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8.5  Best-First and Hill-Climbing Strategies

Recently we equipped Grt planner with two new features: a second optional search strategy, the well known hill-climbing, and a closed-list of visited states, in order to avoid revisiting them.

Grt adopts the enforced hill-climbing strategy, originally presented in Hoffmann & Nebel (2001), according to which, from each intermediate state a limited breadth first search is performed, until an improving state is reached. When an improving state cannot be found, Grt restarts the search from the initial state with the typical best-first strategy.

 Moreover, the hill-climbing strategy has been enhanced with a fast action selection mechanism. As it has been presented in Section 5.3, when Grt estimates the distances between the problem's facts and the goals in the pre-processing phase, it stores in the GRG structure the action that achieved each fact. So, in order to find an improving successor state quickly, the hill-climbing search strategy first attempts to apply the actions that achieved the current state's facts. Once that an improving successor state is found, the remaining of the actions are not processed, thus avoiding to compute all the applicable to the current state actions. Note however that it is not guaranteed that these actions can always be applied to the current state. In case where no improving state can be found, the remaining of the applicable to the current state actions are taken into account.

Figure 13 presents comparative performance results in logistics and elevator problems, using both search strategies. In the logistics problems, the most promising facts selection method of enhancing the goals has been used. As it results from the experimental data, in the logistics problems and with the use of the hill-climbing strategy, there is a significant reduction in the solution time of about 52%. The cost is an increment of about 3% in the length of the plans. In the elevator problems, there is also a reduction in the solution time of about 29%, whereas the produced plans are identical.

 

(a) Logistics domain

 

(b) Elevator domain

Figure 13: Comparative results (solution length and time) between the hill-climbing
and the best-first strategies.

We tested the efficiency of the fast action selection mechanism, by also running Grt with the hill-climbing strategy but without this mechanism in the same logistics and elevator problems. Concerning the logistics problems, the speedup was about 47%, while the increment in the solution length was 3% on average again. Concerning the elevator problems, the speedup was 28%, whereas the produced plans were again identical. The conclusion from these additional measurements is that the speedup is primarily due to the hill-climbing strategy and secondly due to the fast action selection mechanism. The contribution of this mechanism depends on the domain and it is more important in the logistics and less in the elevator. Its inefficiency in the elevator domain means that the actions that are selected by this mechanism do not usually lead to an improving state or they are not applicable, so all the applicable actions have to be computed.

Results for other domains, like blocks-world and freecell, are not presented, since in these domains hill-climbing usually fails to find a plan and Grt restarts on a best-first basis. However, in these domains the closed-list of states has been proved invaluable, improving drastically the performance of Grt. For example, in the freecell domain and without the closed list of visited states, the Grt planner in the Aips-00 planning competition succeeded in solving problems with up to 6 cards per suit, while with this data structure it can solve some of the more difficult ones (13 cards per suit). Note that for an efficient implementation of the closed-list of visited states a hash-table data structure has been adopted.

 

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Next: Comparison to other Planners Up: The GRT Planning System Previous: XOR-constraints

Ioannis Refanidis

14-8-2001