Performance comparison of ACO-HPPFP-3 and PERM on biological and random instances in 2D. Mean CPU time (natural log transformed) required by ACO-HPPFP-3 vs PERM for reaching the best solution quality, as observed over 10 runs with a cut-off time of 1 CPU hour for sequences of length 30 and 50 in 2D. The left and right plots show the results for the biological and random test-sets, respectively. Performance results for instances of size 30 are indicated by circles, while stars mark results for instances of size 50. The dashed lines indicate the band within which performance differences are not statistically significant. Mean run-times were obtained from 10 runs per instance and algorithm, and we only show data points for the runs where the best known solution quality was reached at least in some runs out of 10 by both algorithms (when unsuccessful runs were present, the expected time was calculated as in ); results for both successful and unsuccessful runs are given in the Additional file 1.