Overview of performance values

The following statistics were calculated from the performance values of each algorithm:

obs (number of observations within performance values)
nas (number of NAs, i.e., missing values, within performance values)
min (minimum), mean (arithmetic mean), max (maximum), sd (standard deviation)
qu_1st (1st quartile = lower quartile = 25%-quantile)
med (median = 50%-quantile)
qu_3rd (3rd quartile = upper quartile = 75%-quantile)
coeff_var (coefficient of variation = standard deviation / arithmetic mean)

	obs	qu_1st	med	mean	qu_3rd	max	sd	coeff_var
DSWPM1_924	876	12.295	2100	1200.4	2100	2100	995.552	0.829352
akmaxsat	876	2.24	2100	1247.8	2100	2100	1002.22	0.803194
akmaxsat_ls	876	2.275	2100	1247.79	2100	2100	1002.22	0.803192
pwbo2.1	876	1.825	53.985	718.23	2100	2100	957.566	1.33323
qmaxsat0.21comp	876	1.105	22.92	574.664	1334.94	2100	888.381	1.54591
qmaxsat0.21g2comp	876	0.9175	15.65	534.922	564.725	2100	873.368	1.6327

Summary of the runstatus per algorithm

The following table summarizes the runstatus of each algorithm over all instances (in %).

	ok	timeout
akmaxsat	42.808	57.192
akmaxsat_ls	42.808	57.192
DSWPM1_924	46.575	53.425
pwbo2.1	67.922	32.078
qmaxsat0.21comp	75.799	24.201
qmaxsat0.21g2comp	76.941	23.059

Dominated Algorithms

Here, you'll find an overview of dominating/dominated algorithms:
None of the algorithms was superior to any of the other.

An algorithm (A) is considered to be superior to an other algorithm (B), if it has at least an equal performance on all instances (compared to B) and if it is better on at least one of them. A missing value is automatically a worse performance. However, instances which could not be solved by either one of the algorithms, were not considered for the dominance relation.

Visualisations

Important note w.r.t. some of the following plots:
If appropriate, we imputed performance values for failed or censored runs. We used max + 0.3 * (max - min), in case of minimization problems, or min - 0.3 * (max - min), in case of maximization problems.
In addition, a small noise is added to the imputed values (except for the cluster matrix, based on correlations, which is shown at the end of this page).

Boxplots of performance values

Imputing the performance values of failed or censored runs (as described in the red note at the beginning of this section):

Discarding the performance values of failed or censored runs:

## Warning: Removed 2165 rows containing non-finite values (stat_boxplot).

Estimated densitities of performance values

Imputing the performance values of failed or censored runs (as described in the red note at the beginning of this section):

Discarding the performance values of failed or censored runs:

Estimated cumulative distribution functions of performance values

Imputing the performance values of failed runs (as described in the red note at the beginning of this section):

Discarding the performance values of failed or censored runs:

Scatterplot matrix of the performance values

The figure underneath shows pairwise scatterplots of the performance values.

Imputing the performance values of failed and censored runs (as described in the red note at the beginning of this section):

Clustering algorithms based on their correlations

The following figure shows the correlations of the ranks of the performance values. Per default it will show the correlation coefficient of spearman. Missing values were imputed prior to computing the correlation coefficients. The algorithms are ordered in a way that similar (highly correlated) algorithms are close to each other. Per default the clustering is based on hierarchical clustering, using Ward's method.