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	0.830	2061.802	0.000
baseline	singleBest	0.720	3372.451	122.649
baseline	singleBestByPar	0.720	3372.451	122.649
baseline	singleBestBySuccesses	0.720	3372.451	122.649
classif	rpart	0.730	3280.147	138.178
classif	randomForest	0.760	2890.453	72.435
classif	ksvm	0.790	2533.620	39.595
cluster	XMeans	0.750	3018.366	92.350
regr	lm	0.570	5240.658	370.730
regr	rpart	0.720	3385.046	135.044
regr	randomForest	0.760	2898.195	80.170

The following default feature steps were used for model building:

base

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 95 / 95 instance features:

c_avg_deg_cons, c_avg_dom_cons, c_avg_domdeg_cons, c_bounds_d, c_bounds_r,
c_bounds_z, c_cv_deg_cons, c_cv_dom_cons, c_cv_domdeg_cons, c_domain,
c_ent_deg_cons, c_ent_dom_cons, c_ent_domdeg_cons, c_logprod_deg_cons, c_logprod_dom_cons,
c_max_deg_cons, c_max_dom_cons, c_max_domdeg_cons, c_min_deg_cons, c_min_dom_cons,
c_min_domdeg_cons, c_num_cons, c_priority, c_ratio_cons, c_sum_ari_cons,
c_sum_dom_cons, c_sum_domdeg_cons, d_array_cons, d_bool_cons, d_bool_vars,
d_float_cons, d_float_vars, d_int_cons, d_int_vars, d_ratio_array_cons,
d_ratio_bool_cons, d_ratio_bool_vars, d_ratio_float_cons, d_ratio_float_vars, d_ratio_int_cons,
d_ratio_int_vars, d_ratio_set_cons, d_ratio_set_vars, d_set_cons, d_set_vars,
gc_diff_globs, gc_global_cons, gc_ratio_diff, gc_ratio_globs, o_deg,
o_deg_avg, o_deg_cons, o_deg_std, o_dom, o_dom_avg,
o_dom_deg, o_dom_std, s_bool_search, s_first_fail, s_goal,
s_indomain_max, s_indomain_min, s_input_order, s_int_search, s_labeled_vars,
s_other_val, s_other_var, s_set_search, v_avg_deg_vars, v_avg_dom_vars,
v_avg_domdeg_vars, v_cv_deg_vars, v_cv_dom_vars, v_cv_domdeg_vars, v_def_vars,
v_ent_deg_vars, v_ent_dom_vars, v_ent_domdeg_vars, v_intro_vars, v_logprod_deg_vars,
v_logprod_dom_vars, v_max_deg_vars, v_max_dom_vars, v_max_domdeg_vars, v_min_deg_vars,
v_min_dom_vars, v_min_domdeg_vars, v_num_aliases, v_num_consts, v_num_vars,
v_ratio_bounded, v_ratio_vars, v_sum_deg_vars, v_sum_dom_vars, v_sum_domdeg_vars

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 20 to 2, resulting in a PAR10 score of 2548.355 for the reduced model. Analogously, the model that was generated based on 3 of the originally 82 features resulted in a PAR10 score of 2298.436. Below, you can find the list of the selected features and solvers:

Selected Features:
c_cv_domdeg_cons, c_min_dom_cons, gc_global_cons

Selected Solvers:
LCG.Glucose.UC.free, MZN.Gurobi.free