However, the hardest instances are in fact concentrated at a second, lower, transition point.
The hardest instances were found close to the transition between regions of satisfiable and unsatisfiable instances; furthermore, unsatisfiable instances were found harder to solve than satisfiable ones.
By adding the GP stage to Hamlet, the number of solved problems increases from 58%to85%5% in the blocks world and from 50%to87%7% in the logistics domain (0%to3838% and 0%to42%2% for the hardest instances of problems considered).
Often, tries scored at the base of a maul, with both sets of forwards low to the ground and packed tightly together, are the hardest instances for the referee to see exactly what he needs to in the short time he has to make a decision.
Since longer reads can only make the assembly process easier, these datasets still represent some of the hardest instances of the sequence assembly problem.
Since it is not able to solve the hardest instances, we also present a heuristic based on simulated annealing.
Thus, AdaBoost attempts to produce new "strong" classifiers that are able to better predict the hard instances for the previous ensemble "weak" members.
In Appendix A.2 we prove that enumerating minimal pathway is an NP-complete problem (reduction to 3-SAT) but as examplified in Appendix B the hard instances are rather rare and obviously none of these hard instances were found in our running tests as all pathways returned by FindPath were indeed minimal pathways.
Computing the "easiest" 90%% of all instances requires only 2.8 h; in contrast, the 1 % "hardest" instances use more than 70%% of the total computing time.
Given that the measured effect of eight trials can be approximately compared to the effect of solving a harder instance, it could be concluded that the effect of trials was 5.7 times larger (odds ratio: 2.6/0.45) than increasing the instance difficulty.
