdev_weight, csp_dyn_log_nodes, csp_dyn_log_avg_weight, csp_max_arity,
csp_percent_global, csp_perten_avg_predsize, csp_perten_binext, csp_log_values, csp_log_extra_ranges,
csp_log_search_vars, csp_dyn_log_propags, csp_perten_avg_predshape, csp_log_constants, csp_log_extra_values,
csp_percent_gac_predicate

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 22 to 7, resulting in a PAR10 score of 5785.726 for the reduced model. Analogously, the model that was generated based on 7 of the originally 193 features resulted in a PAR10 score of 5727.016. Below, you can find the list of the selected features and solvers:

Selected Features:
directorder_TRINARY., directorder_POSNEG.RATIO.CLAUSE.coeff.variation, directorder_POSNEG.RATIO.VAR.stdev, csp_log_extra_booleans, csp_log_booleans,
csp_sqrt_max_domsize, csp_perten_avg_predsize

Selected Solvers:
abscon, choco, claspcnf_direct, claspcnf_directorder, lingeling_direct,
riss3g_directorder, riss3g_support