Action Elimination and Plan Neighborhood Graph Search: Two Algorithms for Plan Improvement - Extended Version

Abstract

Compared to optimal planners, satisficing planners can solve much harder problems but may produce overly costly and long plans. Plan quality for satisficing planners has become increasingly important. The most recent planning competition IPC-2008 used the cost of the best known plan divided by the cost of the generated plan as an evaluation metric. This paper proposes and evaluates two simple but effective methods for plan improvement: Action Elimination improves an existing plan by repeatedly removing sets of irrelevant actions. Plan Neighborhood Graph Search finds a new, shorter plan by creating a plan neighborhood graph PNG(π) of a given plan π, and then extracts a shortest path from PNG(π). Both methods are implemented in the ARAS postprocessor and are empirically shown to improve the result of several planners, including the top four planners from IPC-2008, under competition conditions. Improving Plan Quality Satisficing deterministic planners can solve much harder instances than optimal planners but may generate plans that are far from optimal. Earlier planning competitions have emphasized coverage in terms of total number of problems solved, as well as raw speed. The focus of IPC-2008 was on finding the best plan with a given finite amount of resources. Much work in satisficing planning has gone into generating a high quality plan directly. Such systems output a single plan and then stop. In contrast, anytime planners such as LAMA (Richter, Helmert, and Westphal 2008; Richter and Westphal 2008) and LPG (Gerevini, Saetti, and Serina 2008) aim to quickly find a lower-quality plan, then improve it over time. The contribution of this paper are two simple but effective postprocessing methods for plan improvement: Action Elimination (AE) and Plan Neighborhood Graph Search (PNGS). Both methods can take any valid plan as input and attempt to improve it. AE is a fast algorithm, while PNGS works in anytime fashion. Both AE and PNGS improve the performance of all the planners tested as measured by the IPC-2008 metric. In contrast to LAMA, the new methods search for local improvements Technical Report TR 10-01, March 2010. Copyright c © 2010, Dept. of Computing Science, University of Alberta, Canada. All rights reserved. A shorter version of this paper was accepted for publication at ICAPS 2010. “near” an existing plan. In contrast to LPG, they search in state space not plan space. There are many ways to measure plan quality. Two popular metrics for unit cost actions are sequential plan length measured in total number of actions, and makespan, the shortest execution time of a plan if actions can be executed in parallel. The IPC-2008 metric for non-uniform action costs (including zero) was additive cost, with the total cost of a plan defined as the sum of all action costs. What is New in the Extended Version? This version contains further discussions regarding AE: it is shown that the action elimination problem is NP-Hard, and an example where AE fails to find certain kind of redundancies is discussed. There are also more detailed results regarding the cases where the best known plans for IPC-2008 are improved. The rest of this paper is organized as follows: After introducing necessary notation, a greedy algorithm for Action Elimination is developed and its limitations are shown. Plan Neighborhood Graph Search is described next. The experiments evaluate Action Elimination and Plan Neighborhood Graph Search both as standalone methods and in combination.