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	0.875	6344.251	0.000
baseline	singleBest	0.858	7201.556	79.143
baseline	singleBestByPar	0.858	7201.556	79.143
baseline	singleBestBySuccesses	0.858	7201.556	79.143
classif	rpart	0.872	6488.162	10.512
classif	randomForest	0.868	6677.876	22.360
classif	ksvm	0.867	6727.606	27.624
cluster	XMeans	0.862	7005.380	60.833
regr	lm	0.869	6633.481	22.431
regr	rpart	0.863	6952.248	52.167
regr	randomForest	0.871	6540.345	18.228

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 86 / 86 instance features:

stats_varcount, stats_var_bool, stats_var_discrete, stats_var_bound, stats_var_sparsebound,
stats_dom_0, stats_dom_25, stats_dom_50, stats_dom_75, stats_dom_100,
stats_dom_mean, stats_dom_not2_2_ratio, stats_discrete_bool_ratio, stats_branchingvars, stats_auxvars,
stats_auxvar_branching_ratio, stats_conscount, stats_arity_0, stats_arity_25, stats_arity_50,
stats_arity_75, stats_arity_100, stats_arity_mean, stats_arity_mean_normalised, stats_cts_per_var_mean,
stats_cts_per_var_mean_normalised, stats_alldiff_count, stats_alldiff_proportion, stats_sums_count, stats_sums_proportion,
stats_or_atleastk_count, stats_or_atleastk_proportion, stats_ternary_count, stats_ternary_proportion, stats_binary_count,
stats_binary_proportion, stats_reify_count, stats_reify_proportion, stats_table_count, stats_table_proportion,
stats_lex_count, stats_lex_proportion, stats_unary_count, stats_unary_proportion, stats_nullary_count,
stats_nullary_proportion, stats_element_count, stats_element_proportion, stats_minmax_count, stats_minmax_proportion,
stats_occurrence_count, stats_occurrence_proportion, stats_multi_shared_vars, stats_edge_density, stats_Local_Variance,
standard_deviation_of_node_degree, normalised_standard_deviation_of_node_degree, clustering_coefficient, minimum_degree, normalised_minimum_degree,
maximum_degree, normalised_maximum_degree, median_degree, normalised_median_degree, mean_degree,
normalised_mean_degree, width_of_ordering, normalised_width_of_ordering, width_of_graph, normalised_width_of_graph,
SAC_literals, normalised_SAC_literals, stats_tightness_0, stats_tightness_25, stats_tightness_50,
stats_tightness_75, stats_tightness_100, stats_tightness_mean, stats_tightness_mean_normalised, stats_literal_tightness_0,
stats_literal_tightness_25, stats_literal_tightness_50, stats_literal_tightness_75, stats_literal_tightness_100, stats_literal_tightness_mean,
stats_literal_tightness_coeff_of_variation

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 2 to 2, resulting in a PAR10 score of 6516.464 for the reduced model. Analogously, the model that was generated based on 3 of the originally 69 features resulted in a PAR10 score of 6415.798. Below, you can find the list of the selected features and solvers:

Selected Features:
stats_arity_50, stats_table_proportion, normalised_maximum_degree

Selected Solvers:
learning, standard