

![0_image_0.png](0_image_0.png) 

δa function or the parametrized δa with γ = 2 (in the second case, LPG-d solves 198 problems, while the average CPU time and the average δ av are nearly the same as with γ = 3).

Figure 8 shows the results for a middle-size problem in IPC-5 Storage-Propositional. With γ = 2 LPG-d solves 225 (**k, d**)-combinations, 39 of which require less than 10 seconds, while 128 of them require less than 50 seconds. The average CPU time is 64.1 seconds and the average δ av is 0.88. With the original δa LPG-d solves 240 (**k, d**)-combinations, the average CPU time is 41.8 seconds, and the average δ av is 0.87; with γ = 3 LPG-d solves 206 combinations, the average CPU time is 69.4 seconds and the average δ av is 0.89.

The local search in LPG is randomized by a "noise" parameter that is automatically set and updated during search (Gerevini et al., 2003). This randomization is one of the techniques used for escaping local minima, but it also can be useful for computing diverse plans: if we run the search multiple times, each search is likely to consider different portions of the search space,