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	1.000	281.518	0.000
baseline	singleBest	0.963	3007.927	348.427
baseline	singleBestByPar	0.963	3007.927	348.427
baseline	singleBestBySuccesses	0.963	3007.927	348.427
classif	rpart	0.954	3679.414	379.248
classif	randomForest	0.968	2658.477	249.706
classif	ksvm	0.959	3351.690	354.596
cluster	XMeans	0.959	3334.059	336.945
regr	lm	0.890	8228.457	774.482
regr	rpart	0.931	5385.211	605.399
regr	randomForest	0.954	3670.997	377.078

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 143 / 143 instance features:

probtype, n_vars, n_constr, n_nzcnt, nq_vars,
nq_constr, nq_nzcnt, lp_avg, lp_l2_avg, lp_linf,
lp_objval, num_b_variables, num_i_variables, num_c_variables, num_s_variables,
num_n_variables, ratio_b_variables, ratio_i_variables, ratio_c_variables, ratio_s_variables,
ratio_n_variables, num_i._variables, ratio_i._variables, num_unbounded_disc, ratio_unbounded_disc,
support_size_avg, support_size_median, support_size_varcoef, support_size_q90mq10, rhs_c_0_avg,
rhs_c_0_varcoef, rhs_c_1_avg, rhs_c_1_varcoef, rhs_c_2_avg, rhs_c_2_varcoef,
vcg_constr_deg0_avg, vcg_constr_deg0_median, vcg_constr_deg0_varcoef, vcg_constr_deg0_q90mq10, vcg_var_deg0_avg,
vcg_var_deg0_median, vcg_var_deg0_varcoef, vcg_var_deg0_q90mq10, vcg_constr_weight0_avg, vcg_constr_weight0_varcoef,
vcg_var_weight0_avg, vcg_var_weight0_varcoef, A_ij_normalized0_avg, A_ij_normalized0_varcoef, a_normalized_varcoefs0_avg,
a_normalized_varcoefs0_varcoef, obj_coefs0_avg, obj_coefs0_std, obj_coef_per_constr0_avg, obj_coef_per_constr0_std,
obj_coef_per_sqr_constr0_avg, obj_coef_per_sqr_constr0_std, vcg_constr_deg1_avg, vcg_constr_deg1_median, vcg_constr_deg1_varcoef,
vcg_constr_deg1_q90mq10, vcg_var_deg1_avg, vcg_var_deg1_median, vcg_var_deg1_varcoef, vcg_var_deg1_q90mq10,
vcg_constr_weight1_avg, vcg_constr_weight1_varcoef, vcg_var_weight1_avg, vcg_var_weight1_varcoef, A_ij_normalized1_avg,
A_ij_normalized1_varcoef, a_normalized_varcoefs1_avg, a_normalized_varcoefs1_varcoef, obj_coefs1_avg, obj_coefs1_std,
obj_coef_per_constr1_avg, obj_coef_per_constr1_std, obj_coef_per_sqr_constr1_avg, obj_coef_per_sqr_constr1_std, vcg_constr_deg2_avg,
vcg_constr_deg2_median, vcg_constr_deg2_varcoef, vcg_constr_deg2_q90mq10, vcg_var_deg2_avg, vcg_var_deg2_median,
vcg_var_deg2_varcoef, vcg_var_deg2_q90mq10, vcg_constr_weight2_avg, vcg_constr_weight2_varcoef, vcg_var_weight2_avg,
vcg_var_weight2_varcoef, A_ij_normalized2_avg, A_ij_normalized2_varcoef, a_normalized_varcoefs2_avg, a_normalized_varcoefs2_varcoef,
obj_coefs2_avg, obj_coefs2_std, obj_coef_per_constr2_avg, obj_coef_per_constr2_std, obj_coef_per_sqr_constr2_avg,
obj_coef_per_sqr_constr2_std, mipgap, nodecnt, clqcnt, covcnt,
itcnt_max, numnewsolution_sum, newin_sum, nodeleft_avg, nodeleft_varcoef,
diffObj_avg, diffObj_median, diffObj_varcoef, diffObj_q90mq10, numfeas,
iinf_avg, iinf_median, iinf_varcoef, iinf_q90mq10, diffBestInt_avg,
diffBestInt_median, diffBestInt_varcoef, diffBestInt_q90mq10, diffBestObjUp_avg, diffBestObjUp_median,
diffBestObjUp_varcoef, diffBestObjUp_q90mq10, numcuts_sum, diffGap_avg, diffGap_median,
diffGap_varcoef, diffGap_q90mq10, pre_t, rel_t, new_row,
new_col, new_nonzero, clique_table, cliqueCuts, impliedBoundCuts,
flowCuts, mixedIntegerRoundingCuts, gomoryFractionalCuts

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 2, resulting in a PAR10 score of 2027.152 for the reduced model. Analogously, the model that was generated based on 5 of the originally 115 features resulted in a PAR10 score of 751.492. Below, you can find the list of the selected features and solvers:

Selected Features:
vcg_var_deg0_median, vcg_var_deg1_median, obj_coefs1_std, obj_coef_per_sqr_constr1_std, new_nonzero

Selected Solvers:
CPLEX, Gurobi