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	0.797	3752.469	0.000
baseline	singleBest	0.516	8789.168	492.881
baseline	singleBestByPar	0.516	8789.168	492.881
baseline	singleBestBySuccesses	0.516	8789.168	492.881
classif	rpart	0.709	5355.835	143.845
classif	randomForest	0.742	4780.529	98.008
classif	ksvm	0.746	4708.379	92.097
cluster	XMeans	0.572	7805.987	390.310
regr	lm	0.753	4592.359	80.581
regr	rpart	0.736	4904.509	115.085
regr	randomForest	0.777	4167.789	44.622

The following default feature steps were used for model building:

static, dynamic

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 155 / 155 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_all_diff, gc_all_equal, gc_among, gc_array_int, gc_array_set,
gc_at_least_most, gc_bin_packing, gc_bool_lin, gc_circuit, gc_count,
gc_cumulative, gc_decr_inc, gc_diffn, gc_disjoint, gc_global_card,
gc_global_cons, gc_inverse, gc_link_set, gc_max_min_int, gc_member,
gc_nvalue, gc_precede, gc_range, gc_ratio_globs, gc_regular,
gc_schedule, gc_set_weights, gc_sort, gc_table, o_de,
o_de_di, o_deg, o_deg_avg, o_deg_cons, o_deg_std,
o_di, o_di_de, 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, gr_avg_clust_cg,
gr_avg_deg_cg, gr_avg_deg_vg, gr_avg_diam_vg, gr_cv_clust_cg, gr_cv_deg_cg,
gr_cv_deg_vg, gr_cv_diam_vg, gr_ent_clust_cg, gr_ent_deg_cg, gr_ent_deg_vg,
gr_ent_diam_vg, gr_max_clust_cg, gr_max_deg_cg, gr_max_deg_vg, gr_max_diam_vg,
gr_min_clust_cg, gr_min_deg_cg, gr_min_deg_vg, gr_min_diam_vg, dy_sols,
dy_props, dy_nodes, dy_fails, dy_depth, dy_peak,
dy_ratio_props, dy_ratio_nodes, dy_fzn_time, dy_static_time, dy_tot_time

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 11 to 9, resulting in a PAR10 score of 4164.100 for the reduced model. Analogously, the model that was generated based on 5 of the originally 115 features resulted in a PAR10 score of 4125.715. Below, you can find the list of the selected features and solvers:

Selected Features:
c_max_dom_cons, c_ratio_cons, o_di_de, v_ent_deg_vars, v_min_domdeg_vars

Selected Solvers:
bprolog, fzn2smt, g12cpx, g12lazyfd, g12mip,
gecode, izplus, minisatid, ortools