singling-out the lowest found value, instance by instance (see Appendix \[sec:ra\]). This simple procedure represents a statistical pre-characterization of the instance ensemble sensitivity to the parameters, and it is common for quantum annealing benchmarking initial studies of a problem [@venturelli2015quantum; @venturelli2015spinglass; @hamerly2018scaling]. Due to the post-selection of the best embedding and pause location parameters, the reported results then will represent a “best case scenario”, however previous empirical research show that once the distribution of typical optimal parameters has been estimated, it is possible to set up a lightweight on-the-fly procedure to set the parameters dynamically while performing the runs [@perdomo2015performance]. The results of the parameter setting optimization are shown in Figure \[fig:Optimal\_JF\_sp\] for forward and reverse annealing. It should be immediately noted that we don’t optimize over $\tau$ since our experiments (as well as prior research on similar instances [@hamerly2018scaling]) indicates that the best TTS is obtained for the fastest annealing time, $\tau$ = 1 $\textrm{s}$ [^7]. What is shown is that the median best choice for $|J_F|$ is increasing with the problem size (as expected [@venturelli2015spinglass]) and the mean best choice for $s_p$ increases with the pause period. With regard to reverse annealing, we should note that we don’t 